100 THE AIM AND ACHIEVEMENTS OF SCIENTIFIC METHOD. 



sentecl by bodies so circumstanced that the product of mass 

 into velocity is the same for each. To this equivalence is given 

 the name, equality of momentum. Thus the momentum 

 which Descartes thought of as a measure of .the " force " 

 of a moving body is properly a piece of descriptive apparatus 

 by means of which an account may readily be given of cases 

 in which colliding bodies bring one another to rest. By ^,n 

 easy extension of the experiments to cases in which rest does not 

 result, it is found that this descriptive instrument has a still 

 wider range of usefulness. Eecognising that momentum is a 

 " vector quantity,"* we may bring all cases of collision under 

 one formula : " The total momentum of the two bodies is the 

 same after as it was before the impact ; momentum being 

 merely transferred from one body to the other." 



But experience presents us with cases in which twcT BocHes 

 enter into transactions with one another which involve a 

 gradual change of momentum instead of the sensibly instan- 

 taneous transference which characterises impact. In certain 

 cases (e.g., when two bodies of different mass are drawn together 

 by an elastic cord stretched between them) it can be demon- 

 strated that the movements of the bodies under these new con- 

 ditions can still be brought under the old descriptive formula : 

 momentum is not lost during the transaction but is constantly 

 being transferred from one body to the other. But in this 

 case of gradual transference the question of the rate of 

 transference at a given moment is one that is bound to arise ; 



* I.e., a quantity which is completely specified only when its direction 

 and " sense," as well as its magnitude, are given. Such quantities can be 

 represented' by vectors, that is by straight lines of proportional length, 

 drawn in the appropriate directions, the " sense " being indicated by an 

 arrow-head on the line. Vector quantities, must, moreover, follow the 

 law of vector addition ; in other words, two or more of them must be 

 replaceable by a single one, which is represented by the "sum" of the 

 vectors of the others. The "sum" of the vectors, a, j3, y, . . . ., is the 

 vector obtained by drawing a, , y . . . . end to end (the arrows all 

 pointing the same way round) and joining the first point of a to the last 

 point of the last vector. 



