1GO INDUCTION. 



true there are innumerable other theorems which 

 affirm resemblances among phenomena; as that the 

 angle of the reflection of light is equal to its angle of 

 incidence (equality being merely exact resemblance in 

 magnitude). Again, that the heavenly bodies describe 

 equal areas in equal times ; and that their periods of 

 revolution are proportional (another species of resem- 

 blance) to the sesquiplicate powers of their distances 

 from the centre of force. These and similar proposi- 

 tions affirm resemblances, of the same nature with 

 those asserted in the theorems of mathematics: but 

 the distinction is, that the propositions of mathematics 

 are true of all phenomena whatever, or at least with- 

 out distinction of origin; while the truths in question 

 are affirmed only of special phenomena, which origi- 

 nate in a certain way; and the equalities, proportion- 

 alities, or other resemblances, which exist between 

 such phenomena, must necessarily be either derived 

 from, or identical with, the law of their origin the 

 law of causation on which they depend. The equality 

 of the areas described by the planets, is derived from 

 the laws of the causes; and, until its derivation was 

 shown, it was an empirical law. The equality of the 

 angles of reflexion and incidence is identical with the 

 law of the cause ; for the cause is the incidence of a 

 ray of light upon a reflecting surface, and the equality 

 in question is the very law according to which that 

 cause produces its effects. This class, therefore, of the 

 uniformities of resemblance between phenomena, are 

 inseparable, in fact and in thought, from the laws of 

 the production of those phenomena; and the princi- 

 ples of induction applicable to them are no other than 

 those of which we have treated in the preceding chapters 

 of this Book. 



It is otherwise with the truths of mathematics. 



