928 



SCIENCE 



[N. S. Vol. XLIII. No. 1122 



in a preliminary explanation, but the fact 

 should finally be made clear that the second 

 law of motion is quite independent of the law 

 of gravitation and of the facts of terrestrial 

 gravity. The fact that the word weight is 

 usually associated with gravity makes the 

 term "standard weight" misleading and in- 

 appropriate as the name of a " characteristic 

 of the given body" which has nothing to do 

 with gravity.^'^ 



Full comment on the latest communications 

 of Mr. Kent and Professor Huntington would 

 consist largely of the repetition of comments 

 made in previous communications by myself 

 and others, and I shall take space only for a 

 remark regarding their attitude toward the 

 equation F = ma. They agree in objecting 

 most strenuously to the use of this equation. 

 The grounds of the objection as stated by Pro- 

 fessor Huntington are that it implies " a per- 

 fectly arbitrary choice of units " and a choice 

 that is " needlessly complicated and quite un- 

 scientific." When these objections are con- 

 sidered in connection with the units endorsed 

 by both Mr. Kent and Professor Huntington, 

 the implication seems to be that it is less 

 arbitrary, less complicated and more scientific 

 to define a unit force as " the force whicli 

 would give the unit mass 32.1740 units of ac- 

 celeration " than as " the force which would 

 give the unit mass one unit of acceleration." 

 What reason there is for such a supposition 

 it is not easy to see. 



The fact that the choice of units is always 

 arbitrary is indeed a very important fact to 

 emphasize with students, and probably the only 

 way to do this effectively is to give practise in 

 the use of different sets of units in solving the 

 same problems. If any author states or im- 

 plies that the unit force must be defined as the 

 force which would give unit mass imit accel- 



11 This inappropriateness is strikingly apparent 

 in referring to astronomical masses. In a recent 

 lecture by an astronomer of high reputation the 

 statement was made that the sun contains more 

 than 97 per cent, of the matter in the solar sys- 

 tem. How would this fact be expressed by Pro- 

 fessor Huntington? Would he speak of the 

 "standard weights" of the sun and the solar 

 system? 



eration, he makes an unfortunate mistake; 

 but the same may be said of one who states or 

 implies that the force which would give a unit 

 mass 32.1740 units of acceleration is other than 

 an arbitrarily chosen unit. 



L. M. HosKiNS 

 Stantobd Univebsitt, 

 April 8, 1916 



ELECTRICAL ACTION AND THE GRAVITATION 

 CONSTANT 



In Science for December 31 Professor 

 Nipher suggests that previoiis determinations 

 of the gravitation constant may be in error, 

 owing to the force action of electric charges on 

 the attracting masses. The point is interest- 

 ing, but in estimating the possible magnitude 

 of the effect the author seems to have com- 

 mitted a serious error. 



He puts the charge Q on a sphere equal to 

 BV, where B is the radius and V is the ahso- 

 lute potential of the sphere. But this equation 

 holds only when the sphere is alone in space; 

 otherwise it may be nowhere near true. Con- 

 sider, for instance, an insulated uncharged 

 sphere inside a closed metal box. By char- 

 ging up the box we may change the absolute 

 potential of the sphere by a large amoimt 

 without placing any charge whatever upon 

 the sphere itseK. 



If Professor Nipher really has made this 

 slip, he is at least in august company. Por no 

 less an authority than Boltzmann fell into a 

 similar error, when he set the capacity of a 

 conducting molecule hetween two conducting 

 plates equal to its radius.^ 



In the classical experiments on the gravita- 

 tion constant charges certainly existed on the 

 attracting masses, in consequence of contact 

 potentials between metals if for no other rea- 

 son. But Professor Nipher's calculation indi- 

 cates a possible error due to contact potentials 

 of only a per cent, or two. Furthermore, the 

 electric effect would be enormously influenced 

 by the nature and arrangement of other parts 

 of the apparatus, and these have varied widely. 

 It seems doubtful, therefore, whether the actual 

 error due to this cause can exceed the very 



1 Gastheorie, I., p. 79. 



