GENERA LIZA TION. 249 



Properties which are unapparent in the hyperbola may 

 readily be discovered in the ellipse. Most of the complex 

 relations which the old geometers discovered in the circle 

 will be reproduced mutatis mutandis in the other conic 

 sections. The undulatory theory of light might have been 

 unknown at the present day, had not the theory of sound 

 supplied hints by analogy. The study of light has made 

 known many phenomena of interference and polarization, 

 the existence of which had hardly been suspected in the 

 case of sound, but which may now be sought out, and per- 

 haps found to possess unexpected interest and importance. 

 The careful study of water-waves shows how waves may 

 alter in form and velocity with varying depth of water. 

 Analogous changes may sometimes be detected in sound 

 waves. Thus there is a mutual interchange of aid. 



' Every study of a generalization or extension/ as De 

 Morgan has well saidg, f gives additional power over the par- 

 ticular form by which the generalization is suggested. No- 

 body who has ever returned to quadratic equations after the 

 study of equations of all degrees, or who has done the like, 

 will deny my assertion that ov /8XeV f$\eirwv may be pre- 

 dicated of any one who studies a branch or a case, without 

 afterwards making it" part of a larger whole. Accordingly 

 it is always worth while to generalize, were it only to give 

 power over the particular. This principle, of daily fami- 

 liarity to the mathematician, is almost unknown to the 

 logician/ 



Comparative Generality of Physical Properties. 



Much of the value of science depends upon the know- 

 ledge which we gradually acquire of the different degrees 

 of generality of properties and phenomena of various kinds. 



g * Syllabus of a proposed System of Logic,' p. 34. 



