July 13, 1916] 



NATURE 



401 



before rise of temperature, we have GMm/d*. After 

 rise we have 



GMw 



, [_l +a(T + /)J. 



^[l+a'(T/)] 



If we, however, assume that increments in g.m. are 

 multiplied separately, we should have 

 GM///[ 



Neither of these formulae helps us to reconcile the 

 above facts. 



But now suppose that gravitational attraction be- 

 tween two masses consists of two parts : — 



(a) The essential-mass term. Attraction between 

 the masses occurs in virtue of the ether displaced by 

 the Faraday tubes attached to their electrons. This 

 would be like Maxwell's stress theory of gravitation : 

 compression of ether radially from each body and 

 tensions in directions perpendicular to the radii. This 

 term is represented by the usual form fi — G^lm/d-. 

 It is independent of molecular vibration and exists at 

 absolute zero. 



(b) The temperature term. Attraction is due to 

 vibration of the Faraday tubes, which are carried to- 

 and-fro by the molecules in their vibratory motion. 

 This is like Challis's wave theory of gravitation, 

 whereby bodies in a vibrating medium attract one 

 another if their phases are in close agreement. Dr. 

 C. V. Burton suggested that for very high velocity 

 of wave transmission the vibrating bodies might 

 resonate one another and have approximately like 

 phases. Presumably the waves in this case are longi- 

 tudinal and their velocity nearly infinite. If the 

 po-wer that one mass has of setting another to resonate 

 depends on the ratio, mass of vibrator /total mass, 

 this attraction would be 



y:,=;grMaT(-^V+„.a/-^ )m1 



Adding (a) and (&) terms, 

 GMw 



/=/!+/. = - 



iT- 



b-imin')} 



This expression was suggested, though not derived, 

 by Poynting and Phillips. Evidently, when M pre- 

 ponderates greatly over m (the only case we need 

 :onsider), 



/=__(^r+aT) 



so that a change in temperature of M might affect / 

 appreciably, but no such change in m could do so. 



This expression, then, would make all the facts 

 compatible. We have supposed that the temperature 

 effect depends on the first power, but it would be 

 more natural to consider that the intensity of vibration 

 varies as the square or higher power of temperature. 

 In that case we should have for variation in the New- 

 tonian constant, G = G,(i + aT«). 



It may be significant that the coefficient of cubical 

 expansion of lead (the material used), viz. 8"4Xio-*, 

 is of the same order as my result, i-2Xio-*, the 

 increment of / being 1/7 of the increment in volume 

 in the lead. 



Above we have taken g.m. and i.tn., so far as these 

 depend on ether displacement, to be invariable, but 

 as the body rises in temperature from absolute zero, 

 the vibrations may, especially at high temperature, 

 cause such violent agitation of Faraday tubes that 

 the effective displacement of ether is increased. If 

 this were so, of course both g.m. and t.m. would 

 increase, since in that case the essential mass would 

 increase. Mathematicians might assist in deciding 

 this point. But, at present, for temf>eratures up to, 



NO. 2437, VOL. 97] 



say, 500° C, we might suppose neither g.m. nor i.m. 

 to change from this cause to any perceptible amount. 



To make clear the action of the above formula, 

 imagine the case of sun, earth, and moon. If the 

 mean temperature of the earth were to rise greatly, 

 say through sudden radio-activity in its interior of 

 some element previously Inactive, then the tempera- 

 ture term for the earth would Increase by an amount 

 small compared with the essential mass term of (sun 

 + earth), but large compared with that of (earth + 

 moon). Thus the earth's orbital motion would not 

 change appreciably, but attraction between earth and 

 moon would increase and the moon's orbital motion 

 1 might be greatly affected. 



Applying our formula i. to the comments of "'J. L.," 

 we should not anticipate change due to temperature 

 in g.m. or i.m. in the cases of pendulum experiments 

 or planetarj- orbital movements, nor should we expect 

 " kicks " in moving masses the temperatures of which 

 are suddenly changed. In like manner, a comet, even 

 though considerably heated or cooled, would be ex- 

 pected to have regular motion. The great difficulties 

 suggested by " J. L." would all vanish If formula i. 

 or something akin were true. 



It might be thought that my research, standing 

 alone, is slender evidence on which to raise such Im- 

 portant results; but I would mention that, as shown 

 in my paper, my result is buttressed by indirect 

 evidence. 



If the formula I. be true, my contention is 

 strengthened (see Nature, October 7, 1915) that a 

 laboratory value of G should not be considered valid 

 for application to the attraction between masses {e.g. 

 the heavenly bodies) the temp>eratures of which are 

 far from ordinar)'. The whole problem is complicated 

 by the high temperatures involved in the members of 

 the solar system. We know that the rigidity of the 

 earth, taken as a whole, is very great, so that the 

 immense pressure in the core counteracts the fluidising 

 Influence of the very high temperature. Elasticity 

 is, at a surface view, a molecular property ; gravity 

 is primarily an electrony'ether propert}-; nevertheless 

 we are on unsure ground In reasoning that any 

 property will be the same, say, at 5000° C, and at 

 o°C. 



Following the guidance of the formula I., we may 

 expect fruitful research if we vary the temperature 

 of the large mass ; but we should anticipate that no 

 good results could be derived from ex{>eriments on 

 temperature change of the small mass. 



Poincar^ pointed out (Report to the International 

 Congress in Physics, 1900) that the mass of Jupiter, 

 as derived from the orbits of its satellites, as derived 

 from its perturbations of the large planets, and as 

 derived from its perturbations of the small planets, 

 has three different values. This would lead one to 

 give to G a different value in each of the three cases. 

 It will be seen to accord with equation i. above, for 



in the three cases the ratio { ^-i ) is very different. 



It may be a useful fact in the present argument, 



P. E. Shaw. 



University College, Nottingham, June 24. 



Payment for Scientific Research. 



In future discussions on this difficult but important 

 question. It will be well that a distinction should be 

 drawn between the case of a specialist who engages 

 in research on a subject of his own choice, devoting 

 as much or as little of his time as he cares to give 

 to it, and that of a scientific expert who agrees to 

 undertake work for the Government or some other bodv 



