October 7, 1915] 



NATURE 



J 43 



Elementary Photo-micrography. By W. Bag- 

 shavv. Third edition. Pp. 143. (London : 

 Iliflfe and Sons, Ltd., 191 5.) Price 2s. 6d. net. 

 Some idea of the scope of this volume may be 

 gathered from the fact that about ninety of its 

 pages, which are not very large, are devoted more 

 especially to photo-micrography, and rather more 

 than thirty to photography^ — that is, developing 

 and printing. The author takes it for "granted' 

 that the reader is already familiar with the use of 

 the microscope," and also presumably that he is 

 an amateur photographer, and seeks to show how 

 the two may be brought together without the need 

 for expensive appliances, and furnish results 

 which, "though not perfect, are good and accept- 

 able for nearly all purposes." He succeeds not 

 only by precept but also by example, giving 

 twenty-nine good reproductions of photo-micro- 

 i^raphs taken by the simple means that he de- 

 srribes, using only objectives supplied with 

 students' microscopes. These examples are illus- 

 trative of the methods dealt with in the text, and 

 include magnifications from 2 up to 4000 

 diameters, the use of transmitted light, reflected 

 light, a combination of the two, dark ground 

 illumination, the use of polarised light, oblique 

 illumination, illumination by flashlight, multiple- 

 colour illumination, and a photograph on an auto- 

 chrome plate. They are of excellent quality, in- 

 cluding- even a photograph of Bacillus suhtilis, 

 X 1000. But the Amphipleura pellucida, x 4000, 

 shows that such simple methods will not serve for 

 an extreme test, although taken by means of a 

 one-twelfth immersion lens of 1*4 N.A. and an 

 oiled-on condenser. By the way, such an objective 

 and condenser scarcely come within the range of 

 " students' " microscopical apparatus. In giving 

 " pre-war " prices for chemicals, perhaps the 

 author expresses his faith in an early return to 

 peace conditions. 



LETTERS TO THE EDITOR. 



[Tlie Editor does not hold himself responsible for 

 opinions expressed by his correspondents. Neither 

 can he undertake to return, or to correspond with 

 the writers of, rejected manuscripts intended for 

 this or any other part of Nature. No notice is 

 taken of anonymous communications.] 



The Masses of Heavenly Bodies and the Newtonian 

 Constant. 



1m a well-known treatise on physics we find the 



fallowing statement :—" By the third law of Kepler 



w f are led to the conclusion that the same value of 



< I (the Newtonian constant of gravitation) applies to 



sun and all planetary bodies." This conclusion 



pears to be fallacious, as we see by the following 

 ' n inentary considerations : — 



fi) Take the case of Poynting's famous balance 

 experiment for determining G. The attraction of the 

 larcre mass M on the small mass m at distance d is 



couple = Gm.M ma I d'^ = m'gr . . . (i) 



where m', I' are the mass of the balancing rider and 

 Us displacement necessary to counterpoise the gravita- 

 tivo pull of M on m. 



I-^quation (i) gives Gm, for we know all the other 

 NO. 2397, VOL. 96] 



factors. The suffix used here denotes that the "con- 

 stant " Gm only applies to a mass if its temperature is 

 that of M. ' 

 (2) The earth's attraction on mass m is 



w^=rGE.E;///R2 (2) 



where E, R are earth's mass and radius respectively. 



Equation (2) gives us Ge. L. The earth's mean tem- 

 perature may be, say, 4000° C., whereas that of M 

 above is, say, 15° C. We have no experimental 

 knowledge that the Newtonian "constant" is the same 

 at 15° as at 4000°. Hence we cannot write Gj, = Ge 

 and obtain from equation (2) the earth's mass. It is 

 thus evident that the values commonly given for 

 earth's mass and mean density are based on the un- 

 warrantable assumption that Gm = Gh. Thus it is 

 quite possible (for we have no evidence to the contrary) 

 that Gh = 2Gm, in which case the earth's mean density 

 would work out to be 276 instead of 5-52, as generally 

 accepted. 



(3), When we come to the case of the revolution 

 of the earth and other planets round the 

 sun, we have similar considerations to the above. 

 Let two planets have mean radial distances d^, d^ and 

 periodic times f,, t^, we obtain in the form of Kepler's 

 third law 



Gs . S = 4^'«VA') =4-T-(^^2'/^2') =4T'''y&, 

 where S = sun's mass and JGg the Newtonian constant 

 for the sun's temperature, whence we obtain Gs . S ; 

 as we know Kepler's constant k. We do not know 

 S alone, for we may not write G.s = Gh = Gm- 



Thus we see that the masses and densities of all 

 heavenly bodies, including the earth, are based on 

 an assumption for which there is no experimental 

 support, and which (considering the great range of 

 temperature involved) is probably false. 



In the case of the sun, the stars, and all the major 

 planets the mean temperature is certainly as high as 

 four figures, and in many cases probably five figures, 

 on the Centigrade scale. It is thus inconceivable 

 that any laboratory experiment will ever be made to 

 determine the values Gs, Gp, or even Gr. But it is 

 not unlikely that sure experimental evidence will be 

 forthcoming as to the value of G, say, up to 500° C. 



I have recently concluded a long research on the 

 value of G up to 250° C., and I have found an increase 

 in that "constant" of about 1 in 10* per 1° C. The 

 full results I hope to publish shortly. 



No doubt it has been for the sake of simplicity that 

 astronomers and physicists have assumed constancy 

 in G, and have thus obtained the accepted values for 

 mass and density. But in reality these values (by 

 analogy with the terminology of radiation) are not 

 the mass and density, but the effective-mass and the 

 effective-density respectively, and would only be true- 

 mass and true-density if Gs=G,: = Gm, etc. If any 

 temperature effect, such as is mentioned above, can 

 be firmly established, then these terms ought to be 

 adopted in the interests of accuracy. 



So far, for simplicity, we have considered the tem- 

 {>erature effect of gravity on the large mass only and 

 have ignored any effect on the small mass. In equa- 

 tions (i) and (2) we have the small mass m at ordinary 

 temperatures, say 15° C., so that we have not to con- 

 sider temperature effect in connection with it. But in 

 equation (3) the two planets in question may differ in 

 temperature. Even then the equation is correct as it 

 stands, supposing (a) the temperature effect on a mass 

 considered as one member of a gravitative couple is 

 identical with (b) its effect on mass considered as so 

 much inertia ; for these terms (a) and (b) occur on the 

 left and right sides of the equation and cut out. But, 

 on the other hand, if (a) is not identical with (b) the 

 equation would have other factors. But neither in this 



