394 INDUCTION. 



their succession. On a knowledge of these is founded 

 every reasonable anticipation of future facts, and what- 

 ever power we possess of influencing those facts to 

 our advantage. Even the laws of geometry are chiefly 

 of practical importance to us as being a portion of the 

 premisses from which the order of the succession of 

 phenomena may be inferred. 



Inasmuch as the motion of bodies, the action of 

 forces, and the propagation of influences of all sorts, 

 take place in certain lines and over definite spaces, the 

 properties of those lines and spaces are an important 

 part of the laws to which those phenomena are them- 

 selves subject. Moreover, motions, forces or other 

 influences, and times, are numerable quantities; and the 

 properties of number are applicable to them as to all 

 other things. But although the laws of number 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 

 instrumental to that purpose when we combine with 

 them additional premisses, expressive of uniformities 

 of succession already known. By taking, for instance, 

 as premisses these propositions, that bodies acted 

 upon by an instantaneous force move with uniform 

 velocity in straight lines ; that bodies acted upon by 

 a continuous 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 combining 

 these truths with propositions relating to the pro- 

 perties of straight lines and of parallelograms, (as 

 that a triangle is half of a parallelogram of the same 

 base and altitude,) deduce another important uniformity 

 of succession, viz., that a body moving round a centre 



