July 30, 1915] 



SCIENCE 



159 



which he dissociates altogether from iveight. 

 Professor Hoskins makes use of the time- 

 honored device of defining mass as " quantity 

 of matter." He holds that 



the definition (of mass as quantity of matter) has 

 a sufficiently definite meaning, gained from ordi- 

 nary experience, to be of service in a preliminary 

 explanation of the laws of motion. 



This, however, has not always heen his 

 opinion. In his excellent treatise on " Theo- 

 retical Mechanics,"^ on page 2, he says : 



The mass of a body is often briefly defined as its 

 "quantity of matter." These words, however, 

 convey no definite idea of the meaning of mass as 

 a factor in the determination of motion. A satis- 

 factory definition of mass can not be given in 

 advance of a discussion of the fundamental laws 

 of motion. 



This earlier view of Professor Hoskins is 

 precisely the position which I wish to defend. 

 For mass, as a factor in the determination of 

 motion, means the constant ratio of force to 

 acceleration (for example, the statement: 

 " hody A has three times the mass of body B " 

 is precisely equivalent to the statement : " body 

 A requires three times as much force as body 

 B to give it a specified acceleration ") ; and 

 whatever idea the words " quantity of matter " 

 may convey to a beginner's mind, they cer- 

 tainly can not convey this desired idea of mass 

 or inertia until after the ideas of force and 

 acceleration, and the idea of the constancy of 

 their ratio for a given body, have been grasped. 



Why has Professor Hoskins abandoned this 

 excellent position? The only argument which 

 he advances in favor of the definition of mass 

 as quantity of matter is expressed as follows: 



In. comparing the masses of bodies composed of 

 one homogeneous substance, the significance of 

 the words ' ' quantity of matter ' ' is indeed readily 

 recognized, and it is distinctly helpful to gener- 

 alize this notion. 



But when one tries to analyze this argu- 

 ment, one runs at once into difficulty. What 

 is the concept which Professor Hoskins here 

 proposes to generalize? In the comparison of 

 bodies composed of one homogeneous sub- 



- Second edition, 1903. 



stance, the thing that strikes one as most 

 obvious is that doubling the " quantity of 

 matter " in a body is equivalent to doubling 

 its volume or bulk. Two bricks, we say, con- 

 tain twice as much clay as one brick. Are we 

 then to understand that it is the notion of 

 hulkj which, when properly " generalized," is 

 to lead us to the notion of mass? 



This can hardly be the interpretation which 

 Professor Hoskins intends. It is true that 

 the notion of bulk is sufficiently familiar, and 

 it is also true that in the case of a homo- 

 geneous substance, the mass of a body happens 

 to be proportional to its bulk; but it is surely 

 not true that any correct idea of mass as a 

 factor in the determination of motion can ever 

 be obtained by generalizing the idea of bulk. 



What then are we to understand by Pro- 

 fessor Hoskins's appeal to the case of homo- 

 genSous substance? How does this appeal ad- 

 vance us toward the conception of mass as a 

 factor in the determination of motion? Pro- 

 fessor Hoskins's article gives no answer to 

 this question, and I believe that no answer can 

 be given — that in fact the whole attempt to 

 define mass or inertia as " quantity of matter " 

 is utterly vague and futile. 



There are, of course, certain contexts in 

 which the term " quantity of matter " is use- 

 ful. For example, if we start a bonfire in a 

 hermetically sealed box, we may properly say 

 that the " quantity of matter " in the box is 

 the same before and after (for the simple 

 reason that we suppose nothing to have been 

 added and nothing to have escaped). But 

 this tells us merely that for dynamical pur- 

 poses we may properly treat the contents of 

 the box as one hody, in spite of any change in 

 size, shape or chemical constitution. It does 

 not tell us anything about the mass of this 

 body. For the mere fact that the quantity of 

 matter in the body is invariable (and this is 

 the only fact about its " body-constant " which 

 can properly be presupposed in advance of 

 some study of inertia) gives us no information 

 whatever about the motion of the body when 

 acted on by a force. Not until we have ascer- 

 tained by some physical experiment what ac- 

 celeration is produced in the body (or in some 



