xxvn.] GENERALISATION. 599 



possession were known. The reduction of a single comet 

 beneath the sway of gravity was considered sufficient 

 indication that all comets obey the same power. Few 

 persons doubted that the law of gravity extended over the 

 whole heavens ; certainly the fact that a few stars out of 

 many millions manifest the action of gravity, is now held 

 to be sufficient evidence of its general extension over the 

 visible universe. 



Value of Generalisation. 



It might seem that if we know particular facts, there can 

 be little use in connecting them together by a general law. 

 The particulars must be more full of useful information 

 than an abstract general statement. If we know, for 

 instance, the properties of an ellipse, a circle, a parabola, 

 and hyperbola, what is the use of learning all these pro- 

 perties over again in the general theory of curves of the 

 second degree ? If we understand the phenomena of sound 

 and light and water-waves separately, what is the need of 

 erecting a general theory of waves, which, after all, is 

 inapplicable to practice until resolved again into particular 

 cases ? But, in reality, we never do obtain an adequate 

 knowledge of particulars until we regard them as cases of 

 the general. Not only is there a singular delight in dis- 

 covering the many in the one, and the one in the many, 

 but there is a constant interchange of light and knowledge. 

 Properties which are unapparent in the hyperbola may be 

 readily observed in the ellipse. Most of the complex 

 relations which 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 polarisation, the 

 existence of which had hardly been suspected in the case 

 of sound, but which may now be sought out, and perhaps 

 found to possess unexpected interest. The careful study 

 of water-waves shows how waves alter in form and velocity 

 with varying depth of water. Analogous changes may 

 some time be detected in sound waves. Thus there is 

 mutual interchange of aid. 



