THE LAWS OF MOTION 303 



This definition leads us to two important points. We 

 see, namely, that the mass of a corpuscle has relation to 

 some standard corpuscle, or mass is always a relative 

 quantity ; and, further, mass is a mere number represent- 

 ing a ratio of accelerations. We have here, then, a 

 perfectly clear and intelligible definition ; we can grasp 

 what velocity means, and we can understand how its 

 change is measured by acceleration. Mass, accordingly, 

 as the ratio of the numbers of units in two accelerations, 

 is a conception which can easily be appreciated. It is in 

 this manner that mass is invariably determined scientific- 

 ally, yet nevertheless the reader will frequently find mass 

 defined in text -books of physics as "the quantity of 

 matter in a body." After our discussion of matter in 

 Chapter VII. the reader will easily appreciate how idle is 

 a definition of mass in terms of matter.^ 



S 9. — The Fifth Law of Motion. TJie Definition of Force 



We can now pass to the next stage in our investiga- 

 tion of the corpuscular dance. Having selected a 

 standard corpuscle Q, we conceive the masses relative to 

 it of many other corpuscles — A, B, C, etc. — measured. 

 If we tabulated these masses and then compared them 

 with the ratio of the mutual accelerations of A and B, B 

 and C, C and A, etc., with a view of ascertaining whether 

 there were any relation between the mutual accelerations 

 of each pair and their masses, we should very soon dis- 

 cover a fifth important law of motion, namely, that the 

 ratio of the acceleration of A due to B to the acceleration of 

 B due to A is exactly equal to the ratio of the mass ofBto 

 the mass of A, or in simple algebraical notation : — 



Acceleration of A due to B Mass of B , , 



. = ly\ 



Acceleration of B due to A Mass of A 



This is expressed briefly by the statement that mutual 



1 Quantity belongs essentially to the sphere of sense - impression. We 

 cannot consider it to have any meaning when projected beyond that sphere. 

 It seems, therefore, illogical to apply the word c|uantity to the metaphysical 

 " source " of sense-impressions. 



