178 INDUCTION. 



and spaces, which we could not easily, or could not at 

 all, measure by any more direct process. 



9. Such are the few remarks which it seemed 

 necessary to make in this place, respecting the laws of 

 nature which are the peculiar subject of the sciences 

 of number and extension. The immense part which 

 those laws take in giving a deductive character to the 

 other departments of physical science, is well known ; 

 and is not surprising, when we consider that all causes 

 operate according to mathematical laws. The effect 

 is always dependent upon, or, in mathematical lan- 

 guage, is a function of, the quantity of the agent ; and 

 generally of its position also. We cannot, therefore, 

 reason respecting causation, without introducing con- 

 siderations of quantity and extension at every step ; 

 and if the nature of the phenomena admits of our 

 obtaining numerical data of sufficient accuracy, the 

 laws of quantity become the grand instruments for 

 calculating forward to an effect, or backward to a 

 cause. That in all other sciences, as well as/jn geo- 

 metry, questions of quality are scarcely ever indepen- 

 dent of questions of quantity, may be seen from the 

 most familiar phenomena. Even when several colours 

 are mixed on a painter's palette, the comparative 

 quantity of each entirely determines the colour of 

 the mixture. 



With this mere suggestion of the general causes 

 which render mathematical principles and processes so 

 predominant in those deductive sciences which afford 

 precise numerical data, I must, on the present occa- 

 sion, content myself; referring the reader who desires 

 a thorough acquaintance with this great subject, to the 

 first two volumes of M. Comte's systematic work. 



In the same work, and more particularly in the 



