362 



INDUCTION. 



and space are important elements in the ascertainment of 

 uniformities of succession, they can do nothing towards it 

 when taken by themselves. They can only be made instru- 

 mental to that purpose when we combine with them additional 

 premises, expressive of uniformities of succession already known. 

 By taking, for instance, as premises these propositions, that 

 bodies acted upon by an instantaneous force move with uniform 

 velocity in straight lines; that bodies acted upon by a con- 

 tinuous force move with accelerated velocity in straight lines ; 

 and that bodies acted upon by two forces in different directions 

 move in the diagonal of a parallelogram, whose sides represent 

 the direction and quantity of those forces ; we may by com- 

 bining these truths with propositions relating to the properties 

 of straight lines and of parallelograms, (as that a triangle is 

 half a parallelogram of the same base and altitude,) deduce 

 another important uniformity of succession, viz., that a body 

 moving round a centre of force describes areas proportional to 

 the times. But unless there had been laws of succession in 

 our premises, there could have been no truths of succession in 

 our conclusions. A similar remark might be extended to every 

 other class of phenomena really peculiar; and, had it been 

 attended to, would have prevented many chimerical attempts 

 at demonstrations of the indemonstrable, and explanations 

 which do not explain. 



It is not, therefore, enough for us that the laws of space, 

 which are only laws of simultaneous phenomena, and the laws 

 of number, which though true of successive phenomena do not 

 relate to their succession, possess the rigorous certainty and 

 universality of which we are in search. We must endeavour 

 to find some law of succession which has those same attributes, 

 and is therefore fit to be made the foundation of processes for 

 discovering, and of a test for verifying, all other uniformities 

 of succession. This fundamental law must resemble the truths 

 of geometry in their most remarkable peculiarity, that of never 

 being, in any instance whatever, defeated or suspended by any 

 change of circumstances. 



Now among all those uniformities in the succession of 

 phenomena, which common observation is sufficient to bring 



