Relation to Mathematics
722.
It may be expected that the investigator of nature, who proposes to treat the science of natural philosophy in its entire range, should be a mathematician. In the middle ages, mathematics was the chief organ by means of which men hoped to master the secrets of nature, and even now, geometry in certain departments of physics, is justly considered of first importance.
723.
The author can boast of no attainments of this kind, and on this account confines himself to departments of science which are independent of geometry; departments which in modern times have been opened up far and wide.
724.
It will be universally allowed that mathematics, one of the noblest auxiliaries which can be employed by man, has, in one point of view, been of the greatest use to the physical sciences; but that, by a false application of its methods, it has, in many respects, been prejudicial to them, is also not to be denied; we find it here and there reluctantly admitted.
725.
The theory of colours, in particular, has suffered much, and its progress has been incalculably retarded by having been mixed up with optics generally, a science which cannot dispense with mathematics; whereas the theory of colours, in strictness, may be investigated quite independently of optics.
726.
But besides this there was an additional evil. A great mathematician was possessed with an entirely false notion on the physical origin of colours; yet, owing to his great authority as a geometer, the mistakes which he committed as an experimentalist long became sanctioned in the eyes of a world ever fettered in prejudices.
727.
The author of the present inquiry has endeavoured throughout to keep the theory of colours distinct from the mathematics, although there are evidently certain points where the assistance of geometry would be desirable. Had not the unprejudiced mathematicians, with whom he has had, or still has, the good fortune to be acquainted, been prevented by other occupations from making common cause with him, his work would not have wanted some merit in this respect. But this very want may be in the end advantageous, since it may now become the object of the enlightened mathematician to ascertain where the doctrine of colours is in need of his aid, and how he can contribute the means at his command with a view to the complete elucidation of this branch of physics.
728.
In general it were to be wished that the Germans, who render such good service to science, while they adopt all that is good from other nations, could by degrees accustom themselves to work in concert. We live, it must be confessed, in an age, the habits of which are directly opposed to such a wish. Every one seeks, not only to be original in his views, but to be independent of the labours of others, or at least to persuade himself that he is so, even in the course of his life and occupation. It is very often remarked that men who undoubtedly have accomplished much, quote themselves only, their own writings, journals, and compendiums; whereas it would be far more advantageous for the individual, and for the world, if many were devoted to a common pursuit. The conduct of our neighbours the French is, in this respect, worthy of imitation; we have a pleasing instance in Cuvier’s preface to his “Tableau Élémentaire de l’Histoire Naturelle des Animaux.”
729.
He who has observed science and its progress with an unprejudiced eye, might even ask whether it is desirable that so many occupations and aims, though allied to each other, should be united in one person, and whether it would not be more suitable for the limited powers of the human mind to distinguish, for example, the investigator and inventor, from him who employs and applies the result of experiment? Astronomers, who devote themselves to the observation of the heavens and the discovery or enumeration of stars, have in modern times formed, to a certain extent, a distinct class from those who calculate the orbits, consider the universe in its connexion, and more accurately define its laws. The history of the doctrine of colours will often lead us back to these considerations.