466 



SCIENCE 



[N. S. Vol. XXXIX. No. 1004 



pages later we find tliat he himself offers the 

 following definition : 



"Force is the cause of a change or of a 

 tendency to change in the state of rest of a 

 body or of its deviation from uniform rectilin- 

 ear motion. The idea of force is based upon 

 the fundamental concept of the effort neces- 

 sary to change the position of a body at rest 

 or the uniform rectilinear motion of a body. 

 It is assumed to be the cause of such a 

 change, to be proportional to the acceleration 

 produced, and to be in the direction of the 

 added acceleration. It is a vector quantity. 

 A force is measured by the equation F^ma, 

 which may serve as a definition." 



Waiving all considerations which might be 

 urged against this definition on the ground 

 that physics is not at all concerned with 

 " causes," and laying aside all pedagogical 

 considerations, your reviewer would like to 

 ask, purely for information, this one question : 

 Is there any single property, save only the 

 space-variation of energy, which is character- 

 istic of all the physical quantities which one 

 finds labelled as " forces " by the leading 

 physicists of the present time? Is there any 

 single feature, or set of features, which can 

 serve as a defining quality for force? No 

 question is here raised aboiit any general defi- 

 nition of force such as that which occupies 

 ten columns of fine print in the great Oxford 

 Dictionary. The inquiry here made is much 

 simpler. It pertains only to the forces which 

 are employed every day in physics. The one 

 and serious objection against defining force 

 in terms of energy or work is, of course, the 

 fact that work and energy are universally de- 

 fined in terms of force. 



The crux of the situation would then appear 

 to be the following : one is compelled either to 

 employ the vicious circle just indicated or to 

 discover some property other than space-varia- 

 tion of energy, which is common to all forces. 

 It goes without saying, perhaps, that the space- 

 variation here referred to is that employed by 

 Lagrange in his definition of generalized 

 force,^ and is intended to include both angu- 

 lar and linear space. To make it perfectly 

 iMec. Anal., I., p. 334. 



clear that there is nothing hazy or indefinite 

 about the query here raised it may be well to 

 summarize the principal types of force which 

 one meets in any standard discussion, such as 

 that of Thomson and Tait, or Webster. 



1. First of all there is the straightaway 

 mass-acceleration in which the momentum of 

 a particle is altered while its direction of mo- 

 tion remains constant, e. g., a particle falling 

 under gravity. 



3. The force which produces a change in the 

 direction of momentum of a particle, leaving 

 the scalar value of its momentum constant, 

 e. g., contrifugal force, mva. 



3. The non-conservative force which is in- 

 dependent of the speed and is illustrated, 

 within limits, by that of sliding friction. On© 

 may of course assign a part of the force of 

 friction to the mass-acceleration of the small 

 abraded particles. 



4. The non-conservative force which varies 

 directly as the speed, and possesses a dissipa- 

 tion function, illustrated by certain viscous 

 resistances. Here again one may assign ac- 

 celeration, hence speed and heat, to the small 

 invisible particles. 



5. The force which produces a change in the 

 shape or size of an elastic body or in the con- 

 figuration of a gravitational, magnetic or 

 electric system. 



The reader will find a more elegant analysis 

 of the typical mechanical forces in Webster's 

 "Dynamics," p. 123; but the above list suf- 

 fices to show the diversity in which some com- 

 mon factor is sought. If we admit that a 

 mass-acceleration is characteristic of the first 

 four types listed above, can the all-powerful 

 electron theory bring the fifth type also into 

 this category? Or is there some better way 

 around this impasse? Or must we concur 

 with Professor Guthe in his opinion that force 

 can not be defined? To say that it is some- 

 times definable and sometimes not is about as 

 satisfactory as that ancient testimonial of 

 good character which asserted that "the man 

 is honest; at least he is honest nine times out 

 of ten." Even those who believe there is 

 something profound and mysterious about the 

 concept of force, just as there is something 



