Page:Harold Dennis Taylor - A System of Applied Optics.djvu/21



TRUST that the student of Optics who casually scans the pages of this work for the first time, will not be alarmed by the complicated appearance of some of the formulæ employed in the course of working out the conclusions, and therefore infer that it is necessary to be highly trained in mathematics in order to follow the lines of reasoning employed. For such is not the case; all that is really necessary in the mathematical equipment of the student being an easy acquaintance with the ordinary manipulations of Algebra, together with a clear grasp of the Binomial Theorem, the chief propositions of Euclid, and the rudiments of the Differential Calculus. That granted, and given some instinct for the practical application of what he knows, then he will have no insuperable difficulty in following this work from cover to cover.

The greater part is easy compared to the numerous problems and theorems which the average university student is called upon to solve, and which in so many cases are treated as of purely theoretical interest. After all, is not that the truest and most fruitful teaching of mathematics which fully recognises the mutual support between theory and practice ? Otherwise it is but natural if the student cleaves to the one and despises the other.

I do not wish to imply that there is no scope for the employment of the highest mathematical skill in optical science; for, on the contrary, there are numerous problems in connection with the corrections of the third order of approximation, merely glanced at in Section XL of this work, which pre-eminently call for the elucidating and marshalling influence of some clear-headed mathematician who shall be thoroughly familiar with the properties of lenses from practical acquaintance, and not only from the theoretical point of view. The closer approach to perfection in the optical combinations of the future will lie in the more thorough elimination of the corrections of the third order, and in some cases of the fourth order, and the most highly trained mathematical skill, if it should ever deign to busy itself in this