Account of the Skerryvore Lighthouse

Appendix .

APPENDIX, No. I.
TABLE OF CO-ORDINATES OF AN HYPERBOLIC COLUMN WHOSE DIAMETER AT THE TOP = 16 FEET, AT THE BASE = 42 FEET, AND HEIGHT = 120·25 FEET.

The column is generated by the revolution of a rectangular hyperbola about one of its asymptotes. In the annexed figure (No. 98), a f is the height of the column, a c and f h the radii of its base and top; and we have to determine the particular hyperbola which will pass through the points c, h.

Putting b e = x; e g = y, the equation to the curve, referred to its asymptotes, is

x y = a²2,

in which the value of the constant a² 2 is to be found. For this purpose we have the conditions a c = 21; f h = 8; and a f = 120·25. Let the co-ordinates of the point c be x′, y′, and of h, x″, y″, then y′ = 21; y″ = 8; x″ = x′ + 120·25.

Fig. 98.

Hyperbola

And since	x′ y′ = a²2 = x″ y″
we have	21 x′ = 8 (x′ + 120·25)
from which	x′ = 74
and	a²2 = x′ y′ = 74 × 21 = 1554.
Therefore	x y = 1554.

Transferring the origin to a, x becomes x - x′ = x - 74, and y (x - 74) = 1554, and the required equation by which the following Table was computed is, y = 1554 x - 74.

Table of the Radii of the Hyperbolic Column at each foot of its Height.

Height.	Radius.	Height.	Radius.	Height.	Radius.	Height.	Radius.
0	21·000	31	14·800	62	11·426	93	9·305
1	20·720	32	14·660	63	11·343	94	9·250
2	20·447	33	14·523	64	11·261	95	9·195
3	20·182	34	14·389	65	11·180	96	9·141
4	19·923	35	14·257	66	11·100	97	9·088
5	19·671	36	14·127	67	11·021	98	9·035
6	19·425	37	14·000	68	10·944	99	8·983
7	19·185	38	13·875	69	10·867	100	8·931
8	18·951	39	13·752	70	10·792	101	8·880
9	18·723	40	13·632	71	10·717	102	8·830
10	18·500	41	13·513	72	10·644	103	8·780
11	18·282	42	13·397	73	10·571	104	8·730
12	18·070	43	13·282	74	10·500	105	8·681
13	17·862	44	13·170	75	10·430	106	8·633
14	17·659	45	13·059	76	10·360	107	8·586
15	17·461	46	12·950	77	10·291	108	8·539
16	17·267	47	12·843	78	10·224	109	8·492
17	17·077	48	12·738	79	10·157	110	8·446
18	16·891	49	12·634	80	10·091	111	8·400
19	16·710	50	12·532	81	10·026	112	8·355
20	16·532	51	12·432	82	9·962	113	8·310
21	16·358	52	12·333	83	9·898	114	8·266
22	16·188	53	12·236	84	9·835	115	8·222
23	16·021	54	12·141	85	9·774	116	8·179
24	15·857	55	12·046	86	9·712	117	8·136
25	15·697	56	11·954	87	9·652	118	8·094
26	15·540	57	11·862	88	9·593	119	8·052
27	15·386	58	11·773	89	9·534	120	8·010
28	15·235	59	11·684	90	9·476	120·25	8·000
29	15·087	60	11·597	91	9·418	...	...
30	14·942	61	11·511	92	9·361	...	...

APPENDIX, No. II.
NOTES ON THE MANUFACTURE OF PARABOLOÏDAL REFLECTORS,
from Information furnished by Mr James Murdoch, of the Northern Lights Service.

Fig. 99.

Mallet

The reflector-plate consists of virgin-silver and the purest copper (from the ingot), in the proportion of 6 oz. of silver to 16 oz. of copper. The two metals are in pieces, forming a flat parallelopepid of about nine inches of surface. Being first thoroughly scraped and cleared from rust with a file, they are tied together with wire and placed in the furnace, where they are united by means of a flux composed of burnt borax and nitre, mixed to the consistence of cream. Their thickness is sufficient to admit of their being repeatedly passed through the rolling-mill, so as at last to come out a plate twenty-eight inches square. Every time it is passed through the rollers, the plate is annealed in the furnace before being again pressed. It is then cut into a circular disc ready for working; and great care should be taken to keep the metal perfectly clean during the whole of the hammering and polishing processes. The first step towards forming the plate to the curve, is to raise the back or copper side to a slight convexity by beating, with the boxwood mallet (fig. 99), rounded at each end, c and d, its inner or silver side upon a large block of beechwood, of a form slightly concave. This beating is begun at the edge of the plate, and gradually reaches the centre. After the disc has been raised to the proper height on the wooden block, the next step is to take it to the horse (fig. 103, opposite page), where it is beaten with the wooden mallet (fig. 100), its concave face being in contact with the bright steel-head a (fig. 103), until it has nearly reached the proper height for the reflector, for which the workman has a gauge or mould to guide him; in this course of raising, as it is called, the peened face b a b (fig. 100) is first used, and then recourse is had to the opposite or flat face for smoothing it after being raised. In this last course of raising, as well as in the process of smoothing the reflector all over, the workman bestrides the horse.

Fig. 100.

Mallet

Fig. 101.

Mould

During the process of raising with the peened side of the mallet, an external mould FGHF (fig. 101), with a needle-point P, at its vertex, is applied, to indicate its proper position with reference to the mould; and allowance is made on the height and diameter of the reflector to meet the expansion of the metal during the hard-hammering which is to follow. After each course of the raising with the wooden mallets, the reflector must be annealed in the following manner:—The reflector is first damped with clean water, and its surface dusted over with a powder, composed of one pint of powdered charcoal to one ounce of saltpetre, which is applied by means of a thin flannel bag. The reflector is then put on a clear charcoal fire, where it is turned round as the powder flies off, which is an indication that the metal is duly heated. Over-heating is very injurious. When removed from the fire, the reflector is plunged into a large tub, containing what is called the pickle, which is a solution of one quart of vitriol in five or six gallons of water. After this it is washed with clean water, and scoured with Calais sand.

The next step is to put the reflector, thus raised nearly to its true form, into an iron stool, where a small hole being drilled in its vertex, a circle is described from this point with a beam-compass, so as to cut the paraboloïd to the proposed size.

Fig. 102.

Planishing hammer

Fig. 103.

Planishing a mirror

Fig. 104.

Lighter hammer

Fig. 105.

Checking shape of lens

The reflector is next hard-hammered all over (or planished, as it is technically termed) on the bright steel-head a (fig. 103), with the planishing hammer (fig. 102); and to facilitate working, the reflector is slung in a flexible frame SS, and counterbalanced by a weight w, hanging by a cord over the pulleys p p. When the reflector is all planished over, the next process is the smoothing, which is done on the steel-head a, with a lighter hammer (fig. 104 ), muffled with fine parchment at each end. After it is smoothed comes the finishing, or what is called the filling up to the mould. This is a tedious process, and the workman requires continually to have recourse to the marble table at M, on which he lays the reflector, as shewn in fig. 105, and applies to successive portions of its surface the mould g n, which has a needle-point centred at n, in the small hole drilled in the vertex. During this examination, he marks with a fine slate-pencil those portions of the reflector which do not meet the mould g n. The parts, so marked, are gently gone over with the muffled hammer, until every point touches the mould. This last process requires great caution; for, if any part of the surface be raised above the gauge, it is hardly possible to remedy it. Such a mistake, indeed, can only be corrected by annealing the reflector afresh, and bringing it back to the true form with the mallet; but reflectors so cobbled are never good. The table M (fig. 105) rests on a square box C, in which the tools and moulds are kept.

Fig. 106.

Apparatus to adjust burner

When thus finished from the hammer, the reflector is put into the apparatus shewn in fig. 106, which is placed at the end of a long dark corridor. RR is a wooden frame fixed to the wall with projecting brackets at K, which carry the reflector, fixed at E, E, by means of screws, so as always to have a definite position with reference to the bracket B, which carries the lamp and its fountain f, so arranged that its flame may admit of perfect adjustment to the point which ought to be the focus of the reflector. For the purpose of this adjustment, S shews screws for raising and depressing the level of the burner; and the lines or marks M, M′ shewn at the sockets J being brought into line, regulate the position of the burner in the plane of the focus, after it has been raised to the level of that plane by means of the screws at S. The lamp being lighted and thus properly placed, its effect on the reflector’s surface is observed by some one stationed at a convenient distance; and if the whole surface appear luminous, the instrument is considered fit for polishing; but if any dark spaces be found in it, the whole reflector must be again carefully tested by means of the mould, and the defective parts remedied in the manner above described.

The next step is to turn over the edge of the reflector, so as to stiffen it. For this purpose it is placed in the matrix P′P′ (fig. 107), and the needle-point at V is adjusted by the screw at D, so as just to enter the small hole formerly drilled in the vertex of the reflector. The die-plate PP (which is worked by means of the arms AA, which turn the screw S) then descends and presses the edge over, which is finished with a finely polished tool C, revolving round the axis of the instrument, which coincides with the centre of the matrix and die. In order to ensure a steady vertical movement of the die-plate PP, cross-arms FF, which are provided with sockets HH, which slide over the rods GG, GG, are added to prevent any lateral shake or derangement. The whole frame is stiffened by the cross-head in which the screw S works.

Fig. 107.

Matrix for edge stiffening

Fig. 108.

Cast-iron polishing table

Fig. 109.

Cast-iron polishing table

The reflector is then placed on the circular cast-iron table (figs. 108, 109), to which it is attached by the clamp-screws S, S. In this position, the bizzle W (fig. 108) and back-belt NAN (fig. 109), are soldered on. After this the reflector is ready for being finally polished; for which purpose, it is placed in a chaise percée, padded round the edges, and is first scoured all over with a piece of pure charcoal of hard wood, and next with a mixture of Florence oil and finely washed rottenstone, applied by means of a large ball of superfine cloth. It is then carefully cleansed with a piece of fine flannel dipped in Florence oil, and afterwards dusted over with the powder of well washed whiting, and wiped out with a soft cotton cloth. Lastly, it is carefully rubbed by the naked hand, with finely washed rouge and clean water, and wiped with a smooth chamois skin. In all the polishing and cleansing processes, some skill in manipulation is required, as the hand is generally moved in such a manner as to describe successive circles with their planes parallel to the lips of the reflector, and their centres in the axis of the generating curve.

The prices paid to the workmen for the various departments of the reflector-making are generally as follows:—

Raising the plate to the curve, with the wooden mallet,	L.0	10	0
Hammering and smoothing to the mould,	1	5	0
Finishing in the die, and putting on bizzle and back-belt,	0	6	0
Polishing,	0	12	0
	L.2	13	0

The prices paid to the manufacturer were for the large reflectors of 24 inches aperture, L.43; for the small ones of 21 inches, L.31, 12s. The lamp with the sliding-carriage, required for each, costs L.6.

APPENDIX, No. III.
NOTES ON THE GRINDING OF THE VARIOUS PIECES COMPOSING THE INSTRUMENTS USED IN DIOPTRIC LIGHTHOUSES, CHIEFLY FROM NOTES FURNISHED BY M. THEODORE LETOURNEAU OF PARIS.

The glass used in all the parts of the optical apparatus of the dioptric Lighthouses is that of St Gobain, whose index of refraction is 1·51.

As well on account of the difficulty experienced in producing at all times regular castings of glass from the moulds, as in order to compensate for the frequent accidents, which occur in the first application of the rubbers to the inequalities of the surface of the glass, the castings, whether for rings of lenses or prisms, are made from moulds, exceeding the intended size of the finished pieces by one-eighth part.

We shall take as an example, which is well calculated to illustrate the difficulties of the grinding process, one of the prismatic rings of a Catadioptric Light of the first order. The first operation will be to take off the rough arris at the angles of the pieces as they come from the moulds, and to reduce to equality the length of each of the four quadrantal prisms or segments by removing from each the quantity that may be necessary to make those four pieces, when placed on a circle, exactly equal to that of the finished zones. Each of them must have an excess of material at the various surfaces just sufficient to insure the rubber having scope enough to remove all the flaws or defects of the two surfaces to be first ground, which are the (concave and convex) refracting faces of the zone (the sides AC and BC in the Table in the Appendix, No. IV.)

Fig. 110.

Lens pieces on lathe table

The pieces must be placed end to end on the horizontal plane or table of the lathe at AA (fig. 110), and must rest on the exterior arris A of the reflecting side, on which arris there is ground a narrow plane whose width is proportionate to the projection of the outer edge beyond the inner edge of the zone, foreshortened by the bevel or inclination of the reflecting side, when resting (as in fig. 110) on the circular iron belt, which is screwed to the table of the lathe provided for its reception. This narrow plane at the arris A should be sufficient to give the prism a solid and regular bearing on the circular iron belt. In this figure (fig. 110) a b is the vertical axis of the lathe, n the point from which the co-ordinates for O, the grinding centre for the exterior concave refracting surface AC, are measured, and e AC the arc swept by the grinding surface. Conversely, n′ is the origin of the co-ordinates for the grinding centre O of the interior convex refracting surface BC, and e CB the arc swept by its grinding surface. Some skill is required in fixing the prism on the belt, for, on the one hand, there is an obstacle to correct workmanship from the dragging motion of the platform, and, on the other, by the unequal subdivision of the weight of the glass, which should be nearly balanced. This narrow plane being perfectly adjusted for all the segments so as to bed them quite level, the circular iron belt on which the ring should be ground, is placed on its platform, in the manner represented in the figure. It should be as truly levelled as possible, otherwise all the subsequent operations will be deranged by it. This iron belt is heated by means of heating pans; and the degree of heat may be practically judged of by the ebullition of drops of water let fall on it. The segments of glass are also at the same time placed in a stove heated with steam, and are generally raised to about 120° centigrade. The difference between the time required for the two operations of heating the iron belt and the glass segments is employed in laying or bedding a quantity of cement on the reflecting side of the segment, so as to fill up the angular space between the glass and the iron belt, and also to serve as a seat for the segment in the manner shewn in fig. 110. This operation is performed on a plane surface, in order that the lower part of the mastic may be precisely on a level with the narrow plane already ground on the outer arris of the reflecting side. After being sure that the heat is equally spread over every part of the circular iron belt, the segment is arranged on it; and the workman must, at this juncture, exert all his skill in placing the parts of the segment in a position nearly concentric with the belt, or in a truly circular form, making due allowance, however, for the inequalities existing at various parts of the rough material, and at the same time taking care that there should be an interval of at least two millimètres (or about ¹⁄₁₂th inch) between the ends of each of the two adjacent segments. Without this interval the heat evolved during the polishing would either dilate the glass so much as to cause the ends of the segments to fly into splinters, or make it needful to remove the zone before this should take place, the inevitable consequence of which would be the fracture of the pieces. Those intervals between the segments are filled with statuary’s plaster, which must be carefully washed and brushed at each change of the emery employed in grinding.

The exterior diameter of the circular iron belt must be precisely equal to that of the ring, because, if larger, the free movement of the rubbers to and fro on the concave refracting surface AC (fig. 110) could not take place.

By what is already said, it will be obvious that the grinding process is begun at the refracting sides AC and BC, and a few words will shew that this could hardly be otherwise. If a commencement be made on the reflecting side, which appears at first sight more natural, the consequence is obvious. Having provided for an excess of material in every direction, the segment must consequently be larger than it will be when finished; and the surfaces therefore cannot be true and perfect, except they be ground throughout their entire segmental section, from their centres of curvature, in reference to some given apex of the generating triangle. Now, if the reflecting side were finished first, it might continue to possess this excess of size after being finished, and would, therefore, afford no accurate starting point for the grinding of the other surfaces; it would also present no surface or narrow plane for resting firmly on the iron belt, but would then depend merely on its own finished plane, which, being curved and considerably inclined, would not give a solid bearing for the glass. The other mode of commencing with the two refracting sides, on the contrary, gives a solid bearing on the narrow plane already ground on the reflecting side at A; and after these surfaces have been ground, and the segments inverted (as shewn in fig. 111), the outer edge of this narrow plane at the arris A, which has been fully defined by the intersection of the finished surface AC just ground, and also the apex at C, which has been determined by the intersection of AC and BC, combine to fix an accurate starting point for the rubber, in grinding the reflecting surface AB.

Fig. 111.

Inverted ring segment

Dressing off the rough part of the Ring.

The ring is generally reduced from the rough state by means of fixed rubbers, the adjustment of which is more easily regulated than that of the moveable beam or radius of the arc, which is used to give the exact curvature of the surface. Those fixed rubbers are 150 millimètres (nearly 6 inches) wide, by 200 millimètres (nearly 8 inches) long, and are of cast-iron. Three such rubbers are placed at equidistant points of the circle. Two cutters of sheet-iron attached to arms placed vertically (as are also those which carry the rubbers), and moving in grooves radiating towards the centre of the lathe, so as to admit of adjustment to suit the varying radii of the zones, serve gradually to abrade the outer and inner arrises of the segments, so as to prevent the splintering to which, from becoming too sharp, those arrises, without this precaution, would be liable. Those rubbers are, besides, fixed by stems to frames, in the form of quadrants of the circle, which allow of a change in the direction of the planes, as occasion may require.

Instead of the siliceous sand formerly used, the powder of pounded freestone is employed, as it is found to wear the tools less, and to form a better preparation for the subsequent grinding operations. It is easy to conceive that the action of the fixed rubbers necessarily produces ruts or inequalities in the circular direction. The operation of rough dressing, therefore, is not finished until, when those first rubbers are removed, the surfaces of the segments have been subject, for the required time, to the action of moveable rubbers, attached to arms working as radii of curvature, in a plane at right angles to the horizontal movement of the lathe, which carries the zones.

The Emery Grinding.

The form of the segment should be nearly perfect, after the rough grinding is finished. The lathe and the zone are then subjected to an extremely careful washing. Every place where the stone-powder might adhere is dusted. The radius of curvature is verified afresh, agreeably to the co-ordinates (Appendix, No. IV.); and emery is used instead of powdered stone; beginning with that called No. 1, which is drawn after suspension in water for one minute. Brushes are used for spreading the emery on the surface of the glass. The quantity ought always to be sufficient to prevent the direct contact of the cast-iron rubber with the glass. Splintering or scratching, which cannot be easily effaced, may result from the neglect of this precaution.

Practice alone, and an eye duly trained by continual experience, can determine the point of time at which each kind of emery must be discontinued. The celerity of the work depends on circumstances very difficult to appreciate, such as the amount of the pressure of the rubbers, or the degree of accuracy with which the radius of curvature has been adjusted, during the rough grinding. Each kind of emery in succession thus corrects the form of the zone and refines the grain of the surface of the glass; and each change to a fresh material requires the same attention to cleanliness, so as to remove every trace of the substance last used in grinding, and thus to give each successive process its full and legitimate effect. The douci is the fifth and last kind of emery which precedes the polish. It is drawn off after ten minutes’ suspension in water, and is extremely fine. Before applying it, the greatest care is necessary to insure cleanliness, as a single grain of any of the preceding kinds of emery might cause scratches, which the polish cannot remove.

The Polish.

The same considerations which induce the workman most carefully to cleanse the lathe and everything connected with it, before employing the last emery called the douci, are still more urgent in the case of the final polish. The only change which is made at this last stage of the work is to replace the first rubber by a new one, both longer and wider by about 50 millimètres (nearly 2 inches). On its lower face is attached with cement a piece of soft carpet, whose edges are fixed to the rubber by means of flat bands of iron, attached with screws. This security, added to that given by the cement, is necessary to fit it to resist the great pressure it must sustain. A practical question, which experience alone can resolve, occurs at this stage, as the operation of polishing may, in the hands of unskilful persons, be so inopportunely commenced, as to make that work almost endless. Thus, the mere circumstance of spreading at the beginning too thick layers of rouge, or using unsuitable kinds of carpet, would cut scratches in the glass, and thus perhaps make it necessary to return to the use of the emery called douci. Sometimes, also, if the carpets be not washed at the very time of using them, scratches are formed by the dust which they may contain. This shews, that the use of rouge should be rather sparing than otherwise, at the commencement of the polish; and that the carpet-cloths should be brushed and washed twice rather than once. In all cases, the quality of the carpet forms an important element in the success of the working.

When the polish is finished, the ring is detached from the circular belt, simply by the tap of a hammer, on the inner edge of the circle. The division of the zones (which are quarters of the circle) into eighths, is done by means of a sawing machine consisting of a flat copper-wheel, one-half millimètre (¹⁄₅₀th inch) in thickness, attached to an arm with a counterpoise. This wheel descends and cuts the zone by means of emery, which is continually applied to it; the direction of the cut is radial. The two halves of the zone are detached from each other, as soon as their weight exceeds the resistance of the part which remains to be sawn.

Adjustment of the Prisms.

The adjustment of the prisms in the frames, involves an operation which is not without risk. Much care is required in handling the sharp arrises of the glass, which are very acute and delicate and at the same time lie in a curved direction, which makes them liable to be splintered in the hands of unskilful persons.

With the exception of the plane vertical surfaces of the annular lenses, and the central band and rings of the dioptric belts of fixed lights, which are ground by means of vertical rubbers with a reciprocating movement, every other plane surface is executed by hand on a flat table.

Composition of the Cement for fixing the glass on the lathe.

8	parts Swedish pitch.
1	do. of wood ashes.

The whole is heated in an iron pot until fully liquified and thoroughly mixed. This cement is used almost in a state of ebullition, so that it cannot be handled without the precaution of continually dipping the hands in cold water.

Composition of cement used for the adjustment of the pieces of glass which touch each other.

12	parts	white lead.
1	do.	minium or red lead.
5	do.	boiled lintseed oil.

The whole is pounded on an iron table by means of a flat mullet, like that used by painters (fig. 112), whose grinding surface is a b, and c the knob for the hand. This cement is applied liquid so as to offer no resistance to the close union of the pieces, which it is intended to unite.

Fig. 112.

Painter's mullet

Cement for filling up voids, and fixing the rings in the frames.

12	parts	white lead.
3	do.	whiting.
1	do.	minium.
4	do.	boiled lintseed oil.

This last composition differs from the former only in the introduction of whiting, which, while like minium it has a desiccative property, gives more body to the cement and prevents the formation of cracks. The oil is also decreased in quantity, as the cement must be used in a more compact state. The trituration of this cement is performed by means of a cylindric iron roller a b, with a centre-spoke c d for the hand (fig. 113).

Fig. 113.

Roller

It is essential for the production of good cement, that the mixture of the ingredients be complete.

Prices of the various parts of the Dioptric Apparatus.

The expense of the various parts of the Dioptric apparatus is as follows: Great lens of first order, L.58 (8 of which are required); pyramidal lens and mirror, L.14, 12s. (8 of which are required); catadioptric cupola, L.480; catadioptric rings below lenses, L.360; pannel of dioptric belt for fixed light of first order, L.56 (of which 8 are required for the whole circle); apparatus of fourth order, for a fixed light, for whole horizon, L.128; apparatus of sixth order, for whole horizon, L.44. The expense of the mechanical lamp of the first order with four wicks, as made for the Scotch Lighthouses by Mr John Milne of Edinburgh, is L.30.