v EVOLUTION AND TELEOLOGY 343 



A instead of to AX. AX (even if X prove ultimately 

 to be the entire system of reality) will serve in its succes- 

 sive phases as a type of an 'as such relation.' With the 

 same limitations, it will be understood that the successive 

 phases of a uniform process of motion in a straight line 

 or upon a uniform curve, may be held to imply one another 

 as such. The motion may depend on conditions outside 

 the moving body, but wherever these conditions are given 

 so that the first phase comes into being, the remainder is 

 intelligible from that phase alone and needs no further 

 assumption to explain it. Again, more complex changes 

 or processes are derivable from their antecedents c as such,' 

 when they are referable to the impact of elementary pro- 

 cesses upon one another, and when the characteristic of 

 each elementary process is still traceable in the result. 

 Thus, in the typical case of mechanical impact, we have 

 two masses M and m moving with velocities V and v. If 

 unaffected by one another or by any third body they would 

 continue to move in straight lines. But from the paths 

 they are describing, we may be able to see that * as such ' 

 they determine the collision that ensues, and in this colli- 

 sion, if the bodies are elastic, there is a change of motion 

 which is to be understood if we take either body, say M 

 with its momentum which is MV, and conceive this altered 

 in quantity and direction by the amount mv. This gives 

 us the new momentum MV' where the effect of mv is pre- 

 served as a modification, in quantity and direction, of MV. 

 Similarly, MV survives in the modification mv' effected in 

 mv, the proof being that the whole resultant momentum 

 M V' + mv' = the original momentum MV + mv. If the 

 bodies are not elastic, some of the momentum is lost, but 

 a proportionate amount of heat or other energy is evolved 

 proportionate, because by appropriate means it is again 

 convertible into motion equivalent to the missing quantity. 

 The object of mechanics is to get down to equations of 

 this type in which the sum of the elements of a process is 

 seen to remain constant before and after a critical change, 

 an equation which indicates that each element in the new 

 condition of things is the equivalent of a former element 

 as modified by its new concomitants. Mechanics is thus 



