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.