Page:Observations on Man 1834.djvu/255

 conversant in mathematical inquiries; but to me they appear to cast light and evidence upon the methods of pursuing knowledge in other matters, to sharpen the natural sagacity, and to furnish loci for invention. It appears also not impossible, that future generations should put all kinds of evidences and inquiries into mathematical forms; and, as it were, reduce Aristotle’s ten Categories, and Bishop Wilkins’s forty Summa Genera, to the head of quantity alone, so as to make mathematics and logic, natural history and civil history, natural philosophy and philosophy of all other kinds, coincide omni ex parte.

I will add two more remarks relating to the present subject.

First, then, as in many mechanical problems, which fall strictly under the consideration of mathematicians, the quantities considered depend on several others, so as to increase in the simple or compound, direct or inverse, ratio of several others, and not to be greatest or least, when one or two of these are so, but when the factum of the proper powers of all is so; so throughout natural philosophy, in physic, in the analysis of the mind, &c., it is necessary to inquire, as carefully as we can, upon how many considerable causes each effect depends; also whether the ratios be simple or compound, direct or inverse. For though it will seldom happen, that one can bring the practical problems that occur in real life, to an exact estimate in this way, yet one may avoid part of that uncertainty and confusion, to which persons who take things merely in the gross are liable. Or, in other words, it is better in every thing to have probable or tolerable limits for the data, with a regular method of computation, or even an approximation thereto, than to have only such gross and general conceptions, as result from the more or less frequent recurrency of impressions, even though they be somewhat improved by natural or acquired sagacity, arising, in a kind of implicit indefinite way, from experience.

Secondly, it seems to me, that the rays of light may be considered as a kind of fluxions in respect of the biggest component particles of matter; I mean those upon which Sir Isaac Newton supposes the colours of natural bodies, and the changes effected in chemical processes, to depend. For, as the increments of variable quantities, when diminished so as to bear no finite ratio to the quantities of which they are the increments, shew, in a simple way, the velocities with which these quantities are increased; and so give rise to the determination of fluxions from fluents, and fluents from fluxions, and to all the applications of these determinations to real quantities, all which is entirely grounded upon the supposition, that the fluxions are not increments, but relative nothings; so, since the rays of light are so small in respect of the biggest component particles, as to be relatively and practically nothing in respect of them, to bear no relation to any of them, all the differences observable in the actions of light upon these particles, and of these particles upon