172 Mr. N. Campbell on the 



We must first note that the " distance between two bodies 

 of finite size " is, in general, meaningless ; distances can in 

 strictness only refer to the smallest portions or! a body which 

 are distinguishable. Accordingly, in order that any propo- 

 sition about the motion of a system of bodies may be stated, 

 it must be supposed that they are subdivided into the smallest 

 portions which are distinguishable. These portions are called 

 particles. 



§ 7. It is obvious that among the quantities occurring in 

 the equations which we are going to establish must be (1) a 

 quantity t, the Time, which bears relation A to the time, 

 and (2) Distances r, 2 ... r ln ... r mn ... so correlated with the 

 distances between the various particles (supposed to be 

 distinguished by numbers 1, 2, ... m } ... n). The briefest 

 inspection shows, however, that these quantities are not 

 sufficient ; it may be possible to deduce for any particular 

 system the distances at one time from the distances given at 

 another, but the form of the relation between t, r 12 . . . r liul 

 will certainly be different for different systems. In order to 

 obtain relations of the same form for all systems, we must 

 introduce quantities which depend upon the nature of the 

 particles of the particular system. It is the first postulate 

 of dynamics that, in order to establish equations applicable 

 to all systems, the number of such quantities which must be 

 introduced is equal to the number of particles, so that one 

 quantity may be assigned to each particle. These quantities 

 will be termed the Masses, and will be denoted by m 1 ... w? n . 

 A further postulate is made — for excellent reasons into which 

 we need not inquire here — as to the form which the equations 

 are to take. It is stated that the equations are to be linear 

 in the m'p, and that the quantity t is to occur only in 



functions of the form — ' 13 l,.'," — — • 



at" 



§ 8. When we endeavour to frame with these quantities 

 and with these postulates equations which shall fulfil the 

 fundamental purposes which are demanded of them, we find 

 that the task is impossible. In order to attain success we 

 must either reject one of the postulates, and so change the 

 form of our equations, or w r e must introduce new quantities. 

 Again we need not inquire into the reason of our choice, 

 which falls upon the latter alternative. 



We introduce a number of new quantities 



fw>.9l2i "32 Jlnt 9ln) A in fmn} ffrnni 'hnn 



