Apbil 13, 1906.] 



SCIENCE. 



575 



' The opening chapter of Part II. gives the 

 author's formulation of the axioms or funda- 

 mental principles of mechanics. His point 

 of view here is that of those critics who reject 

 force as a physical reality and state the funda- 

 mental laws simply in terms of acceleration. 

 The term force is afterward introduced and 

 defined as a convenient name for the product 

 of mass into acceleration. In the statement 

 and explanation of the second of the three 

 ' principles ' the term ' field of force ' is, how- 

 ever, used in advance of the formal definition 

 of force. 



The three ' principles of mechanics ' are 

 stated as follows: 



An isolated particle has no acceleration with 

 respect to the absolute axes. 



The acceleration which a particle takes in a 

 resultant field of force is the geometric sum of the 

 accelerations produced by the component fields, 

 and is independent of the particle and of its 

 motion. 



Two isolated particles under their mutual ac- 

 tions take accelerations in opposite directions 

 along the line joining them, and these accelera- 

 tions are in a constant ratio. 



Regarding this formulation and the accom- 

 panying explanations two matters invite com- 

 ment. The first is the definition of the abso- 

 lute axes, the second the explanation of the 

 meaning of " component fields ' in the second 

 principle. 



The notion of the fixed axes is first intro- 

 duced at p. 23 : 



But while, in kinematics, the choice of the 

 absolutely fixed system is perfectly arbitrary, it 

 is no longer so in mechanics, and there we shall 

 see that the fixed stars must be chosen as the 

 system of reference. 



Again' on p. 104: 



In kinematics the choice of the absolute axes 

 was arbitrary. The state of aflairs in mechanics 

 is difi'eTent. The principles just spoken of are 

 asserted true of the motion of a particle referred 

 to a particular set of axes in/variably connected 

 ■with the so-called fi,xed stars. These I term the 

 absolute axes. Referred to any other set the 

 principles must be modified. 



This method of defining the absolute axes 

 has been adopted by several critics who are 

 unwilling to accept Newton's doctrine of ab- 



solute space and time. To call the axes deter- 

 mined by the fixed stars ' absolutely fixed axes ' 

 is, however, to evade rather than to avoid 

 whatever difficulty theVe is in Newton's con- 

 ception. From the Newtonian point of view 

 axes thus defined are not really absolutely 

 fixed, but are merely the axes most nearly 

 fixed in direction which it is possible to specify 

 practically. We can not doubt that the stars 

 move relatively to one another, and that the 

 line joining the centers of two stars really 

 changes in direction, although observation does 

 not detect such motions; and we thereby im- 

 plicitly assume the reality of a more funda- 

 mental base of reference than the fixed stars. 

 Whether or not we are willing to adopt New- 

 ton's language and speak of absolute space 

 and time, we are driven to substantially his 

 position when we attempt to define the axes of 

 reference for which the fundamental prin- 

 ciples of mechanics are true. 



The meaning of component and resultant 

 fields in the statement of the second principle 

 is explained substantially as follows: If a 

 system of particles n is made up of systems 

 p and q, the field due to n is the resultant 

 of two component fields, one of which is the 

 field which p would produce if q ;were absent, 

 the other the field which q would produce if p 

 were absent. The ' principle ' affirms that the 

 acceleration of a particle due to n is the 

 geometric sum of the acceleration which p 

 would cause in the absence of q and that 

 which q would produce in the absence of p. 



The second principle as thus explained 

 affirms more than should really be included 

 in the law of composition. An accurate 

 formulation of this law involves the law of 

 action and reaction. The essence of the two 

 laws may be stated as follows : Considering 

 any system of particles, the actual accelera- 

 tion of any one particle due to the influence 

 of all the others may be vectorially resolved 

 into components regarded as ' due to ' the sev- 

 eral other particles ; and these components may 

 always be taken in such a way that the law of 

 action and reaction is satisfied, i. e., that the 

 acceleration of any particle A due to B and 

 the acceleration of B due to A are in the in- 

 verse ratio of the masses of A and B and 



