INTRODUCTION. 13 



number of vibrations belonging to a sound of that pitch. 

 To measure a sound of the same pitch is as good as to 

 measure the sound itself. 



Sir David Brewster, in a somewhat similar manner, 

 succeeded in measuring the refractive index of irregular 

 fragments of transparent minerals. It was a troublesome, 

 and sometimes impracticable work to grind the minerals 

 into prisms, so that their powers of refracting light could 

 be directly observed ; but he fell upon the ingenious device 

 of forming a liquid possessing exactly the same refractive 

 power as the transparent fragment under examination. 

 The moment when this equality was attained could be 

 known by the fragments ceasing to reflect or refract light 

 when immersed in the liquid, so that they became almost 

 invisible in it. The refractive power of the liquid being 

 then measured gives that of the solid ; and a more beau- 

 tiful instance of representative measurement, depending 

 immediately upon the principle of inference, could not 

 be found 1 . 



Throughout the various logical processes which we are 

 about to consider Deduction, Induction, Generalisation, 

 Analogy, Classification, Quantitative Eeasoning we shall 

 find the one same principle operating in a more or less 

 disguised form. 



Deduction and Induction. 







The processes of inference always depend on the one 

 same method of substitution ; but they may nevertheless 

 be distinguished according as the results are inductive or 

 deductive. As generally stated, deduction consists in 



i Brewster, 'Treatise on New Philosophical Instruments,' p. 273. 

 See also "Whewell, ' Philosophy of the Inductive Sciences,' vol. ii. p. 355 ; 

 Tomlinson, ' Philosophical Magazine,' Fourth Series, vol. xl. p. 328 ; 

 Tyndall, in Youman's ' Modern Culture/ p. 1 6. 



