sict. n.] DISSERTATION SECOND. 95 



stance arising from (hem, can only be found out by geome- 

 try, which, therefore, becomes a necessary instrument in 

 completing the work of induction. An example, which the 

 science of opticks furnishes, will make this clearer than 

 any general description. When light passes from one 

 transparent medium to another it is refracted, that is, it 

 ceases to go on in a straight line, and the angle which the 

 incident ray makes with the superficies which bounds the 

 two media, determines that which the refracted ray makes 

 with the same superficies. Now, if we would learn any 

 thing about the relation wiich these angles bear to one ano=. 

 ther, we must have recourse to experiment, and all that ex- 

 periment can do is, for any particular angle of incidence, to 

 determine the corresponding angle of refraction. This 

 may be done in innumerable cases ; but, with respect to the 

 general rule which, in every possible case, determines the 

 one of those angles from the other, or expresses the con- 

 stant and invariable relation which subsists between them, — 

 with respect to it, experiment gives no direct information. 

 The methods of geometry must therefore be called in to 

 our assistance, which, when a constant though unknown re- 

 lation subsists between two angles, or two variable quantities 

 of any kind, and when an indefinite number of values of 

 those quantities are given, furnishes infallible means of dis- 

 covering that unknown relation, either accurately, or at 

 least by approximation. In this way it has been found, 

 that, when the two media remain the same, the cosines of 

 the angles above mentioned have a constant ratio to one 

 another. Thus it appears, that, after experiment has done 

 its utmost, geometry must be applied before the business 

 of induction can be completed. This can only happen 

 when the experiments affoi'd accurate measures of the quan- 

 tities concerned, like the instantiae radii, curriculi, Sec. 

 and this advantage of admitting generalization with so mm) 



