Appendix
I
OPINIONS EXPRESSED PREVIOUS TO 1864 REGARDING THE INFLUENCE OF THE ECCENTRICITY OF THE EARTH’S ORBIT ON CLIMATE.312
M. de Mairan
M. de Mairan, in an article in the Memoirs of the Royal Academy of France313 “On the General Cause of Heat in Summer and Cold in Winter, in so far as depends on the internal and permanent Heat of the Earth,” makes the following remarks on the influence of the difference of distance of the sun in apogee and perigee:—
“Cet élément est constant pour les deux solstices; tandis que les autres (height of the sun and obliquity of his rays) y varient à raison des latitudes locales; et il y a encore cela de particulier, qu’il tend à diminuer la valeur de notre été, et à augmenter celle de notre hiver dans l’hémisphère boréal où nous sommes, et tout au contraire dans l’austral. Remarquons cependant que de ces mêmes distances, qui constituent ce troisième élément, naît en partie un autre principe de chaleur tout opposé, et qui semble devoir tempérer les effets du précédent; sçavoir, la lenteur et la vitesse réciproques du mouvement annuel apparent, en vertu duquel et du réel qui s’y mêle, le soleil emploie 8 jours de plus à parcourir les signes septentrionaux. C’est-à-dire, que le soleil passe 186½ jours dans notre hémisphère, et seulement 178½ dans l’hémisphère opposé. Ce qui, en général, ne peut manquer de répandre un pen plus de chaleur sur l’été du premier, et un peu moins sur son hiver.”
Mr. Richard Kirwan
“Œpinus,314 reasoning on astronomical principles, attributes the inferior temperature of the southern hemisphere to the shorter abode of the sun in the southern tropic, shorter by seven days, which produces a difference of fourteen days in favour of the northern hemisphere, during which more heat is accumulated, and hence he infers that the temperature of the northern hemisphere is to that of the southern, as 189·5 to 175·5, or as 14 to 13.”—Trans. of the Royal Irish Academy, vol. viii., p. 417. 1802.
Sir Charles Lyell
“Before the amount of difference between the temperature of the two hemispheres was ascertained, it was referred by astronomers to the acceleration of the earth’s motion in its perihelion; in consequence of which the spring and summer of the southern hemisphere are shorter by nearly eight days than those seasons north of the equator. A sensible effect is probably produced by this source of disturbance, but it is quite inadequate to explain the whole phenomena. It is, however, of importance to the geologist to bear in mind that in consequence of the precession of the equinoxes, the two hemispheres receive alternately, each for a period of upwards of 10,000 years, a greater share of solar light and heat. This cause may sometimes tend to counterbalance inequalities resulting from other circumstances of a far more influential nature; but, on the other hand, it must sometimes tend to increase the extreme of deviation, which certain combinations of causes produce at distant epochs.”—Principles, First Edition, 1830, p. 110, vol. i.
Sir John F. Herschel, Bart
The following, in so far as it relates to the effects of eccentricity, is a copy of Sir John Herschel’s memoir, “On the Astronomical Causes which may influence Geological Phenomena,” read before the Geological Society, Dec. 15th, 1830.—Trans. Geol. Soc., vol. iii., p. 293, Second Series:—
“... Let us next consider the changes arising in the orbit of the earth itself about the sun, from the disturbing action of the planets. In so doing it will be obviously unnecessary to consider the effect produced on the solar tides, to which the above reasoning applies much more forcibly than in the case of the lunar. It is, therefore, only the variations in the supply of light and heat received from the sun that we have now to consider.
“Geometers having demonstrated the absolute invariability of the mean distance of the earth from the sun, it would seem to follow that the mean annual supply of light and heat derived from that luminary would be alike invariable; but a closer consideration of the subject will show that this would not be a legitimate conclusion, but that, on the contrary, the mean amount of solar radiation is dependent on the eccentricity of the orbit, and therefore liable to variation. Without going at present into any geometrical investigations, it will be sufficient for the purpose here to state it as a theorem, of which any one may easily satisfy himself by no very abstruse geometrical reasoning, that ‘the eccentricity of the orbit varying, the total quantity of heat received by the earth from the sun in one revolution is inversely proportional to the minor axis of the orbit.’ Now since the major axis is, as above observed, invariable, and therefore, of course, the absolute length of the year, it will follow that the mean annual average of heat will also be in the same inverse ratio of the minor axis; and thus we see that the very circumstance which on a cursory view we should have regarded as demonstrative of the constancy of our supply of solar heat, forms an essential link in the chain of strict reasoning by which its variability is proved.
“The eccentricity of the earth’s orbits is actually diminishing, and has been so for ages, beyond the records of history. In consequence, the ellipse is in a state of approach to a circle, and its minor axis being, therefore, on the increase, the annual average of solar radiation is actually on the decrease.
“So far this is in accordance with the testimony of geological evidence, which indicates a general refrigeration of climate; but when we come to consider the amount of diminution which the eccentricity must be supposed to have undergone to render an account of the variation which has taken place, we have to consider that, in the first place, a great diminution of the eccentricity is required to produce any sensible increase of the minor axis. This is a purely geometrical conclusion, and is best shown by the following table:—
| Eccentricity. | Minor Axis. | Reciprocal or Ratio of Heat received. |
|---|---|---|
| 0·00 | 1·000 | 1·000 |
| 0·05 | 0·999 | 1·002 |
| 0·10 | 0·995 | 1·005 |
| 0·15 | 0·989 | 1·011 |
| 0·20 | 0·980 | 1·021 |
| 0·25 | 0·968 | 1·032 |
| 0·30 | 0·954 | 1·048 |
By this it appears that a variation of the eccentricity of the orbit from the circular form to that of an ellipse, having an eccentricity of one-fourth of the major axis, would produce only a variation of 3 per cent. on the mean annual amount of solar radiation, and this variation takes in the whole range of the planetary eccentricities, from that of Pallas and Juno downwards.
“I am not aware that the limit of increase of the eccentricity of the earth’s orbit has ever been determined. That it has a limit has been satisfactorily proved; but the celebrated theorem of Laplace, which is usually cited as demonstrating that none of the planetary orbits can ever deviate materially from the circular form, leads to no such conclusion, except in the case of the great preponderant planets Jupiter and Saturn, while for anything that theorem proves to the contrary, the orbit of the earth may become elliptic to any amount.
“In the absence of calculations which though practicable have, I believe, never been made,315 and would be no slight undertaking, we may assume that eccentricities which exist in the orbits of planets, both interior and exterior to that of the earth, may possibly have been attained, and may be attained again by that of the earth itself. It is clear that such eccentricities existing they cannot be incompatible with the stability of the system generally, and that, therefore, the question of the possibility of such an amount in the particular case of the earth’s orbit will depend on the particular data belonging to that case, and can only be determined by executing the calculations alluded to, having regard to the simultaneous effects of at least the four most influential planets, Venus, Mars, Jupiter, and Saturn, not only on the orbit of the earth, but on those of each other. The principles of this calculation are detailed in the article of Laplace’s work cited. But before entering on a work of so much labour, it is quite necessary to inquire what prospect of advantage there is to induce any one to undertake it.
“Now it certainly at first sight seems clear that a variation of 3 per cent. only in the mean annual amount of solar radiation, and that arising from an extreme supposition, does not hold out such a prospect. Yet it might be argued that the effects of the sun’s heat is to maintain the temperature of the earth’s surface at its actual mean height, not above the zero of Fahrenheit’s or any other thermometer, but above the temperature of the celestial spaces, out of the reach of the sun’s influence, and what that temperature is may be a matter of much discussion. M. Fourier has considered it as demonstrated that it is not greatly inferior to that of the polar regions of our own globe, but the grounds of this decision appear to me open to considerable objection.316 If those regions be really void of matter, their temperature can only arise, according to M. Fourier’s own view of the subject, from the radiation of the stars. It ought, therefore, to be as much inferior to that due to solar radiation, as the light of a starlight night is to that of the brightest noon day, in other words it should be very nearly a total privation of heat—almost the absolute zero respecting which so much difference of opinion exists, some placing it at 1,000°, some at 5,000° of Fahrenheit below the freezing-point, and some still lower, in which case a single unit per cent. in the mean annual amount of radiation would suffice to produce a change of climate fully commensurate to the demands of geologists.317
“Without attempting, however, to enter further into the perplexing difficulties in which this point is involved, which are far greater than appear on a cursory view, let us next consider, not the mean, but the extreme effects which a variation in the eccentricity of the earth’s orbit may be expected to produce in the summer and winter climates in particular regions of its surface, and under the influence of circumstances favouring a difference of effect. And here, if I mistake not, it will appear that an amount of variation, which we need not hesitate to admit (at least, provisionally) as a possible one, may be productive of considerable diversity of climate, and may operate during great periods of time either to mitigate or to exaggerate the difference of winter and summer temperatures, so as to produce alternately, in the same latitude of either hemisphere, a perpetual spring, or the extreme vicissitudes of a burning summer and a rigorous winter.
“To show this, let us at once take the extreme case of an orbit as eccentric as that of Juno or Pallas, in which the greatest and least distances of the sun are to each other as 5 to 3, and consequently the radiations at those distances as 25 to 9, or very nearly as 3 to 1. To conceive what would be the extreme effects of this great variation of the heat received at different periods of the year, let us first imagine in our latitude the place of the perigee of the sun to coincide with the summer solstice. In that case, the difference between the summer and winter temperature would be exaggerated in the same degree as if three suns were placed side by side in the heavens in the former season and only one in the latter, which would produce a climate perfectly intolerable. On the other hand, were the perigee situated in the winter solstice our three suns would combine to warm us in the winter, and would afford such an excess of winter radiation as would probably more than counteract the effect of short days and oblique sunshine, and throw the summer season into the winter months.
“The actual diminution of the eccentricity is so slow, that the transition from a state of the orbit such as we have assumed to the present nearly circular figure would occupy upwards of 600,000 years, supposing it uniformly changeable—this, of course, would not be the case; when near the maximum, however, it would vary slower still, so that at that point it is evident a period of 10,000 years would elapse without any perceptible change in the state of the data of the case we are considering.
“Now this adopting the very ingenious idea of Mr. Lyell318 would suffice, by reason of the combined effect of the precession of the equinoxes and the motion of the apsides of the orbit itself, to transfer the perigee from the summer to the winter solstice, and thus to produce a transition from the one to the other species of climate in a period sufficiently great to give room for a material change in the botanical character of country.
“The supposition above made is an extreme, but it is not demonstrated to be an impossible one, and should even an approach to such a state of things be possible, the same consequences, in a mitigated degree, would follow. But if, on executing the calculations, it should appear that the limits of the eccentricity of the earth’s orbit are really narrow, and if, on a full discussion of the very difficult and delicate point of the actual effect of solar radiation, it should appear that the mean, as well as the extreme, temperature of our climates would not be materially affected,—it will be at least satisfactory to know that the causes of the phenomena in question are to be sought elsewhere than in the relations of our planet to the system to which it belongs, since there does not appear to exist any other conceivable connections between these relations and the facts of geology than those we have enumerated, the obliquity of the ecliptic being, as we know, confined within too narrow limits for its variation to have any sensible influence.”—J. F. W. Herschel.
The influence which this paper might have had on the question as to whether eccentricity may be regarded as a cause of changes in geological climate appears to have been completely neutralized by the following, which appeared shortly afterwards both in his “Treatise” and “Outlines of Astronomy,” showing evidently that he had changed his mind on the subject.
“It appears, therefore, from what has been shown, the supplies of heat received from the sun will be equal in the two segments, in whatever direction the line PTQ be drawn. They will, indeed, be described in unequal times: that in which the perihelion A lies in a shorter, and the other in a longer, in proportion to their unequal area; but the greater proximity of the sun in the smaller segment compensates exactly for its more rapid description, and thus an equilibrium of heat is, as it were, maintained.
“Were it not for this the eccentricity of the orbit would materially influence the transition of seasons. The fluctuation of distance amounts to nearly 1/30th of the mean quantity, and, consequently, the fluctuation of the sun’s direct heating power to double this, or 1/15th of the whole.... Were it not for the compensation we have just described, the effect would be to exaggerate the difference of summer and winter in the southern hemisphere, and to moderate it in the northern; thus producing a more violent alternation of climate in the one hemisphere and an approach to perpetual spring in the other. As it is, however, no such inequality subsists, but an equal and impartial distribution of heat and light is accorded to both.”—“Treatise of Astronomy,” Cabinet Cyclopædia, § 315; Outlines of Astronomy, § 368.
“The fact of a great change in the general climate of large tracts of the globe, if not of the whole earth, and of a diminution of general temperature, having been recognised by geologists, from their examination of the remains of animals and vegetables of former ages enclosed in the strata, various causes for such diminution of temperature have been assigned.... It is evident that the mean temperature of the whole surface of the globe, in so far as it is maintained by the action of the sun at a higher degree than it would have were the sun extinguished, must depend on the mean quantity of the sun’s rays which it receives, or, which comes to the same thing, on the total quantity received in a given invariable time; and the length of the year being unchangeable in all the fluctuations of the planetary system, it follows that the total annual amount of solar radiation will determine, cæteris paribus, the general climate of the earth. Now, it is not difficult to show that this amount is inversely proportional to the minor axis of the ellipse described by the earth about the sun, regarded as slowly variable; and that, therefore, the major axis remaining, as we know it to be, constant, and the orbit being actually in a state of approach to a circle, and consequently the minor axis being on the increase, the mean annual amount of solar radiation received by the whole earth must be actually on the decrease. We have here, therefore, an evident real cause of sufficient universality, and acting in the right direction, to account for the phenomenon. Its adequacy is another consideration.”319—Discourse on the Study of Natural Philosophy, pp. 145−147 (1830).
Sir Charles Lyell, Bart
“Astronomical Causes of Fluctuations in Climate.—Sir John Herschel has lately inquired, whether there are any astronomical causes which may offer a possible explanation of the difference between the actual climate of the earth’s surface, and those which formerly appear to have prevailed. He has entered upon this subject, he says, ‘impressed with the magnificence of that view of geological revolutions, which regards them rather as regular and necessary effects of great and general causes, than as resulting from a series of convulsions and catastrophes, regulated by no laws, and reducible to no fixed principles.’ Geometers, he adds, have demonstrated the absolute invariability of the mean distance of the earth from the sun; whence it would seem to follow that the mean annual supply of light and heat derived from that luminary would be alike invariable; but a closer consideration of the subject will show that this would not be a legitimate conclusion, but that, on the contrary, the mean amount of solar radiation is dependent on the eccentricity of the earth’s orbit, and, therefore, liable to variation.
“Now, the eccentricity of the orbit, he continues, is actually diminishing, and has been so for ages beyond the records of history. In consequence, the ellipse is in a state of approach to a circle, and the annual average of solar heat radiated to the earth is actually on the decrease. So far, this is in accordance with geological evidence, which indicates a general refrigeration of climate; but the question remains, whether the amount of diminution which the eccentricity may have ever undergone can be supposed sufficient to account for any sensible refrigeration.320 The calculations necessary to determine this point, though practicable, have never yet been made, and would be extremely laborious; for they must embrace all the perturbations which the most influential planets, Venus, Mars, Jupiter, and Saturn, would cause in the earth’s orbit and in each other’s movements round the sun.
“The problem is also very complicated, inasmuch as it depends not merely on the ellipticity of the earth’s orbit, but on the assumed temperature of the celestial spaces beyond the earth’s atmosphere; a matter still open to discussion, and on which M. Fourier and Sir J. Herschel have arrived at very different opinions. But if, says Herschel, we suppose an extreme case, as if the earth’s orbit should ever become as eccentric as that of the planet Juno or Pallas, a great change of climate might be conceived to result, the winter and summer temperatures being sometimes mitigated and at others exaggerated, in the same latitudes.
“It is much to be desired that the calculations alluded to were executed, as even if they should demonstrate, as M. Arago thinks highly probable, that the mean of solar radiation can never be materially affected by irregularities in the earth’s motion, it would still be satisfactory to ascertain the point.”—Principles of Geology, Ninth Edition, 1853, p. 127.
M. Arago
“Can the variations which certain astronomical elements undergo sensibly modify terrestrial climates?
“The sun is not always equally distant from the earth. At this time its least distance is observed in the first days of January, and the greatest, six months after, or in the first days of July. But, on the other hand, a time will come when the minimum will occur in July, and the maximum in January. Here, then, this interesting question presents itself,—Should a summer such as those we now have, in which the maximum corresponds to the solar distance, differ sensibly, from a summer with which the minimum of this distance should coincide?
“At first sight every one probably would answer in the affirmative; for, between the maximum and the minimum of the sun’s distance from the earth there is a remarkable difference, a difference in round numbers of a thirtieth of the whole. Let, however, the consideration of the velocities be introduced into the problem, elements which cannot fairly be neglected, and the result will be on the side opposite to that we originally imagined.
“The part of the orbit where the sun is found nearest the earth, is, at the same time, the point where the luminary moves most rapidly along. The demi-orbit, or, in other words, the 180° comprehended betwixt the two equinoxes of spring-time and autumn, will then be traversed in the least possible time, when, in moving from the one of the extremities of this arc to the other, the sun shall pass, near the middle of this course of six months, at the point of the smallest distance. To resume—the hypothesis we have just adopted would give, on account of the lesser distance, a spring-time and summer hotter than they are in our days; but on account of the greater rapidity, the sum of the two seasons would be shorter by about seven days. Thus, then, all things considered, the compensation is mathematically exact. After this it is superfluous to add, that the point of the sun’s orbit corresponding to the earth’s least distance changes very gradually; and that since the most distant periods, the luminary has always passed by this point, either at the end of autumn or beginning of winter.
“We have thus seen that the changes which take place in the position of the solar orbit, have no power in modifying the climate of our globe. We may now inquire, if it be the same concerning the variations which this orbit experiences in its form....
“Herschel, who has recently been occupying himself with this problem, in the hope of discovering the explanation of several geological phenomena, allows that the succession of ages might bring the eccentricity of the terrestrial orbit to the proportion of that of the planet Pallas, that is to say, to be the 25/100 of a semi-greater axis. It is exceedingly improbable that in these periodical changes the eccentricity of our orbit should ever experience such enormous variations, and even then these twenty-five hundredth parts (25/100), would not augment the mean annual solar radiation except by about one hundredth part (1/100). To repeat, an eccentricity of 25/100 would not alter in any appreciated manner the mean thermometrical state of the globe....
“The changes of the form, and of the position, of the terrestrial orbit are mathematically inoperative, or, at most, their influence is so minute that it is not indicated by the most delicate instruments. For the explanation of the changes of climates, then, there only remains to us either the local circumstances, or some alteration in the heating or illuminating power of the sun. But of these two causes, we may continue to reject the last. And thus, in fact, all the changes would come to be attributed to agricultural operations, to the clearing of plains and mountains from wood, the draining of morasses, &c.
“Thus, at one swoop, to confine, the whole earth, the variations of climates, past and future, within the limits of the naturally very narrow influence which the labour of man can effect, would be a meteorological result of the very last importance.”—pp. 221−224, Memoir on the “Thermometrical State of the Terrestrial Globe,” in the Edinburgh New Philosophical Journal, vol. xvi., 1834.
Baron Humboldt
“The question,” he says, “has been raised as to whether the increasing value of this ellipticity is capable during thousands of years of modifying to any considerable extent the temperature of the earth, in reference to the daily and annual quantity and distribution of heat? Whether a partial solution of the great geological problem of the imbedding of tropical vegetable and animal remains in the now cold zones may not be found in these astronomical causes proceeding regularly in accordance with eternal laws?... It might at the first glance be supposed that the occurrence of the perihelion at an opposite time of the year (instead of the winter, as, is now the case, in summer) must necessarily produce great climatic variations; but, on the above supposition, the sun will no longer remain seven days longer in the northern hemisphere; no longer, as is now the case, traverse that part of the ecliptic from the autumnal equinox to the vernal equinox, in a space of time which is one week shorter than that in which it traverses the other half of its orbit from the vernal to the autumnal equinox.
“The difference of temperature which is considered as the consequence to be apprehended from the turning of the major axis, will on the whole disappear, principally from the circumstance that the point of our planet’s orbit in which it is nearest to the sun is at the same time always that over which it passes with the greatest velocity....
“As the altered position of the major axis is capable of exerting only a very slight influence upon the temperature of the earth; so likewise the limit of the probable changes in the elliptical form of the earth’s orbit are, according to Arago and Poisson, so narrow that these changes could only very slightly modify the climates of the individual zones, and that in very long periods.”321—Cosmos, vol. iv., pp. 458, 459. Bohn’s Edition. 1852.
Sir Henry T. de la Beche
“Mr. Herschel, viewing this subject with the eye of an astronomer, considers that a diminution of the surface-temperature might arise from a change in ellipticity of the earth’s orbit, which, though slowly, gradually becomes more circular. No calculations having yet been made as to the probable amount of decreased temperature from this cause, it can at present be only considered as a possible explanation of those geological phenomena which point to considerable alterations in climates.”—Geological Manual. Third Edition. 1833. p. 8.
Professor Phillips
“Temperature of the Globe.—Influence of the Sun.—No proposition is more certain than the fundamental dependence of the temperature of the surface of the globe on the solar influence.
“It is, therefore, very important for geologists to inquire whether this be variable or constant; whether the amount of solar heat communicated to the earth is and has always been the same in every annual period, or what latitude the laws of planetary movements permit in this respect.
“Sir John Herschel has examined this question in a satisfactory manner, in a paper read to the Geological Society of London. The total amount of solar radiation which determines the general climate of the earth, the year being of invariable length, is inversely proportional to the minor axis of the ellipse described by the earth about the sun, regarded as slowly variable; the major axis remaining constant and the orbit being actually in a state of approach to a circle, and, consequently, the minor axis being on the increase, it follows that the mean annual amount of solar radiation received by the whole earth must be actually on the decrease. The limits of the variation in the eccentricity of the earth’s orbit are not known. It is, therefore, impossible to say accurately what may have been in former periods of time, the amount of solar radiation; it is, however, certain that if the ellipticity has ever been so great as that of the orbit of Mercury or Pallas, the temperature of the earth must have been sensibly higher than it is at present. But the difference of a few degrees of temperature thus occasioned, is of too small an order to be employed in explaining the growth of tropical plants and corals in the polar or temperate zones, and other great phenomena of Geology.”—From A Treatise on Geology, p. 11, forming the article under that head in the seventh edition of the Encyclopædia Britannica. 1837.
Mr. Robert Bakewell
“A change in the form of the earth’s orbit, if considerable, might change the temperature of the earth, by bringing it nearer to the sun in one part of its course. The orbit of the earth is an ellipsis approaching nearly to a circle; the distance from the centre of the orbit to either focus of the ellipsis is called by astronomers ‘the eccentricity of the orbit.’ This eccentricity has been for ages slowly decreasing, or, in other words, the orbit of the earth has been approaching nearer to the form of a perfect circle; after a long period it will again increase, and the possible extent of the variation has not been yet ascertained. From what is known respecting the orbits of Jupiter and Saturn, it appears highly probable that the eccentricity of the earth’s orbit is confined within limits that preclude the belief of any great change in the mean annual temperature of the globe ever having been occasioned by this cause.”—Introduction to Geology, p. 600. 1838. Fifth Edition.
Mrs. Somerville
“Sir John Herschel has shown that the elliptical form of the earth’s orbit has but a trifling share in producing the variation of temperature corresponding to the difference of the seasons.”—Physical Geography, vol. ii., p. 20. Third Edition.
Mr. L. W. Meech, A.M.
“Let us, then, look back to that primeval epoch when the earth was in aphelion at midsummer, and the eccentricity at its maximum value—assigned by Leverrier near to ·0777. Without entering into elaborate computation, it is easy to see that the extreme values of diurnal intensity, in Section IV., would be altered as by the multiplier (1 ± e/1 ± e′)2, that is 1 − 0·11 in summer, and 1 + 0·11 in winter. This would diminish the midsummer intensity by about 9°, and increase the midwinter intensity by 3° or 4°; the temperature of spring and autumn being nearly unchanged. But this does not appear to be of itself adequate to the geological effects in question.
“It is not our purpose, here, to enter into the inquiry whether the atmosphere was once more dense than now, whether the earth’s axis had once a different inclination to the orbit, or the sun a greater emissive power of heat and light. Neither shall we attempt to speculate upon the primitive heat of the earth, nor of planetary space, nor of the supposed connection of terrestrial heat and magnetism; nor inquire how far the existence of coal-fields in this latitude, of fossils, and other geological remains, have depended upon existing causes. The preceding discussion seems to prove simply that, under the present system of physical astronomy, the sun’s intensity could never have been materially different from what is manifested upon the earth at the present day. The causes of notable geological changes must be other than the relative position of the sun and earth, under their present laws of motion.”—“On the Relative Intensity of the Heat and Light of the Sun.” Smithsonian Contributions to Knowledge, vol. ix.
M. Jean Reynaud
“La révolution qui pourrait y causer les plus grands changements thermométriques, celle qui porte l’orbite à s’élargir et à se rétrécir alternativement et, par suite, la planète à passer, aux époques de périhélie, plus ou moins près du soleil, embrasse une période de plus de cent mille années terrestres et demeure comprise dans de si étroites limites que les habitants doivent être à peine avertis que la chaleur décroît, par cette raison, depuis une haute antiquité et décroîtra encore pendant des siècles en variant en même temps dans sa répartition selon les diverses époques de l’année.... Enfin, le tournoiement de l’axe du globe s’empreint également d’une manière particulière sur l’ètablissement des saisons qui, à tour de rôle, dans chacun des deux hémisphères, deviennent graduellement, durant une période d’environ vingt-cinq mille ans, de plus en plus uniformes, ou, à l’inverse, de plus en plus dissemblables. C’est actuellement dans l’hémisphère boréal que règne l’uniformité, et quoique les étés et les hivers y tendent, dès à présent, à se trancher de plus en plus, il ne paraît pas douteux que la modération des saisons n’y produise, pendant longtemps encore, des effets appréciables. En résumé, de tous ces changements il n’en est donc aucun ni qui suive un cours précipité, ni qui s’élève jamais à des valeurs considérables; ils se règlent tous sur un mode de développement presque insensible, et il s’ensuit que les années de la terre, malgré leur complexité virtuelle, se distinguent par le constance de leurs caractères non-seulement de ce qui peut avoir lieu, en vertu des mêmes principes, dans les autres systèmes planétaires de l’univers, mais même de ce qui s’observe dans plusieurs des mondes qui composent le nôtre.”—Philosophie Religieuse: Terre et Ciel.
M. Adhémar
Adhémar does not consider the effects which ought to result from a change in the eccentricity of the earth’s orbit; he only concerns himself with those which, in his opinion, arise from the present amount of such eccentricity. He admits, of course, that both hemispheres receive from the sun equal quantities of heat per annum; but, as the southern hemisphere has a winter longer by 168 hours than the corresponding season in the northern hemisphere, an accumulation of heat necessarily takes place in the latter, and an accumulation of cold in the former. Adhémar also measures the loss of heat sustained by the southern hemisphere in a year by the number of hours by which the southern exceeds the northern winter. “The south pole,” he says, “loses in one year more heat than it receives, because the total duration of its nights surpasses that of the days by 168 hours; and the contrary takes place for the north pole. If, for example, we take for unity the mean quantity of heat which the sun sends off in one hour, the heat accumulated at the end of the year at the north pole will be expressed by 168, while the heat lost by the south pole will be equal to 168 times what the radiation lessens it by in one hour; so that at the end of the year the difference in the heat of the two hemispheres will be represented by 336 times what the earth receives from the sun or loses in an hour by radiation,”322 and at the end of 100 years the difference will be 33,600 times, and at the end of 1,000 years 336,000 times, or equal to what the earth receives from the sun in 38½ years, and so on during the 10,000 years that the southern winter exceeds in length the northern. This, in his opinion, is all that is required to melt the ice off the arctic regions, and cover the antarctic regions with an enormous ice-cap. He further supposes that in about 10,000 years, when our northern winter will occur in aphelion and the southern in perihelion, the climatic conditions of the two hemispheres will be reversed; that is to say, the ice will melt at the south pole, and the northern hemisphere will become enveloped in one continuous mass of ice, leagues in thickness, extending down to temperate regions.
This theory, as shown in Chapter V., is based upon a misconception regarding the laws of radiant heat. The loss of heat sustained by the southern hemisphere from radiation, resulting from the greater length of the southern winter, is vastly over-estimated by M. Adhémar, and could not possibly produce the effects which he supposes. But I need not enter into this subject here, as the reader will find the whole question discussed at length in the chapter above referred to. By far the most important part of Adhemar’s theory, however, is his conception of the submergence of the land by means of a polar ice-cap. He appears to have been the first to put forth the idea that a mass of ice placed on the globe, say, for example, at the south pole, will shift the earth’s centre of gravity a little to the south of its former position, and thus, as a physical consequence, cause the sea to sink at the north pole and to rise at the south. According to Adhémar, as the one hemisphere cools and the other grows warmer, the ice at the pole of the former will increase in thickness and that at the pole of the latter diminish.
The sea, as a consequence, will sink on the warm hemisphere where the ice is decreasing and rise on the cold hemisphere where the ice is increasing. And, again, in 10,000 years, when the climatic conditions of the two hemispheres are reversed, the sea will sink on the hemisphere where it formerly rose, and rise on the hemisphere where it formerly sank, and so on in like manner through indefinite ages.
Adhémar, however, acknowledges to have derived the grand conception of a submergence of the land from the shifting of the earth’s centre of gravity from the following wild speculation of one Bertrand, of Hamburgh:—
“Bertrand de Hambourg, dans un ouvrage imprimé en 1799 et qui a pour titre: Renouvellement périodique des Continents, avait déjà émis cette idée, que la masse des eaux pouvait être alternativement entraînée d’un hémisphère à l’autre par le déplacement du centre de gravité du globe. Or, pour expliquer ce déplacement, il supposait que la terre était creuse et qu’il y avait dans son intérieur un gros noyau d’aimant auquel les comètes par leur attraction communiquaient un mouvement de va-et-vient analogue à celui du pendule.”—Révolutions de la Mer, p. 41.
The somewhat extravagant notions which Adhémar has advanced in connection with his theory of submergence have very much retarded its acceptance. Amongst other remarkable views he supposes the polar ice-cap to rest on the bottom of the ocean, and to rise out of the water to the enormous height of twenty leagues. Again, he holds that on the winter approaching perihelion and the hemisphere becoming warm the ice waxes soft and rotten from the accumulated heat, and the sea now beginning to eat into the base of the cap, this is so undermined as, at last, to be left standing upon a kind of gigantic pedestal. This disintegrating process goes on till the fatal moment at length arrives, when the whole mass tumbles down into the sea in huge fragments which become floating icebergs. The attraction of the opposite ice-cap, which has by this time nearly reached its maximum thickness, becomes now predominant. The earth’s centre of gravity suddenly crosses the plain of the equator, dragging the ocean along with it, and carrying death and destruction to everything on the surface of the globe. And these catastrophes, he asserts, occur alternately on the two hemispheres every 10,000 years.—Révolutions de la Mer, pp. 316−328.
Adhémar’s theory has been advocated by M. Le Hon, of Brussels, in a work entitled Périodicité des Grands Déluges. Bruxelles et Leipzig, 1858.
II
ON THE NATURE OF HEAT-VIBRATIONS.323
From the Philosophical Magazine for May, 1864.
In a most interesting paper on “Radiant Heat,” by Professor Tyndall, read before the Royal Society in March last, it is shown conclusively that the period of heat-vibrations is not affected by the state of aggregation of the molecules of the heated body; that is to say, whether the substance be in the gaseous, the liquid, or, perhaps, the solid condition, the tendency of its molecules to vibrate according to a given period remains unchanged. The force of cohesion binding the molecules together exercises no effect on the rapidity of vibration.
I had arrived at the same conclusion from theoretical considerations several years ago, and had also deduced some further conclusions regarding the nature of heat-vibrations, which seem to be in a measure confirmed by the experimental results of Professor Tyndall. One of these conclusions was, that the heat-vibration does not consist in a motion of an aggregate mass of molecules, but in a motion of the individual molecules themselves. Each molecule, or rather we should say each atom, acts as if there were no other in existence but itself. Whether the atom stands by itself as in the gaseous state, or is bound to other atoms as in the liquid or the solid state, it behaves in exactly the same manner. The deeper question then suggested itself, viz., what is the nature of that mysterious motion called heat assumed by the atom? Does it consist in excursions across centres of equilibrium external to the atom itself? It is the generally received opinion among physicists that it does. But I think that the experimental results arrived at by Professor Tyndall, as well as some others which will presently be noticed, are entirely hostile to such an opinion. The relation of an atom to its centre of equilibrium depends entirely on the state of aggregation. Now if heat-vibrations consist in excursions to and fro across these centres, then the period ought to be affected by the state of aggregation. The higher the tension of the atom in regard to the centre, the more rapid ought its movement to be. This is the case in regard to the vibrations constituting sound. The harder a body becomes, or, in other words, the more firmly its molecules are bound together, the higher is the pitch. Two harp-cords struck with equal force will vibrate with equal force, however much they may differ in the rapidity of their vibrations. The vis viva of vibration depends upon the force of the stroke; but the rapidity depends, not on the stroke, but upon the tension of the cord.
That heat-vibrations do not consist in excursions of the molecules or atoms across centres of equilibrium, follows also as a necessary consequence from the fact that the real specific heat of a body remains unchanged under all conditions. All changes in the specific heat of a body are due to differences in the amount of heat consumed in molecular work against cohesion or other forces binding the molecules together. Or, in other words, to produce in a body no other effect than a given rise of temperature, requires the same amount of force, whatever may be the physical condition of the body. Whether the body be in the solid, the fluid, or the gaseous condition, the same rise of temperature always indicates the same quantity of force consumed in the simple production of the rise. Now, if heat-vibrations consist in excursions of the atom to and fro across a centre of equilibrium external to itself, as is generally supposed, then the real specific heat of a solid body, for example, ought to decrease with the hardness of the body, because an increase in the strength of the force binding the molecules together would in such a case tend to favour the rise in the rapidity of the vibrations.
These conclusions not only afford us an insight into the hidden nature of heat-vibrations, but they also appear to cast some light on the physical constitution of the atom itself. They seem to lead to the conclusion that the ultimate atom itself is essentially elastic.324 For if heat-vibrations do not consist in excursions of the atom, then it must consist in alternate expansions and contractions of the atom itself. This again is opposed to the ordinary idea that the atom is essentially solid and impenetrable. But it favours the modern idea, that matter consists of forces of resistance acting from a centre.
Professor Tyndall in a memoir read before the Royal Society “On a new Series of Chemical Reactions produced by Light,” has subsequently arrived at a similar conclusion in reference to the atomic nature of heat-vibrations. The following are his views on the subject:—
“A question of extreme importance in molecular physics here arises:—What is the real mechanism of this absorption, and where is its seat?
“I figure, as others do, a molecule as a group of atoms, held together by their mutual forces, but still capable of motion among themselves. The vapour of the nitrite of amyl is to be regarded as an assemblage of such molecules. The question now before us is this:—In the act of absorption, is it the molecules that are effective, or is it their constituent atoms? Is the vis viva of the intercepted waves transferred to the molecule as a whole, or to its constituent parts?
“The molecule, as a whole, can only vibrate in virtue of the forces exerted between it and its neighbour molecules. The intensity of these forces, and consequently the rate of vibration, would, in this case, be a function of the distance between the molecules. Now the identical absorption of the liquid and of the vaporous nitrite of amyl indicates an identical vibrating period on the part of liquid and vapour, and this, to my mind, amounts to an experimental demonstration that the absorption occurs in the main within the molecule. For it can hardly be supposed, if the absorption were the act of the molecule as a whole, that it could continue to affect waves of the same period after the substance had passed from the vaporous to the liquid state.”—Proc. of Roy. Soc., No. 105. 1868.
Professor W. A. Norton, in his memoir on “Molecular Physics,”325 has also arrived at results somewhat similar in reference to the nature of heat-vibrations. “It will be seen,” he says, “that these (Mr. Croll’s) ideas are in accordance with the conception of the constitution of a molecule adopted at the beginning of the present memoir (p. 193), and with the theory of heat-vibrations or heat-pulses deduced therefrom (p. 196).”326
III
ON THE REASON WHY THE DIFFERENCE OF READING BETWEEN A THERMOMETER EXPOSED TO DIRECT SUNSHINE AND ONE SHADED DIMINISHES AS WE ASCEND IN THE ATMOSPHERE.327
From the Philosophical Magazine for March, 1867.
The remarkable fact was observed by Mr. Glaisher, that the difference of reading between a black-bulb thermometer exposed to the direct rays of the sun and one shaded diminishes as we ascend in the atmosphere. On viewing the matter under the light of Professor Tyndall’s important discovery regarding the influence of aqueous vapour on radiant heat, the fact stated by Mr. Glaisher appears to be in perfect harmony with theory. The following considerations will perhaps make this plain.
The shaded thermometer marks the temperature of the surrounding air; but the exposed thermometer marks not the temperature of the air, but that of the bulb heated by the direct rays of the sun. The temperature of the bulb depends upon two elements: (1) the rate at which it receives heat by direct radiation from the sun above, the earth beneath, and all surrounding objects, and by contact with the air; (2) the rate at which it loses heat by radiation and by contact with the air. As regards the heat gained and lost by contact with the surrounding air, both thermometers are under the same conditions, or nearly so. We therefore require only to consider the element of radiation.
We begin by comparing the two thermometers at the earth’s surface, and we find that they differ by a very considerable number of degrees. We now ascend some miles into the air, and on again comparing the thermometers we find that the difference between them has greatly diminished. It has been often proved, by direct observation, that the intensity of the sun’s rays increases as we rise in the atmosphere. How then does the exposed thermometer sink more rapidly than the shaded one as we ascend? The reason is obviously this. The temperature of the thermometers depends as much upon the rate at which they are losing their heat as upon the rate at which they are gaining it. The higher temperature of the exposed thermometer is the result of direct radiation from the sun. Now, although this thermometer receives by radiation more heat from the sun at the upper position than at the lower, it does not necessarily follow on this account that its temperature ought to be higher. Suppose that at the upper position it should receive one-fourth more heat from the sun than at the lower, yet if the rate at which it loses its heat by radiation into space be, say, one-third greater at the upper position than at the lower, the temperature of the bulb would sink to a considerable extent, notwithstanding the extra amount of heat received. Let us now reflect on how matters stand in this respect in regard to the actual case under our consideration. When the exposed thermometer is at the higher position, it receives more heat from the sun than at the lower, but it receives less from the earth; for a considerable part of the radiation from the earth is cut off by the screen of aqueous vapour intervening between the thermometer and the earth. But, on the whole, it is probable that the total quantity of radiant heat reaching the thermometer is greater in the higher position than in the lower. Compare now the two positions in regard to the rate at which the thermometer loses its heat by radiation. When the thermometer is at the lower position, it has the warm surface of the ground against which to radiate its heat downwards. The high temperature of the ground thus tends to diminish the rate of radiation. Above, there is a screen of aqueous vapour throwing back upon the thermometer a very considerable part of the heat which the instrument is radiating upwards. This, of course, tends greatly to diminish the loss from radiation. But at the upper position this very screen, which prevented the thermometer from throwing off its heat into the cold space above, now affects the instrument in an opposite manner; for the thermometer has now to radiate its heat downwards, not upon the warm surface of the ground as before, but upon the cold upper surface of the aqueous screen intervening between the instrument and the earth. This of course tends to lower the mercury. We are now in a great measure above the aqueous screen, with nothing to protect the thermometer from the influence of cold stellar space. It is true that the air above is at a temperature little below that of the thermometer itself; but then the air is dry, and, owing to its diathermancy, it does not absorb the heat radiated from the thermometer, and consequently the instrument radiates its heat directly into the cold stellar space above, some hundreds of degrees below zero, almost the same as it would do were the air entirely removed. The enormous loss of heat which the thermometer now sustains causes it to fall in temperature to a great extent. The molecules of the comparatively dry air at this elevation, being very bad radiators, do not throw off their heat into space so rapidly as the bulb of the exposed thermometer; consequently their temperature does not (for this reason) tend to sink so rapidly as that of the bulb. Hence the shaded thermometer, which indicates the temperature of those molecules, is not affected to such an extent as the exposed one. Hence also the difference of reading between the two instruments must diminish as we rise in the atmosphere.
This difference between the temperature of the two thermometers evidently does not go on diminishing to an indefinite extent. Were we able to continue our ascent in the atmosphere, we should certainly find that a point would be reached beyond which the difference of reading would begin to increase, and would continue to do so till the outer limits of the atmosphere were reached. The difference between the temperatures of the two thermometers beyond the limits of the atmosphere would certainly be enormous. The thermometer exposed to the direct rays of the sun would no doubt be much colder than it had been when at the earth’s surface; but the shaded thermometer would now indicate the temperature of space, which, according to Sir John Herschel and M. Pouillet, is more than 200° Fahrenheit below zero.
It follows also, from what has been stated, that even under direct sunshine the removal of the earth’s atmosphere would tend to lower the temperature of the earth’s surface to a great extent. This conclusion also follows as an immediate inference from the fact that the earth’s atmosphere, as it exists at present charged with aqueous vapour, affects terrestrial radiation more than it does radiation from the sun; for the removal of the atmosphere would increase the rate at which the earth throws off its heat into space more than it would increase the rate at which it receives heat from the sun; therefore its temperature would necessarily fall until the rate of radiation from the earth’s surface exactly equalled the rate of radiation to the surface. Let the atmosphere again envelope the earth, and terrestrial radiation would instantly be diminished; the temperature of the earth’s surface would therefore necessarily begin to rise, and would continue to do so till the rate of radiation from the surface would equal the rate of radiation received by the surface. Equilibrium being thus restored, the temperature would remain stationary. It is perfectly obvious that if we envelope the earth with a substance such as our atmosphere, that offers more resistance to terrestrial radiation than to solar, the temperature of the earth’s surface must necessarily rise until the heat which is being radiated off equals that which is being received from the sun. Remove the air and thus get quit of the resistance, and the temperature of the surface would fall, because in this case a lower temperature would maintain equilibrium.
It follows, therefore, that the moon, which has no atmosphere, must be much colder than our earth, even on the side exposed to the sun. Were our earth with its atmosphere as it exists at present removed to the orbit of Venus or Mars, for example, it certainly would not be habitable, owing to the great change of temperature that would result. But a change in the physical constitution of the atmospheric envelope is really all that would be necessary to retain the earth’s surface at its present temperature in either position.
IV
REMARKS ON MR. J. Y. BUCHANAN’S THEORY OF THE VERTICAL DISTRIBUTION OF TEMPERATURE OF THE OCEAN.328
Since the foregoing was in type, a paper on the “Vertical Distribution of Temperature of the Ocean,” by Mr. J. Y. Buchanan, chemist on board the Challenger, has been read before the Royal Society.329 In that paper Mr. Buchanan endeavours to account for the great depth of warm water in the middle of the North Atlantic compared with that at the equator, without referring it to horizontal circulation of any kind.
The following is the theory as stated by Mr. Buchanan:—
“Let us assume the winter temperature of the surface-water to be 60° F. and the summer temperature to be 70° F. If we start from midwinter, we find that, as summer approaches, the surface-water must get gradually warmer, and that the temperature of the layers below the surface must decrease at a very rapid rate, until the stratum of winter temperature, or 60° F., is reached; in the language of the isothermal charts, the isothermal line for degrees between 70° F. (if we suppose that we have arrived at midsummer) and 60° F. open out or increase their distance from each other as the depth increases. Let us now consider the conditions after the summer heat has begun to waver. During the whole period of heating, the water, from its increasing temperature, has been always becoming lighter, so that heat communication by convection with the water below has been entirely suspended during the whole period. The heating of the surface-water has, however, had another effect, besides increasing its volume; it has, by evaporation, rendered it denser than it was before, at the same temperature. Keeping in view this double effect of the summer heat upon the surface-water, let us consider the effect of the winter cold upon it. The superficial water having assumed the atmospheric temperature of, say 60° F., will sink through the warmer water below it, until it reaches the stratum of water having the same temperature as itself. Arrived here, however, although it has the same temperature as the surrounding water, the two are no longer in equilibrium, for the water which has come from the surface, has a greater density than that below at the same temperature. It will therefore not be arrested at the stratum of the same temperature, as would have been the case with fresh water; but it will continue to sink, carrying of course its higher temperature with it, and distributing it among the lower layers of colder water. At the end of the winter, therefore, and just before the summer heating recommences, we shall have at the surface a more or less thick stratum of water having a nearly uniform temperature of 60° F., and below this the temperature decreasing at a considerable but less rapid rate than at the termination of the summer heating. If we distinguish between surface-water, the temperature of which rises with the atmospheric temperature (following thus, in direction at least, the variation of the seasons), and subsurface-water, or the stratum immediately below it, we have for the latter the, at first sight, paradoxical effect of summer cooling and winter heating. The effect of this agency is to diffuse the same heat to a greater depth in the ocean, the greater the yearly range of atmospheric temperature at the surface. This effect is well shown in the chart of isothermals, on a vertical section, between Madeira and a position in lat. 3° 8′ N., long. 14° 49′ W. The isothermal line for 45° F. rises from a depth of 740 fathoms at Madeira to 240 fathoms at the above-mentioned position. In equatorial regions there is hardly any variation in the surface-temperature of the sea; consequently we find cold water very close to the surface all along the line. On referring to the temperature section between the position lat. 3° 8′ N., long. 14° 49′ W., and St. Paul’s Rocks, it will be seen that, with a surface-temperature of from 75° F. to 79° F., water at 55° F. is reached at distances of less than 100 fathoms from the surface. Midway between the Azores and Bermuda, with a surface-temperature of 70° F., it is only at a depth of 400 fathoms that we reach water of 55° F.”
What Mr. Buchanan states will explain why the mean annual temperature of the water at the surface extends to a greater depth in the middle of the North Atlantic than at the equator. It also explains why the temperature from the surface downwards decreases more rapidly at the equator than in the middle of the North Atlantic; but, if I rightly understand the theory, it does not explain (and this is the point at issue) why at a given depth the temperature of the water in the North Atlantic should be higher than the temperature at a corresponding depth at the equator. Were there no horizontal circulation the greatest thickness of warm water would certainly be found at the equator and the least at the poles. The isothermals would in such a case gradually slope downwards from the poles to the equator. The slope might not be uniform, but still it would be a continuous downward slope.
V
ON THE CAUSE OF THE COOLING EFFECT PRODUCED ON SOLIDS BY TENSION.330
From the Philosophical Magazine for May, 1864.
From a series of experiments made by Dr. Joule with his usual accuracy, he found that when bodies are subjected to tension, a cooling effect takes place. “The quantity of cold,” he says, “produced by the application of tension was sensibly equal to the heat evolved by its removal; and further, that the thermal effects were proportional to the weight employed.”331 He found that when a weight was applied to compress a body, a certain amount of heat was evolved; but the same weight, if applied to stretch the body, produced a corresponding amount of cold.
This, although it does not appear to have been remarked, is a most singular result. If we employ a force to compress a body, and then ask what has become of the force applied, it is quite a satisfactory answer to be told that the force is converted into heat, and reappears in the molecules of the body as such; but if the same force be employed to stretch the body, it will be no answer to be told that the force is converted into cold. Cold cannot be the force under another form, for cold is a privation of force. If a body, for example, is compressed by a weight, the vis viva of the descending weight is transmitted to the molecules of the body and reappears under that form of force called heat; but if the same weight is applied so as to stretch or expand the body, not only does the force of the weight disappear without producing heat, but the molecules which receive the force lose part of that which they already possessed. Not only does the force of the weight disappear, but along with it a portion of the force previously existing in the molecules under the form of heat. We have therefore to inquire, not merely into what becomes of the force imparted by the weight, but also what becomes of the force in the form of heat which disappears from the molecules of the body itself. That the vis viva of the descending weight should disappear without increasing the heat of the molecules is not so surprising, because it may be transformed into some other form of force different from that of heat. For it is by no means evident à priori that heat should be the only form under which it may exist. But it is somewhat strange that it should cause the force previously existing in the molecules in the form of heat also to change into some other form.
When a weight, for example, is employed to stretch a solid body, it is evident that the force exerted by the weight is consumed in work against the cohesion of the particles, for the entire force is exerted so as to pull them separate from each other. But the cooling effect which takes place shows that more force disappears than simply what is exerted by the weight; for the cooling effect is caused by the disappearance of force in the shape of heat from the body itself. The force exerted by the weight disappears in performing work against the cohesion of the particles of the body stretched. But what becomes of the energy in the form of heat which disappears from the body at the same time? It must be consumed in performing work of some kind or other. The force exerted by the weight cannot be the cause of the cooling effect. The transferrence of force from the weight to the body may be the cause of a heating effect—an increase of force in the body; but this transferrence of force to the body cannot be the cause of a decrease of force in the body. If a decrease of force actually follows the application of tension, the weight can only be the occasion, not the cause of the decrease.
In what manner, then, does the stretching of the body by the weight become the occasion of its losing energy in the shape of heat? Or, in other words, what is the cause of the cooling effects which result from tension? The probable explanation of the phenomenon seems to be this: if the molecules of a body are held together by any force, of whatever nature it may be, which prevents any further separation taking place, then the entire heat applied to such a body will appear as temperature; but if this binding force becomes lessened so as to allow further expansion, then a portion of the heat applied will be lost in producing expansion. All solids at any given temperature expand until the expansive force of their heat exactly balances the cohesive force of their molecules, after which no further expansion at the same temperature can possibly take place while the cohesive force of the molecules remains unchanged. But if, by some means or other, the cohesive force of the molecules become reduced, then instantly the body will expand under the heat which it possesses, and of course a portion of the heat will be consumed in expansion, and a cooling effect will result. Now tension, although it does not actually lessen the cohesive force of the molecules of the stretched body, yet produces, by counteracting this force, the same effect; for it allows the molecules an opportunity of performing work of expansion, and a cooling effect is the consequence. If the piston of a steam-engine, for example, be loaded to such an extent that the steam is unable to move it, the steam in the interior of the cylinder will not lose any of its heat; but if the piston be raised by some external force, the molecules of the steam will assist this force, and consequently will suffer loss of heat in proportion to the amount of work which they perform. The very same occurs when tension is applied to a solid. Previous to the application of tension, the heat existing in the molecules is unable to produce any expansion against the force of cohesion. But when the influence of cohesion is partly counteracted by the tension applied, the heat then becomes enabled to perform work of expansion, and a cooling effect is the result.
VI
THE CAUSE OF REGELATION.332
There are two theories which have been advanced to explain Regelation, the one by Professor Faraday, and the other by Professor James Thomson.
According to Professor James Thomson, pressure is the cause of regelation. Pressure applied to ice tends to lower the melting-point, and thus to produce liquefaction; but the water which results is colder than the ice, and refreezes the moment it is relieved from pressure. When two pieces of ice are pressed together, a melting takes place at the points in contact, resulting from the lowering of the melting-point; the water formed, re-freezing, joins the two pieces together.
The objection which has been urged against this theory is that regelation will take place under circumstances where it is difficult to conceive how pressure can be regarded as the cause. Two pieces of ice, for example, suspended by silken threads in an atmosphere above the melting-point, if but simply allowed to touch each other, will freeze together. Professor J. Thomson, however, attributes the freezing to the pressure resulting from the capillary attraction of the two moist surfaces in contact. But when we reflect that it requires the pressure of a mile of ice—135 tons on the square foot—to lower the melting-point one degree, it must be obvious that the lowering effect resulting from capillary attraction in the case under consideration must be infinitesimal indeed.
The following clear and concise account of Faraday’s theory, I quote from Professor Tyndall’s “Forms of Water:”—
“Faraday concluded that in the interior of any body, whether solid or liquid, where every particle is grasped, so to speak, by the surrounding particles, and grasps them in turn, the bond of cohesion is so strong as to require a higher temperature to change the state of aggregation than is necessary at the surface. At the surface of a piece of ice, for example, the molecules are free on one side from the control of other molecules; and they therefore yield to heat more readily than in the interior. The bubble of air or steam in overheated water also frees the molecules on one side; hence the ebullition consequent upon its introduction. Practically speaking, then, the point of liquefaction of the interior ice is higher than that of the superficial ice....
“When the surfaces of two pieces of ice, covered with a film of the water of liquefaction, are brought together, the covering film is transferred from the surface to the centre of the ice, where the point of liquefaction, as before shown, is higher than at the surface. The special solidifying power of ice upon water is now brought into play on both sides of the film. Under these circumstances, Faraday held that the film would congeal, and freeze the two surfaces together.”—The Forms of Water, p. 173.
The following appears to be a more simple explanation of the phenomena than either of the preceding:—
The freezing-point of water, and the melting-point of ice, as Professor Tyndall remarks, touch each other as it were at this temperature. At a hair’s-breadth lower water freezes; at a hair’s-breadth higher ice melts. Now if we wish, for example, to freeze water, already just about the freezing-point, or to melt a piece of ice already just about the melting-point, we can do this either by a change of temperature or by a change of the melting-point. But it will be always much easier to effect this by the former than by the latter means. Take the case already referred to, of the two pieces of ice suspended in an atmosphere above the melting-point. The pieces at their surfaces are in a melting condition, and are surrounded by a thin film of water just an infinitesimal degree above the freezing-point. The film has on the one side solid ice at the freezing-point, and on the other a warm atmosphere considerably above the freezing-point. The tendency of the ice is to lower the temperature of the film, while that of the air is to raise its temperature. When the two pieces are brought into contact the two films unite and form one film separating the two pieces of ice. This film is not like the former in contact with ice on the one side and warm air on the other. It is surrounded on both sides by solid ice. The tendency of the ice, of course, is to lower the film to the same temperature as the ice itself, and thus to produce solidification. It is evident that the film must either melt the ice or the ice must freeze the film, if the two are to assume the same temperature. But the power of the ice to produce solidification, owing to its greater mass, is enormously greater than the power of the film to produce fluidity, consequently regelation is the result.
VII
LIST OF PAPERS WHICH HAVE APPEARED IN DR. A. PETERMANN’S GEOGRAPHISCHE MITTHEILUNGEN RELATING TO THE GULF-STREAM AND THERMAL CONDITION OF THE ARCTIC REGIONS.
The most important memoir which we have on the Gulf-stream and its influence on the climate of the arctic regions is the one by Dr. A. Petermann, entitled “Der Golfstrom und Standpunkt der thermometrischen Kenntniss des nord-atlantischen Oceans und Landgebiets im Jahre 1870.” Geographische Mittheilungen, Band XVI. 1870.
Dr. Petermann has, in this memoir, by a different line of argument from that which I have pursued in this volume, shown in the most clear and convincing manner that the abnormally high temperature of the north-western shores of Europe and the seas around Spitzbergen is owing entirely to the Gulf-stream, and not to any general circulation such as that advocated by Dr. Carpenter. From a series of no fewer than 100,000 observations of temperature in the North Atlantic and in the arctic seas, he has been enabled to trace with accuracy on his charts the very footsteps of the heat in its passage from the Gulf of Mexico up to the shores of Spitzbergen.
The following is a list of the more important papers bearing on the subject which have recently appeared in Dr. Petermann’s Geogr. Mittheilungen:—
An English translation of Dr. Petermann’s Memoir, and of a few more in the subjoined list, has been published in a volume, with supplements, by the Hydrographic Department of the United States, under the superintendence of Commodore R. H. Wyman.
The papers whose titles are in English have appeared in the American volume. In that volume the principal English papers on the subject, in as far as they relate to the north-eastern extension of the Gulf-stream, have also been reprinted.
The System of Oceanic Currents in the Circumpolar Basin of the Northern Hemisphere. By Dr. A. Mühry. Vol. XIII., Part II. 1867.
The Scientific Results of the first German North Polar Expedition. By Dr. W. von Freeden. Vol. XV., Part VI. 1869.
The Gulf-stream, and the Knowledge of the Thermal Properties of the North Atlantic Ocean and its Continental Borders, up to 1870. By Dr. A. Petermann. Geographische Mittheilungen, Vol. XVI., Part VI. 1870.
The Temperature of the North Atlantic Ocean and the Gulf-stream. By Rear-Admiral C. Irminger. Vol. XVI., Part VI. 1870.
Meteorological Observations during a Winter Stay on Bear Island, 1865−1866. By Sievert Tobilson. Vol. XVI., Part VII. 1870.
Die Temperatur-verhältnisse in den arktischen Regionen. Von Dr. Petermann. Band XVI., Heft VII. 1870.
Preliminary Reports of the Second German North Polar Expedition, and of minor Expeditions, in 1870. Vol. XVII.
Preliminary Report of the Expedition for the Exploration of the Nova-Zembla Sea (the sea between Spitzbergen and Nova Zembla), by Lieutenants Weyprecht and Payer, June to September, 1871. By Dr. A. Petermann. Vol. XVII. 1871.
Der Golfstrom ostwärts vom Nordkap. Von A. Middendorff. Band XVII., Heft I. 1871.
Kapitän E. H. Johannesen’s Umfahrung von Nowaja Semlä im Sommer 1870, und norwegischer Finwalfang östlich vom Nordkap. Von Th. v. Heuglin. Band XVII., Heft I. 1871.
Die Nordpol-Expeditionen, das sagenhafte Gillis-land und der Golfstrom im Polarmeere. Von Dr. A. Petermann. 5 Nov. 1870.
Th. v. Heuglin’s Aufnahmen in Ost-Spitzbergen. Begleitworte zur neuen Karte dieses Gebiets. Tafel 9. 1870. Band XVII., Heft V. 1871.
Die zweite deutsche Nordpolar-Expedition, 1869−70. Schlittenreise an der Küste Grönlands nach Norden, 8 März−27 April, 1870. Von Ober-Lieutenant Julius Payer. Band XVII., Heft V. 1871.
Die Entdeckung des Kaiser Franz Josef-Fjordes in Ost-Grönland, August, 1870. Von Ober-Lieutenant Julius Payer. Band XVII., Heft V. 1871.
Die Erschliessung eines Theiles des nördlichen Eismeeres durch die Fahrten und Beobachtungen der norwegischen Seefahrer Torkildsen, Ulve, Mack Qvale, und Nedrevaag im karischen Meere, 1870. Von Dr. A. Petermann. Band XVII., Heft III. 1871.
Die zweite deutsche Nordpolar-Expedition, 1869−70. Schlittenreise nach Ardencaple Inlet, 8−29 Mai, 1870. Von Ober-Lieutenant Julius Payer. Band XVII., Heft XI. 1871.
Ein Winter unter dem Polarkreise. Von Ober-Lieutenant Julius Payer. Band XVII., Heft XI. 1871.
Die Entdeckung eines offenen Polarmeeres durch Payer und Weyprecht im September, 1871. Von Dr. A. Petermann. Band XVII., Heft XI. 1871.
James Lamont’s Nordfahrt, Mai-August, 1871. Die Entdeckungen von Weyprecht, Payer, Tobiesen, Mack, Carlsen, Ulve, und Smyth im Sommer, 1871.
Stand der Nordpolarfrage zu Ende des Jahres 1871. Von Dr. A. Petermann. Band XVII., Heft XII. 1871.
Das Innere von Grönland. Von Dr. Robert Brown. Band XVII., Heft X. 1871.
Captain T. Torkildsen’s Cruise from Tromsö to Spitzbergen, July 26 to September 26, 1871. Vol. XVIII. 1872.
The Sea north of Spitzbergen, and the most northern Meteorological Observations. Vol. XVIII. 1872.
Results of the Observations of the Deep-sea Temperature in the Sea between Greenland, Northern Europe, and Spitzbergen. By Professor H. Möhn. Vol. XVIII. 1872.
The Norwegian Cruises to Nova Zembla and the Kara Sea in 1871. Vol. XVIII. 1872.
The Cruises in the Polar Sea in 1872. Vol. XVIII. 1872.
The Cruise of Smyth and Ulve, June 19 to September 27, 1871. Vol. XVIII. 1872.
Die fünfmonatliche Schiffbarkeit des sibirischen Eismeeres um Nowaja Semlja, erwiesen durch die norwegischen Seefahrer in 1869 und 1870, ganz besonders aber in 1871. Von Dr. A. Petermann. Band XVIII., Heft X. 1872.
Die neuen norwegischen Aufnahmen des nordöstlichen Theiles von Nowaja Semlja durch Mack, Dörma, Carlsen, u. A., 1871. Von Dr. Petermann. Band XVIII., Heft X. 1872.
Nachrichten über die sieben zurückgekehrten Expeditionen unter Graf Wiltschek, Altmann, Johnsen, Nilsen, Smith, Gray, Whymper; die drei Überwinterungs-Expeditionen; die Amerikanische, Schwedische, Österreichisch-Ungarische; und die zwei neuen: die norwegische Winter-Expedition und diejenige unter Kapitän Mack. Von Dr. A. Petermann. Band XVIII., Heft XII. 1872.
Konig Karl-Land im Osten von Spitzbergen und seine Erreichung und Aufnahme durch norwegische Schiffer im Sommer 1872. Von Professor H. Möhn. Band XIX., Heft IV. 1873.
Resultate der Beobachtungen angestellt auf der Fahrt des Dampfers “Albert” nach Spitzbergen im November und Dezember, 1872. Von Professor Möhn. Band XIX., Heft VII. 1873.
Die amerikanische Nordpolar-Expedition unter C. F. Hall, 1871−3. Von Dr. A. Petermann. Band XIX., Heft VIII. 1873.
Die Trift der Hall’schen Nordpolar-Expedition, 16 August bis 15 Oktober, 1872, und die Schollenfahrt der 20 bis zum 30 April, 1873. Von Dr. A. Petermann. Band XIX., Heft X. 1873.
Das offene Polarmeer bestätigt durch das Treibholz an der Nordwestküste von Grönland. Von Dr. A. Petermann. Band XX., Heft V. 1874.
Das arktische Festland und Polarmeer. Von Dr. Joseph Chavanne. Band XX., Heft VII. 1874.
Die Umkehr der Hall’schen Polar-Expedition nach den Aussagen der Offiziere. Von Dr. A. Petermann. Band XX., Heft VII. 1874.
Die zweite österreichisch-ungarische Nordpolar-Expedition unter Weyprecht und Payer, 1872−4. Von Dr. A. Petermann. Band XX., Heft X. 1874.
Beiträge zur Klimatologie und Meteorologie des Ost-polar-Meeres. Von Professor Möhn. Band XX., Heft V. 1874.
Kapitän David Gray’s Reise und Beobachtungen im ost-grönländischen Meere, 1874, und seine Ansichten über den besten Weg zum Nordpol. Original-Mittheilungen an A. Petermann, d.D., Peterhead, Dezember, 1874. Band XXI., Heft III. 1875.
VIII
LIST OF PAPERS BY THE AUTHOR TO WHICH REFERENCE IS MADE IN THIS VOLUME.
On the Influence of the Tidal Wave on the Earth’s Rotation and on the Acceleration of the Moon’s Mean Motion.—Phil. Mag., April, 1864.
On the Nature of Heat-vibrations.—Phil. Mag., May, 1864.
On the Cause of the Cooling Effect produced on Solids by Tension.—Phil. Mag., May, 1864.
On the Physical Cause of the Change of Climate during Geological Epochs.—Phil. Mag., August, 1864.
On the Physical Cause of the Submergence of the Land during the Glacial Epoch.—The Reader, September 2nd and October 14th, 1865.
On Glacial Submergence.—The Reader, December 2nd and 9th, 1865.
On the Eccentricity of the Earth’s Orbit.—Phil. Mag., January, 1866.
Glacial Submergence on the Supposition that the Interior of the Globe is in a Fluid Condition.—The Reader, January 13th, 1866.
On the Physical Cause of the Submergence and Emergence of the Land during the Glacial Epoch, with a Note by Professor Sir William Thomson.—Phil. Mag., April, 1866.
On the Influence of the Tidal Wave on the Motion of the Moon.—Phil. Mag., August and November, 1866.
On the Reason why the Change of Climate in Canada since the Glacial Epoch has been less complete than in Scotland.—Trans. Geol. Soc. of Glasgow, 1866.
On the Eccentricity of the Earth’s Orbit, and its Physical Relations to the Glacial Epoch.—Phil. Mag., February, 1867.
On the Reason why the Difference of Reading between a Thermometer exposed to direct Sunshine and one shaded diminishes as we ascend in the Atmosphere.—Phil. Mag., March, 1867.
On the Change in the Obliquity of the Ecliptic; its Influence on the Climate of the Polar Regions and Level of the Sea.—Trans. Geol. Soc. of Glasgow, vol. ii., p. 177. Phil. Mag., June, 1867.
Remarks on the Change in the Obliquity of the Ecliptic, and its Influence on Climate.—Phil. Mag., August, 1867.
On certain Hypothetical Elements in the Theory of Gravitation and generally received Conceptions regarding the Constitution of Matter.—Phil. Mag., December, 1867.
On Geological Time, and the probable Date of the Glacial and the Upper Miocene Period.—Phil. Mag., May, August, and November, 1868.
On the Physical Cause of the Motions of Glaciers.—Phil. Mag., March, 1869. Scientific Opinion, April 14th, 1869.
On the Influence of the Gulf-stream.—Geol. Mag., April, 1869. Scientific Opinion, April 21st and 28th, 1869.
On Mr. Murphy’s Theory of the Cause of the Glacial Climate.—Geol. Mag., August, 1869. Scientific Opinion, September 1st, 1869.
On the Opinion that the Southern Hemisphere loses by Radiation more Heat than the Northern, and the supposed Influence that this has on Climate.—Phil. Mag., September, 1869. Scientific Opinion, September 29th and October 6th, 1869.
On Two River Channels buried under Drift belonging to a Period when the Land stood several hundred feet higher than at present.—Trans. Geol. Soc. of Edinburgh, vol. i., p. 330.
On Ocean-currents: Ocean-currents in Relation to the Distribution of Heat over the Globe.—Phil. Mag., February, 1870.
On Ocean-currents: Ocean-currents in Relation to the Physical Theory of Secular Changes of Climate.—Phil. Mag., March, 1870.
The Boulder Clay of Caithness a Product of Land-ice.—Geol. Mag., May and June, 1870.
On the Cause of the Motion of Glaciers.—Phil. Mag., September, 1870.
On Ocean-currents: On the Physical Cause of Ocean-currents. Examination of Lieutenant Maury’s Theory.—Phil. Mag., October, 1870.
On the Transport of the Wastdale Granite Boulders.—Geol. Mag., January, 1871.
On a Method of determining the Mean Thickness of the Sedimentary Rocks of the Globe.—Geol. Mag., March, 1871.
Mean Thickness of the Sedimentary Rocks.—Geol. Mag., June, 1871.
On the Age of the Earth as determined from Tidal Retardation.—Nature, August 24th, 1871.
Ocean-currents: On the Physical Cause of Ocean-currents. Examination of Dr. Carpenter’s Theory.—Phil. Mag., October, 1871.
Ocean-currents: Further Examination of the Gravitation Theory.—Phil. Mag., February, 1874.
Ocean-currents: The Wind Theory of Oceanic Circulation.—Phil. Mag., March, 1874.
Ocean-currents.—Nature, May 21st, 1874.
The Physical Cause of Ocean-currents.—Phil. Mag., June, 1874. American Journal of Science and Art, September, 1874.
On the Physical Cause of the Submergence and Emergence of the Land during the Glacial Epoch.—Geol. Mag., July and August, 1874.
Footnotes
1 Trans. of Edin. Geol. Soc., vol. ii. p. 252.
2 Phil. Mag., January, 1863.
3 Athenæum, September 22, 1860.
4 Trans. Glasgow Geol. Soc., vol. iv., p. 313.
5 See Mr. Hopkin’s remarks on this theory, Quart. Journ. Geol. Soc., vol. viii.
6 See Chap. xxv.
7 See Chap. iv.
8 “Treatise on Astronomy,” § 315; “Outlines,” § 368.
9 Annuaire for 1834, p. 199. Edin. New Phil. Journ., April, 1834, p. 224.
10 “Cosmos,” vol. iv. p. 459 (Bohn’s Edition). “Physical Description of the Heavens,” p. 336.
11 Phil. Mag. for February, 1867, p. 127.
12 The Gulf-stream at the narrowest place examined by the Coast Survey, and where also its velocity was greatest, was found to be over 30 statute miles broad and 1,950 feet deep. But we must not suppose that this represents all the warm water which is received by the Atlantic from the equator; a great mass flows into the Atlantic without passing through the Straits of Florida.
13 It is probable that a large proportion of the water constituting the south-eastern branch of the Gulf-stream is never cooled down to 40°; but, on the other hand, the north-eastern branch, which passes into the arctic regions, will be cooled far below 40°, probably below 30°. Hence I cannot be over-estimating the extent to which the water of the Gulf-stream is cooled down in fixing upon 40° as the average minimum temperature.
14 “Physical Geography of the Sea,” § 24, 6th edition.
15 “Physical Geography,” § 54.
16 Trans. of Roy. Soc. of Edin., vol. xxi., p. 57. Phil. Mag., § 4, vol. ix., p. 36.
17 “Smithsonian Contributions to Knowledge,” vol. ix.
18 “Heat as a Mode of Motion,” art. 240.
19 Trans. Roy. Soc. of Edin., vol. xxv., part 2.
20 See “Smithsonian Contributions to Knowledge,” vol. ix.
21 “Meteorology,” section 36.
22 Comptes-Rendus, July 9, 1838. Taylor’s “Scientific Memoirs,” vol. iv., p. 44 (1846).
23 The mean temperature of the Atlantic between the tropics and the arctic circle, according to Admiral Fitzroy’s chart, is about 60°. But he assigns far too high a temperature for latitudes above 50°. It is probable that 56° is not far from the truth.
24 The probable physical cause of this will be considered in the Appendix.
25 The mean temperature of the equator, according to Dove, is 79°·7, and that of the north pole 2°·3. But as there is, of course, some uncertainty regarding the actual mean temperature of the poles, we may take the difference in round numbers at 80°.
26 Trans. of Roy. Soc. Edin., vol. xxii., p. 75.
27 Connaissance des Temps for 1863 (Additions). Lagrange’s determination makes the superior limit 0·07641 (Memoirs of the Berlin Academy for 1782, p. 273). Recently the laborious task of re-investigating the whole subject of the secular variations of the elements of the planetary orbits was undertaken by Mr. Stockwell, of the United States. He has taken into account the disturbing influence of the planet Neptune, the existence of which was not known when Leverrier’s computations were made; and he finds that the eccentricity of the earth’s orbit will always be included within the limits of 0 and 0·0693888. Mr. Stockwell’s elaborate Memoir, extending over no fewer than two hundred pages, will be found in the eighteenth volume of the “Smithsonian Contributions to Knowledge.”
28 When the eccentricity is at its superior limit, the absolute quantity of heat received by the earth during the year is, however, about one three-hundredth part greater than at present. But this does not affect the question at issue.
29 Scoresby’s “Arctic Regions,” vol. ii., p. 379. Daniell’s “Meteorology,” vol. ii., p. 123.
30 Tyndall, “On Heat,” article 364.
31 Tyndall, “On Heat,” article 364.
32 See Phil. Mag., March, 1870, p.
[33] Captain Cook’s “Second Voyage,” vol. ii., pp. 232, 235.
34 “Antarctic Regions,” vol. ii., pp. 345−349.
35 Ibid., vol. i., p. 167.
36 Ibid., vol. ii., p. 362.
37 Edinburgh Philosophical Journal, vol. iv., p. 266.
38 Scoresby’s “Arctic Regions,” vol. i., p. 378.
39 Ibid., p. 425.
40 See Meech’s memoir “On the Intensity of the Sun’s Heat and Light,” “Smithsonian Contributions,” vol. ix.
41 “Antarctic Regions,” vol. i., p. 240.
42 Challenger Reports, No. 2, p. 10.
43 See “Smithsonian Contributions,” vol. ix.
44 Quart. Journ. Geol. Soc., vol. xxv., p. 350.
45 Trans. of Glasgow Geol. Soc. for 1866.
46 Revue des Deux Mondes for 1867.
47 Letter to the author, February, 1870.
48 “Révolutions de la Mer,” p. 37 (second edition).
49 Edin. Phil. Journ., vol. iv., p. 262 (1821).
50 Phil. Mag., § 4, vol. xxviii., p. 131. Reader, December 2nd, 1865.
51 This point will be found discussed at considerable length in the Phil. Mag. for September, 1869.
52 See Phil. Mag. for October, 1870, p. 259.
53 Proceedings of the Royal Society, No. 138, p. 596, foot-note.
54 The edition from which I quote, unless the contrary is stated, is the one published by Messrs. T. Nelson and Sons, 1870, which is a reprint of the new edition published in 1859 by Messrs. Sampson Low and Co.
55 “Physical Geography,” article 57.
56 Philosophical Magazine, vol. xii. p. 1 (1838).
57 “Mémoires par divers Savans,” tom. i., p. 318, St. Petersburgh, 1831. See also twelfth number of Meteorological Papers, published by the Board of Trade, 1865, p. 16.
58 Dubuat’s “Hydraulique,” tom. i., p. 64 (1816). See also British Association Report for 1834, pp. 422, 451.
59 See Proceedings of the Royal Society for December, 1868, November, 1869. Lecture delivered at the Royal Institute, Nature, vol. i., p. 490. Proceedings of the Royal Geographical Society, vol. xv.
60 Trans. of Glasgow Geol. Soc. for April, 1867. Phil. Mag. for February, 1867, and June, 1867 (Supplement).
61 Phil. Mag. for February, 1870.
62 “The Depths of the Sea,” pp. 376 and 377.
63 “The Threshold of the Unknown Region,” p. 95.
64 See “Physical Geography of the Sea,” chap. ix., new edition, and Dr. A. Mühry “On Ocean-currents in the Circumpolar Basin of the North Hemisphere.”
65 “Depths of the Sea,” Nature for July 28, 1870.
66 “Memoir on the Gulf-stream,” Geographische Mittheilungen, vol. xvi. (1870).
67 Dr. Carpenter “On the Gulf-stream,” Proceedings of Royal Geographical Society for January 9, 1871, § 29.
68 Dr. Petermann’s Mittheilungen for 1872, p. 315.
69 Proceedings of the Royal Society, vol. xvii., p. 187, xviii., p. 463.
70 The average depth of the Pacific Ocean, as found by the soundings of Captain Belknap, of the U.S. steamer Tuscarora, made during January and February, 1874, is about 2,400 fathoms. The depth of the Atlantic is somewhat less.
71 Proceedings of Royal Geographical Society, vol. xv., § 22.
72 It is a well-established fact that in polar regions the temperature of the sea decreases from the surface downwards; and the German Polar Expedition found that the water in very high latitudes is actually less dense at the surface than at considerable depths, thus proving that the surface-water could not sink in consequence of its greater density.
73 Proceedings of the Royal Society, vol. xix., p. 215.
74 Nature for July 6, 1871.
75 Since the above objection to the Gravitation Theory of the Gibraltar Current was advanced three years ago, Dr. Carpenter appears to have abandoned the theory to a great extent. He now admits (Proceedings of Royal Geographical Society, vol. xviii., pp. 319−334, 1874) that the current is almost wholly due not to difference of specific gravity, but to an excess of evaporation in the Mediterranean over the return by rain and rivers.
76 Proceedings of Royal Society, No. 138, § 26.
77 Proceedings of Royal Geographical Society, January 9, 1871.
78 Ibid.
79 See §§ 20, 34; also Brit. Assoc. Report for 1872, p. 49, and other places.
80 See also to the same effect Brit. Assoc. Report, 1872, p. 50.
81 Phil. Mag. for Oct. 1871.
82 The actual slope, however, does not amount to more than 1 in 7,000,000.
83 Proc. of Roy. Geog. Soc., January 9, 1871, § 29.
84 Trans. of Geol. Soc. of Glasgow for April, 1867; Phil. Mag. for June, 1867.
85 Nature, vol. i., p. 541. Proc. Roy. Soc., vol. xviii., p. 473.
86 Chapter II.
87 Chapter II.
88 Chapter II.
89 Mr. Findlay considers that the daily discharge does not exceed 333 cubic miles (Brit. Assoc. Rep., 1869, p. 160). My estimate makes it 378 cubic miles. Mr. Laughton’s estimate is 630 cubic miles (Paper “On Ocean-currents,” Journal of Royal United-Service Institution, vol. xv.).
90 Proceedings of the Royal Geographical Society, vol. xviii., p. 393.
91 Phil. Mag. for October, 1871, p. 274.
92 Proceedings of the Royal Geographical Society, vol. xv.
93 Phil. Mag., February, 1870.
94 Brit. Assoc. Report, 1869, Sections, p. 160.
95 Journal of Royal United-Service Institute, vol. xv.
96 Dr. Carpenter (Proc. of Roy. Geog. Soc., vol. xviii., p. 334) misapprehends me in supposing that I attribute the Gibraltar current wholly to the Gulf-stream. In the very page from which he derives or could derive his opinion as to my views on the subject (Phil. Mag. for March, 1874, p. 182), I distinctly state that “the excess of evaporation over that of precipitation within the Mediterranean area would of itself produce a considerable current through the Strait.” That the Gibraltar current is due to two causes, (1) the pressure of the Gulf-stream, and (2) excess of evaporation over precipitation in the Mediterranean, has always appeared to me so perfectly obvious, that I never held nor could have held any other opinion on the subject.
97 Paper read to the Edinburgh Botanical Society on January 8, 1874.
98 Proc. Roy. Geog. Soc., vol. xviii., p. 362. A more advantageous section might have been chosen, but this will suffice. The section referred to is shown in Plate III. The peculiarity of this section, as will be observed, is the thinness of the warm strata at the equator, as compared with that of the heated water in the North Atlantic.
99 The temperature of column C in Dr. Carpenter’s section is somewhat less than that given in the foregoing table; so that, according to that section, the difference of level between column C and columns A and B would be greater than my estimate.
100 Captain Nares’s Report, July 30, 1874.
101 See Chapter IV.
102 Phil. Mag. for August, 1864, February, 1867, March, 1870; see Chap. IV.
103 Quarterly Journal of Science for October, 1874.
104 See a paper by M. Morlot, on “The Post-Tertiary and Quaternary Formations of Switzerland.” Edin. New Phil. Journal, New Series, vol. ii., 1855.
105 Edin. New Phil. Journ., New Series, vol. ii., p. 28.
106 Vogt’s “Lectures on Man,” pp. 318−321.
107 See Mr. Prestwich on Flint Implements, Phil. Trans. for 1860 and 1864. Lyell’s “Antiquity of Man,” Second Edition, p. 168.
108 Edin. New Phil. Journ., New Series, vol. ii., p. 28. Silliman’s Journ., vol. xlvii., p. 259 (1844).
109 Quart. Journ. Geol. Soc., vol. xxvii., p. 534.
110 Ibid., vol. xxviii., p. 17.
111 “Glacial Drift of Scotland,” p. 54.
112 “Glacial Drift of Scotland,” p. 58.
113 Quart. Journ. Geol. Soc., vol. v., p. 22.
114 “Glacial Drift of Scotland,” p. 64.
115 Trans. Edin. Geol. Soc., vol. ii., p. 391.
116 Trans. of Geol. Soc. of Glasgow, vol. iv., p. 146.
117 Geol. Mag., vi., p. 391.
118 See “Memoirs of Geological Survey of Scotland,” Explanation of sheet 22, p. 29. See also Trans. Glasgow Geol. Soc., iv., p. 150.
119 “Great Ice Age,” p. 374.
120 “Great Ice Age,” p. 384.
121 “Geological Survey of Ohio, 1869,” p. 165. See also “Great Ice Age,” chap. xxviii.
122 Quart. Journ. Geol. Soc., xxviii., p. 435.
123 Brit. Assoc. Report, 1863.
124 Trans. Glasgow Nat. Hist. Soc., vol. i., p. 115.
125 Trans. of the Geol. Soc. of Glasgow, vol. iii., p. 133. See also “Great Ice Age,” chaps. xii. and xiii.
126 Chap. XXIX.
127 Edin. New Phil. Journ., vol. liv., p. 272.
128 “Newer Pliocene Geology,” p. 129. John Gray & Co., Glasgow.
129 “Glacial Drift of Scotland,” p. 67.
130 “Glacial Drift of Scotland,” p. 12.
131 See Chapter IV.
132 “Discovery of the North-West Passage,” p. 213.
133 “Voyage of the Resolute,” p. 294.
134 Quart. Journ. Geol. Soc., vol. xi., p. 540.
135 “McClure’s North-West Passage,” p. 214. Second Edition.
136 “British Association Report for 1855,” p. 381. “The Last of the Arctic Voyages,” vol. i., p. 381.
137 Mr. James Geikie informs me that the great accumulations of gravel which occur so abundantly in the low grounds of Switzerland, and which are, undoubtedly, merely the re-arranged materials originally brought down from the Alps as till and as moraines by the glaciers during the glacial epoch, rarely or never yield a single scratched or glaciated stone. The action of the rivers escaping from the melting ice has succeeded in obliterating all trace of striæ. It is the same, he says, with the heaps of gravel and sand in the lower grounds of Sweden and Norway, Scotland and Ireland. These deposits are evidently in the first place merely the materials carried down by the swollen rivers that issued from the gradually melting ice-fields and glaciers. The stones of the gravel derived from the demolition of moraines and till, have lost all their striæ and become in most cases well water-worn and rounded.
138 Report on Icebergs, read before the Association of American Geologists, Silliman’s Journal, vol. xliii., p. 163 (1842).
139 “Manual of Geology,” p. 677.
140 Quart. Journ. Geol. Soc., vol. ix., p. 306.
141 Dana’s “Manual of Geology,” p. 677.
142 Quart. Journ. Geol. Soc., vol. ix., p. 306.
143 “Journal,” vol. i., p. 38.
144 “Short American Tramp,” pp. 168, 174.
145 “Short American Tramp,” pp. 239−241.
146 “Travels in North America,” vol. ii., p. 137.
147 Ibid., vol. ii., p. 174.
148 Proceedings of the Royal Society of Edinburgh, Session 1865−66, p. 537.
149 “Short American Tramp,” pp. 77, 81, 111.
150 “Second Visit,” vol. ii., p. 367.
151 “Memoirs of Boston Society of Natural History,” vol. i. (1867), p. 228.
152 “Antiquity of Man,” p. 268. Third Edition.
153 “Great Ice Age,” p. 512.
154 Brit. Assoc., 1870, p. 88.
155 Quart. Journ. Geol. Soc., vol. v., p. 10. Phil. Mag. for April, 1865, p. 289.
156 “Great Ice Age,” p. 512.
157 Jukes’ “Manual of Geology,” p. 421.
158 See also Quarterly Journal Geological Society, vol. xi., p. 510.
159 The Reader for August 12, 1865.
160 “History of the Isle of Man,” p. 86. My colleague, Mr. John Horne, in his “Sketch of the Geology of the Isle of Man,” Trans. of Edin. Geol. Soc., vol. ii., part iii., considers this conglomerate to be of Lower Carboniferous age.
161 See Selwyn, “Phys. Geography and Geology of Victoria.” 1866. pp. 15−16; Taylor and Etheridge, Geol. Survey Vict., Quarter Sheet 13, N.E.
162 Report on the Geology of the District of Ballan, Victoria. 1866. p. 11.
163 Atrypa reticularis.
164 Quart. Journ. Geol. Soc., vol. xii., p. 58.
165 “Great Ice Age,” p. 513.
166 “Great Ice Age,” p. 513.
167 Brit. Assoc. Report for 1873.
168 Quart. Journ. Geol. Soc., vol. xi., p. 519.
169 Orthis resupinata.
170 Prod. semireticulatus var. Martini. Sow.
171 “Belcher’s Voyage,” vol. ii., p. 377.
172 “Journal of a Boat Voyage through Rupert-Land,” vol. ii., p. 208.
173 Quart. Journ. Geol. Soc., vol. xi., p. 197.
174 Explanation Memoir to Sheet 47, “Geological Survey of Ireland.”
175 Phil. Mag., vol. xxix., p. 290.
176 “Memoirs of the Geological Survey of India,” vol. i., part i.
177 Quart. Journ. Geol. Soc., vol. xxvi., p. 514.
178 Ibid., vol. xxvii., p. 544.
179 Phil. Mag., vol. xxix., p. 290.
180 Journal of the Royal Dublin Society for February, 1857.
181 Quart. Journ. Geol. Soc., vol. xi., p. 519.
182 “The Last of the Arctic Voyages,” by Captain Sir E. Belcher, vol. ii., p. 389. Appendix Brit. Assoc. Report for 1855, p. 79.
183 Ibid., vol. ii., p. 379. Appendix.
184 “Manual of Geology,” pp. 395, 493.
185 Appendix to McClintock’s “Arctic Discoveries.”
186 Quart. Journ. Geol. Soc., vol. xiv., p. 262. Brit. Assoc. Report for 1857, p. 62.
187 Quart. Journ. Geol. Soc., vol. xvi., p. 327. Geologist, 1860, p. 38.
188 Phil. Mag., vol. xxix., p. 290.
189 Trans. Geol. Soc. of Glasgow, vol. v., p. 64.
190 “Principles,” vol. i., p. 209. Eleventh Edition.
191 “Memoirs of the Royal Academy of Science of Turin,” Second Series, vol. xx. I am indebted for the above particulars to Professor Ramsay, who visited the spot along with M. Gastaldi.
192 “Antiquity of Man,” Second Edition, p. 237.
193 Dr. Robert Brown, in a recent Memoir on the Miocene Beds of the Disco District (Trans. Geol. Soc. Glasg., vol. v., p. 55), has added considerably to our knowledge of these deposits. He describes the strata in detail, and gives lists of the plant and animal remains discovered by himself and others, and described by Professor Heer. Professor Nordenskjöld has likewise increased the data at our command (Transactions of the Swedish Academy, 1873); and still further evidence in favour of a warm climate having prevailed in Greenland during Miocene times has been obtained by the recent second German polar expedition.
194 The following are M. Leverrier’s formulæ for computing the eccentricity of the earth’s orbit, given in his “Memoir” in the Connaissance des Temps for 1843:—
Eccentricity in (t) years after January 1, 1800 = √h2 + l2 where
h = 0·000526 Sin (gt + ß) + 0·016611 Sin (g1t + ß1) + 0·002366 Sin (g2t + ß2)
+ 0·010622 Sin (g3t + ß3) − 0·018925 Sin (g4t + ß4)
+ 0·011782 Sin (g5t + ß5) − 0·016913 Sin (g6t + ß6)
and
l = 0·000526 Cos (gt + ß) + 0·016611 Cos (g1t + ß1) + 0·002366 Cos (g2t + ß2)
+ 0·010622 Cos (g3t + ß3) − 0·018925 Cos (g4t + ß4)
+ 0·011782 Cos (g5t + ß5) − 0·016913 Cos (g6t + ß6)
| g = 2″·25842 | ß = 126° 43′ 15″ |
| g1 = 3″·71364 | ß1 = 27 21 26 |
| g2 = 22″·4273 | ß2 = 126 44 8 |
| g3 = 5″·2989 | ß3 = 85 47 45 |
| g4 = 7″·5747 | ß4 = 35 38 43 |
| g5 = 17″·1527 | ß5 = −25 11 33 |
| g6 = 17″·8633 | ß6 = −45 28 59 |
195 See Professor C. V. Zenger’s paper “On the Periodic Change cf Climate caused by the Moon,” Phil. Mag. for June, 1868.
196 Phil. Mag. for February, 1867.
197 Phil. Mag. for May, 1868.
198 Student’s “Elements of Geology,” p. 91. Second Edition.
199 In an interesting memoir, published in the Phil. Mag. for 1850, Mr. Alfred Tylor estimated that the basin of the Mississippi is being lowered at the rate of one foot in 10,000 years by the removal of the sediment; and he proceeds further, and reasons that one foot removed off the general surface of the land during that period would raise the sea-level three inches. Had it not been that Mr. Tylor’s attention was directed to the effects produced by the removal of sediment in raising the level of the ocean rather than in lowering the level of the land, he could not have failed to perceive that he was in possession of a key to unfold the mystery of geological time.
200 Proc. Roy. Soc., No. 152, 1874.
201 I have taken for the volume and mass of the sun the values given in Professor Sir William Thomson’s memoir, Phil. Mag., vol. viii. (1854).
202 Phil. Mag., § 4, vol. xi., p. 516 (1856).
203 Phil. Mag. for July, 1872, p. 1.
204 “Principles,” p. 210. Eleventh Edition.
205 “Principles,” vol. i., p. 107. Tenth Edition.
206 The conception of submergence resulting from displacement of the earth’s centre of gravity, caused by a heaping up of ice at one of the poles, was first advanced by M. Adhémar, in his work “Révolutions de la Mer,” 1842. When the views stated in this chapter appeared in the Reader, I was not aware that M. Adhémar had written on the subject. An account of his mode of viewing the question is given in the Appendix.
207 Petermann’s Geog. Mittheilungen, 1871, Heft. x., p. 377.
208 Geol. Mag., 1872, vol. ix., p. 360.
209 “Open Polar Sea,” p. 134.
210 Journal of the Royal Geographical Society, 1853, vol. xxiii.
211 “Physics of Arctic Ice,” Quart. Journ. Geol. Soc. for February, 1871.
212 Some writers have objected to the conclusion that the antarctic ice-cap is thickest at the pole, on the ground that the snowfall there is probably less than at lower latitudes. The fact is, however, overlooked, that the greater thickness of an ice-cap at its centre is a physical necessity not depending on the rate of snowfall. Supposing the snowfall to be greater at, say, lat. 70° than at 80°, and greater at 80° than at the pole; nevertheless, the ice will continue to accumulate till it is thicker at 80° than at 70°, and at the pole than it is at 80°.
213 It is a pity that at present no record is kept, either by the Board of Trade or by the Admiralty, of remarkable icebergs which may from time to time be met with. Such a record might be of little importance to navigation, but it would certainly be of great service to science.
214 See Chapter XXVII., and also Geol. Mag. for May and June, 1870, and January, 1871.
215 Phil. Mag. for April, 1866, p. 323.
216 Ibid., for March, 1866, p. 172.
217 Reader, February 10, 1866.
218 In a former paper I considered the effects of another cause, viz., the melting of polar ice resulting from an increase of the Obliquity of the Earth’s Orbit.—Trans. Glasgow Geol. Soc., vol. ii., p. 177. Phil. Mag., June, 1867. See also Chapter XXV.
219 Phil. Mag. for November, 1868, p. 376.
220 Phil. Mag., November, 1868.
221 “Origin of Species,” chap. xi. Fifth Edition.
222 Lieutenant-Colonel Drayson (“Last Glacial Epoch of Geology”) and also Mr. Belt (Quart. Journ. of Science, October, 1874) state that Leverrier has lately investigated the question as to the extent of the variation of the plane of the ecliptic, and has arrived at results differing considerably from those of Laplace; viz., that the variation may amount to 4° 52′, whereas, according to Laplace, it amounts to only 1° 21′. I fear they are comparing things that are totally different; viz., the variation of the plane of the ecliptic in relation to its mean position with its variation in relation to the equator. Laplace estimated that the plane of the ecliptic would oscillate to the extent of 4° 53′ 33″ on each side of its mean position, a result almost identical with that of Leverrier, who makes it 4° 51′ 42″. But neither of these geometricians ever imagined that the ecliptic could change in relation to the equator to even one-third of that amount.
Laplace demonstrated that the change in the plane of the ecliptic affected the position of the equator, causing it to vary along with it, so that the equator could never possibly recede further than 1° 22′ 34″ from its mean position in relation to the ecliptic (“Mécanique Céleste,” vol. ii., p. 856, Bowditch’s Translation; see also Laplace’s memoir, “Sur les Variations de l’Obliquité de l’Écliptique,” Connaissance des Temps for 1827, p. 234), and I am not aware that Leverrier has arrived at a different conclusion.
223 Memoir on the Secular Variations of the Elements of the Orbits of the Planets, “Smithsonian Contributions to Knowledge,” vol. xvii.
224 “Smithsonian Contributions to Knowledge,” vol. ix.
225 “Distribution of Heat on the Surface of the Globe,” p. 14.
226 Chapter IV.
227 Quart. Journ. Geol. Soc., June, 1866, p. 564.
228 Quart. Journ. Geol. Soc., vol. xxi., p. 186.
229 “Geological Observer,” p. 446. See also Mr. James Geikie’s valuable Memoir, “On the Buried Forests and Peat Mosses of Scotland.” Trans. of the Royal Society of Edinburgh, vol. xxiv., and Chambers’ “Ancient Sea-Margins.”
230 See Lyell’s “Antiquity of Man,” Second Edition, p. 282; “Elements,” Sixth Edition, p. 162.
231 In order to determine the position of the solstice-point in relation to the aphelion, it will not do to assume, as is commonly done, that the point makes a revolution from aphelion to aphelion in any regular given period, such as 21,000 years; for it is perfectly evident that owing to the great irregularity in the motion of the aphelion, no two revolutions will probably be performed in the same length of period. For example, the winter solstice was in the aphelion about the following dates: 11,700, 33,300, and 61,300 years ago. Here are two consecutive revolutions, the one performed in 21,600 years and the other in 28,000 years; the difference in the length of the two periods amounting to no fewer than 6,400 years.
232 Quart. Journ. Geol. Soc., vol. xxvii., p. 232. See also “The Last Glacial Epoch of Geology,” by the same author.
233 Quart. Journ. of Science, October, 1874.
234 The longer diameter passes from long. 14° 23′ E. to long. 165° 37′ W.
235 “Principles,” vol. i., p. 294. Eleventh Edition.
236 Phil. Mag. for August, 1864.
237 “Elementary Geology,” p. 399.
238 “The Past and Present Life of the Globe,” p. 102.
239 “Memoirs of the Geological Survey,” vol. ii., Part 2, p. 404.
240 “Coal Fields of Great Britain,” p. 45. Third Edition.
241 “Journal of Researches,” chap. xiii.
242 “Coal Fields of Great Britain,” p. 67.
243 See “Smithsonian Report for 1857,” p. 138.
244 Quart. Journ. Geol. Soc., May, 1865, p. civ.
245 “Geology of Fife and the Lothians,” p. 116.
246 “Life on the Earth,” p. 133.
247 Quart. Journ. Geol. Soc., vol. xi., p. 535.
248 Ibid., vol. xii., p. 39.
249 Miller’s “Sketch Book of Practical Geology,” p. 192.
250 From Geological Magazine, May and June, 1870; with a few verbal corrections, and a slight re-arrangement of the paragraphs.
251 See Phil. Mag. for November, 1868, p. 374.
252 See Phil. Mag. for November, 1868, pp. 366−374.
253 Journ. Geol. Soc., vol. xxi., p. 165.
254 Specimens of the striated summit and boulder clay stones are to be seen in the Edinburgh Museum of Science and Art.
[255] Phil. Mag. for April, 1866.
256 “Tracings of the North of Europe,” 1850, pp. 48−51.
257 Quart. Journ. Geol. Soc., vol. ii., p. 364.
258 “Tracings of the North of Europe,” by Robert Chambers, pp. 259, 285. “Observations sur les Phénomènes d’Erosion en Norvège,” by M. Hörbye, 1857. See also Professor Erdmann’s “Formations Quaternaires de la Suède.”
259 “Glacial Drift of Scotland,” p. 29.
260 Geological Magazine, vol. ii., p. 343. Brit. Assoc. Rep., 1864 (sections), p. 59.
261 Trans. Roy. Soc. Edin., vol. vii., p. 265.
262 “Tracings of Iceland and the Faroe Islands,” p. 49.
263 See Chap. XXIII.
264 Mr. Thomas Belt has subsequently advanced (Quart. Jour. Geol. Soc., vol. xxx., p. 490), a similar explanation of the steppes of Siberia. He supposes that an overflow of ice from the polar basin dammed back all the rivers flowing northward, and formed an immense lake which extended over the lowlands of Siberia, and deposited the great beds of sand and silt with occasional freshwater shells and elephant remains, of which the steppes consist.
265 Proc. Roy. Phys. Soc., Edin., vols. ii. and iii.
266 From Geol. Mag. for January, 1871.
267 Quart. Journ. Geol. Soc., xxvi., p. 517.
268 British Assoc. Report for 1864 (sections), p. 65.
269 Quart. Journ. Geol. Soc., xxvi., p. 90.
270 Geol. Mag., vii., p. 349.
271 Trans. Edin. Geol. Soc., vol. i., p. 136.
272 Geol. Mag. for June, 1870. See Chap. XXVII.
273 This was done by Mr. R. H. Tiddeman of the Geological Survey of England (Quart. Journ. Geol. Soc. for November, 1872), and the result established the correctness of the above opinion as to the existence of a North of England ice-sheet. Additional confirmation has been derived from the important observations of Mr. D. Mackintosh, and also of Mr. Goodchild, of the Geological Survey of England.
274 Trans. Geol. Soc., vol. v., p. 516 (first series).
275 Quart. Journ. Geol. Soc., vol. xi., p. 492. “Memoir of the Country around Cheltenham,” 1857. “Geology of the Country around Woodstock,” 1859.
276 Geol. Mag., vol. vii., p. 497.
277 Quart. Journ. Geol. Soc., vol. xxvi., p. 90.
278 My colleague, Mr. R. L. Jack.
279 The greater portion of this chapter is from the Trans. of Geol. Soc. of Edinburgh, for 1869.
280 Chapter XV., p. 253.
281 Trans. of the Geol. Soc. of Glasgow, vol. iii., part i., page 133.
282 Mr. Milne Home has advanced, in his “Estuary of the Firth of Forth,” p. 91, the theory that this trough had been scooped out during the glacial epoch by icebergs floating through the Midland valley from west to east when it was submerged. The bottom of the trough, be it observed, at the watershed at Kilsyth, is 300 feet above the level of its bottom at Grangemouth; and this Mr. Milne Home freely admits. But he has not explained how an iceberg, which could float across the shallow water at Kilsyth, say, 100 feet deep, could manage to grind the rocky bottom at Grangemouth, where it was not less than 400 feet deep. “The impetus acquired in the Kyle at Kilsyth,” says Mr. Milne Home, “would keep them moving on, and the prevailing westerly winds would also aid, so that when grating on the subjacent carboniferous rocks they would not have much difficulty in scooping out a channel both wider and deeper than at Kilsyth.” But how could they “grate on the subjacent carboniferous rocks” at Grangemouth, if they managed to float at Kilsyth? Surely an iceberg that could “grate” at Grangemouth would “ground” at Kilsyth.
283 Trans. of the Geol. Soc. of Glasgow, vol. iii., p. 141.
284 Mr. John Young and Mr. Milne Home advanced the objection, that several trap dykes cross the valley of the Clyde near Bowling, and come to so near the present surface of the land, that the Clyde at present flows across them with a depth not exceeding 20 feet. I fear that Mr. Young and Mr. Milne Home have been misinformed in regard to the existence of these dykes. About a mile above Bowling there are one or two dykes which approach to the river-bank, and may probably cross, but these could not possibly cut off a channel entering the Clyde at Bowling. In none of the borings or excavations which have been made by the Clyde Trustees has the rock been reached from Bowling downwards. I may also state that the whole Midland valley, from the Forth of Clyde to the Firth of Forth, has been surveyed by the officers of the Geological Survey, and only a single dyke has been found to cross the buried channels, viz., one (Basalt rock) running eastward from Kilsyth to the canal bridge near Dullatur. But as this is not far from the watershed between the two channels it cannot affect the question at issue. See sheet 31 of Geological Survey Map of Scotland.
285 Trans. Geol. Soc. Glasgow, vol. iv., p. 166.
286 “Great Ice Age,” chap. xiii.
287 See further particulars in Mr. Bennie’s paper on the Surface Geology of the district around Glasgow, Trans. Geol. Soc. of Glasgow, vol. iii.
288 See also Smith’s “Newer Pliocene Geology,” p. 139.
289 British Association Report for 1863, p. 89. Geologist for 1863, p. 384.
290 See Geological Magazine, vol. ii., p. 38.
291 Proc. Geol. Soc., vol. iii., 1840, p. 342.
292 “Antiquity of Man” (Third Edition), p. 249.
293 “Glacial Drift of Scotland,” p. 65. Trans. Geol. Soc. Glas., vol. i., part 2.
294 “Memoir, Geological Survey of Scotland,” Sheet 23, p. 42.
295 Mr. Robert Dick had previously described, in the Trans. Geol. Soc. Edinburgh, vol. i., p. 345, portions of these buried channels. He seems, however, to have thought that they formed part of one and the same channel.
296 A description of this channel was read to the Natural History Society of Glasgow by Mr. James Coutts, the particulars of which will appear in the Transactions of the Society.
297 “Occasional Papers,” pp. 166, 223.
298 Memoir read before the Royal Society, January 7, 1869.
299 “Alpine Journal,” February, 1870.
300 Phil. Mag., January, 1872.
301 Phil. Mag., July, 1870; February, 1871.
302 Philosophical Magazine for January, 1870, p. 8; Proceedings of the Royal Society for January, 1869.
303 Philosophical Magazine for March, 1869.
304 Proceedings of Bristol Naturalists’ Society, p. 37 (1869).
305 Ibid., vol. iv., p. 37 (new series).
306 Phil. Mag., S. 4, vol. x., p. 303.
307 Proceedings of the Bristol Naturalists’ Society, vol. iv., p. 39 (new series).
308 See Philosophical Transactions, December, 1857.
309 There is one circumstance tending slightly to prevent the rupture of the glacier, when under tension, which I do not remember to have seen noticed; that is, the cooling effect which is produced in solids, such as ice, when subjected to tension. Tension would tend to lower the temperature of the ice-molecules, and this lowering of temperature would have the tendency of freezing them more firmly together. The cause of this cooling effect will be explained in the Appendix.
310 Phil. Mag., March, 1869; September, 1870.
311 “Forms of Water,” p. 127.
312 See text, p. 10.
313 Mathematical and Physical Series, vol. xxxvi. (1765).
314 “Memoirs of St. Petersburg Academy,” 1761.
315 The calculations here referred to were made by Lagrange nearly half a century previous to the appearance of this paper, and published in the “Mémoires de l’Académie de Berlin,” for 1782, p. 273. Lagrange’s results differ but slightly from those afterwards obtained by Leverrier, as will be seen from the following table; but as he had assigned erroneous values to the masses of the smaller planets, particularly that of Venus, the mass of which he estimated at one-half more than its true value, full confidence could not be placed in his results.
Superior limits of eccentricity as determined by Lagrange, Leverrier,and Mr. Stockwell:—
| By Lagrange. | By Leverrier. | By Mr. Stockwell. | |
|---|---|---|---|
| Mercury | 0·22208 | 0·225646 | 0·2317185 |
| Venus | 0·08271 | 0·086716 | 0·0706329 |
| Earth | 0·07641 | 0·077747 | 0·0693888 |
| Mars | 0·14726 | 0·142243 | 0·139655 |
| Jupiter | 0·06036 | 0·061548 | 0·0608274 |
| Saturn | 0·08408 | 0·084919 | 0·0843289 |
| Uranus | — | 0·064666 | 0·0779652 |
| Neptune | — | — | 0·0145066 |
[J. C.]
316 “Mém. de l’Acad. royale des Sciences.” 1827. Tom. vii., p. 598.
317 Absolute zero is now considered to be only 493° Fah. below the freezing-point, and Herschel himself has lately determined 271° below the freezing-point to be the temperature of space. Consequently, a decrease, or an increase of one per cent. in the mean annual amount of radiation would not produce anything like the effect which is here supposed. But the mean annual amount of heat received cannot vary much more than one-tenth part of one per cent. In short, the effect of eccentricity on the mean annual supply of heat received from the sun, in so far as geological climate is concerned, may be practically disregarded.—[J. C.]
318 “Principles of Geology,” p. 110. “Mr. Lyell, however, in stating the actual excess of eight days in the duration of the sun’s presence in the northern hemisphere over that in the southern as productive of an excess of light and heat annually received by the one over the other hemisphere, appears to have misconceived the effect of elliptic motion in the passage here cited, since it is demonstrable that whatever be the ellipticity of the earth’s orbit the two hemispheres must receive equal absolute quantities of light and heat per annum, the proximity of the sun in perigee exactly compensating the effect of its swifter motion. This follows from a very simple theorem, which may be thus stated: ‘The amount of heat received by the earth from the sun while describing any part of its orbit is proportional to the angle described round the sun’s centre,’ so that if the orbit be divided into two portions by a line drawn in any direction through the sun’s centre, the heats received in describing the two unequal segments of the ellipse so produced will be equal.”
319 When the eccentricity of the earth’s orbit is at its superior limit, the absolute quantity of heat received by the globe during one year will be increased by only 1/300th part; an amount which could produce no sensible influence on climate.—[J. C.]
320 Sir Charles has recently, to a certain extent, adopted the views advocated in the present volume, viz., that the cold of the glacial epoch was brought about not by a decrease, but by an increase of eccentricity. (See vol. i. of “Principles,” tenth and eleventh editions.) The decrease in the mean annual quantity of heat received from the sun, resulting from the decrease in the eccentricity of the earth’s orbit—the astronomical cause to which he here refers—could have produced no sensible effect on climate.—[J. C.]
321 It is singular that both Arago and Humboldt should appear to have been unaware of the researches of Lagrange on this subject.
322 “Révolutions de la Mer,” p. 37. Second Edition.
323 See text, p. 37.
324 See Philosophical Magazine for December, 1867, p. 457.
325 Silliman’s American Journal for July, 1864. Philosophical Magazine for September, 1864, pp. 193, 196.
326 Philosophical Magazine for August, 1865, p. 95.
327 See text, p. 80.
328 See text, p. 222.
329 Proc. Roy. Soc., No. 157, 1875.
330 See text, p. 522.
331 Phil. Trans. for 1859, p. 91.
332 See text, p. 527.