September 8, 1916] 



SCIENCE 



351 



It will be noticed that we are here concerned 

 not with a single particle, but with a collec- 

 tion of two particles, so that we may expect the 

 principle of action and reaction to be called 

 into service. (This principle was included in 

 my paper, in a footnote.) The solution I 

 would propose is as follows: 



Since the force F applied to the composite 

 body must be applied at some point, let us sup- 

 pose that it is applied at the A' end of the 

 body; and since the two parts A' and A" must 

 be connected together by some means, let Q be 

 the force which each part exerts on the other. 

 If now we confine our attention to the first 

 body, A', we see that the net force acting on 

 this body in the forward direction is F — Q, 

 while the acceleration produced is the required 

 acceleration of the combined body, say a; 

 hence, by the fundamental proportion as ap- 

 plied to the first body, 



(F—Q)/F = a/a'. 

 Similarly, if we confine our attention to the 

 second body, A", we see that the net force 

 acting is Q, while the acceleration produced is 

 the same as before, namely a; hence, by the 

 fundamental proportion as applied to the sec- 

 ond body, 



Q/F=-a/a". 



Solving these two equations for a, we have at 

 once the required answer : 



l/a=.l/a +l/a". 

 It is obvious that the proof just given — in- 

 volving the elimination of the internal forces 

 Q — is nothing more than a special case of the 

 proof regularly employed for the familiar 

 theorem on the motion of the center of mass of 

 any collection of particles. In fact, as far as 

 I can make out his meaning, all that Pro- 

 fessor Hoskins values so highly in his (rather 

 vague) principle of the additivity of mass is 

 really contained in this well-known theorem on 

 the motion of the center of mass. If this is 

 true, the chief difference between the methods 

 advocated by Professor Hoskins and myself 

 comes down to this : he would regard as a 

 fundamental assumption, to he stated as such 

 at the very outset of the course, a rather com- 

 plicated proposition called the additivity of 



mass, while I would prefer to treat this proposi- 

 tion as a theorem to be deduced by easy steps 

 from much simpler fundamental assumptions. 



In conclusion, there are two minor points in 

 Professor Hoskins's paper on which I may be 

 permitted to comment. 



First, I can not assent to Professor Hoskins's 

 characterization of my method as one that 

 " purports to be independent of mass." It is 

 true that my method purports to require, at the 

 start, only three fundamental concepts, 

 namely: force, length and time; but the con- 

 cept of mass is no more " ignored " or 

 " evaded "• in the development than are the con- 

 cepts of energy, momentum, etc., all of which 

 take their proper places in the theory as de- 

 rived concepts. The kinetic idea of mass or 

 inertia (namely, force over acceleration) is as 

 difficult as it is important, and should be led 

 up to gradually, by easy and very definite 



Secondly, I can not admit that my method 

 requires me to define " the unit force " as " the 

 force which would give the unit mass 32.1740 

 units of acceleration." On the contrary, my 

 idea of a force is a spring balance, and my idea 

 of a unit force is any spring which may happen 

 to be selected as a standard. It is a matter 

 of entire indifference in my method whether 

 the unit force is a pound or a dyne or a penny- 

 weight. Edward V. Huntington 



Harvard University 



sir clements markham 

 To the Editor of Science: It was a great 

 pleasure to me to read the appreciation of 

 Sir Clements Markham which came out in 

 Science for April 21. Too often have the 

 admirers of Sir Clements in this country had 

 reason to believe that his anthropological 

 labors are not properly appreciated here. Such 

 a full, generous and complete resume of his 

 great accomplishment as that given by A. C. B. 

 contributes toward a contrary belief. 



Through Sir Clements Markham's extraor- 

 dinary diligence and scholarship, students of 

 South American anthropology are given ready 

 access to Gareilasso de la Vega's " Eoyal Com- 

 3 Compare the excellent remarks of Professor 

 Willard J. Fisher in Science for July 7, 1916. 



