April ii, 1918] 



NATURE 



10 



LETTERS TO THE EDITOR. 

 [The 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 Eotvos "Tour de Force." 



May I add to my article in Nature of March 21, on 

 the revolving balance of Baron Eotvos, that the method 

 lends itself to determine the mass of the earth, or, more 

 <lirectly, the Newtonian constant of gravitation, with 

 the same simplicity as it does to find the rotation of 

 the earth. For this purpose it is merely necessary 

 to place a large mass ahove the balance, say at the 

 north end, and below the balance at the south end. 

 Then if the direction of rotation is such that the 

 north end is moving in the same direction as the 

 ^rth the gravitational couple will act in the same 

 direction as the ^Vv difference of centrifugal force, 

 whereas if it turns in the opposite direction, the gravi- 

 tational couple will be opposed to the centrifugal 

 couple. If the large masses of radius c are spherical 

 and are made of material of density d, and the ficti- 

 tious distances of their centres vertically above and 

 below the small masses at the ends of the balance, 

 arms are also equal to c, the arm lengths being r, 

 then the time of rotation necessary to make the one 

 action equal to the other is given by the equation — 



T = 4|5^cos2<^. 



Making provisionally r = c, and taking for d the 

 density of lead, the time T comes out as thirty-one 

 minutes, which, I fear, is much greater than that 

 which could be realised as a free period. If, however, 

 the period were one minute, the gravitational couple 

 would add or subtract 1/31 part of the centrifugal 

 effect, according to the direction of rotation, or the 

 ultimate deflections in the two cases would have 

 the ratio 15:16, a difference which might be 

 observable. By fictitious distance I mean the equiva- 

 lent distance vertically above or below the centre of 

 the small mass m at which the centre of the large 

 mass may be imagined acting on the small 

 masses with a cosine distribution of force. Actually it 

 would have to be larger and further away. This could 

 more readily be determined in any particular case by 

 arithmetical treatment than otherwise. 



I have been considering in some detail the best way 

 of constructing an Eotvos tour de force, if I may be 

 allowed so to call it, with a view to the utmost possible 

 delicacy, and as I have all the material, I am hoping 

 to set one up in a cellar in the country admirably 

 adapted to the purpose in such time as I can glean 

 from other occupations. C. V. Boys. 



The Motion of the Perihelion of Mercury. 



In Nature for March 21 Sir Oliver Lodge suggests 

 that the unexplained part of the motion of the peri- 

 helion of Mercury may be attributed to the action of a 

 resisting medium. Such a medium would not neces- 

 sarily produce any effect on the mean distance of a 

 planet^ for such an effect depends entirely on the rela- 

 tive velocity, and it is probable that the medium would 

 revolve with the planets. The principal effect of the 

 medium would be to reduce the eccentricity, and de/dt 

 would contain e as a factor. There would be no 

 motion of the perihelion if e were small enough. Any 

 motion of this could arise onlv if the eccentricity were 

 considerable, and thus would contain it as a factor. 

 Hence drs/dt and de/dt would be of the same order. 

 Now the observed anornalous variations of m and e in 

 a century are 43" and' -088", so that they are of ' 



NO. 2528, VOL. lOl] 



different orders, and therefore cannot be due to a resist- 

 ing medium. 



Of, again, consider the density needed to produce 

 the effect. The average resultant velocity of Mercury 

 relative to the medium is of the order of the eccen- 

 tricity multiplied by the planet's mean orbital velocity, 

 or about eight kilometres per second. If p be the 

 density of the medium, a the radius of Mercury, U this 

 relative velocity, and M the mass of the planet, the 

 retarding force would be nearly pa^V, and de/edt 

 would be of the order pa^U^/MU. Substituting for all 

 these quantities, except p, their known values, we see 

 that p must be of the order 3X 10-'^ gm./cm.', while 

 the maximum density consistent with the observed 

 luminosity of the Zodiacal light is only about 

 2 X 10- ^^ gm./cm.*. To account for the motion of the 

 perihelion would, of course, require a still greater 

 density. 



Many recent writers on this subject have treated the 

 discordance in the motion of the perihelion of Mercury 

 as if it were the only unexplained perturbation in the 

 solar system. Yet there is an unexplained advance of 

 the node of Venus of the same order of magnitude, 

 the motions in a century being 43" and 10" respec- 

 tively. The latter estimate is admittedly subject to 

 greater uncertainty, but it is 3-5 times its mean error, 

 and the probability that so large a discrepancy is acci- 

 dental is only about 0-0004. Now, whatever may be the 

 effect of departure from simple Newtonian dynamics, 

 it cannot alter the plane of an orbit, which can be 

 done only by the attraction of other matter, or to a 

 negligible extent by a moving resisting medium. It is 

 found that a distribution of gravitating matter that 

 would represent the motion of the node of Venus would 

 necessarily account also for the whole of the dis- 

 crepancy in the perihelion of Mercury, so that depar- 

 tures from Newtonian dynamics to explain the latter 

 make the former impossible to account for. It is, of 

 course, possible that the excess motion of the node of 

 Venus may be due to errors of observation, but the 

 probability against this is about 2500 to i, and it must 

 be admitted that any theory with such an a priori 

 probability against it is open to very grave suspicion. 



Harold Jeffreys. 



Bee Disease. 



In connection with the article on bee disease which 

 appeared in Nature of March 21, perhaps my ex- 

 perience with diseased bees may be of interest. I have 

 subjected to microscopic examination the contents of 

 the intestines and chyle stomachs of several dozen 

 bees, all guaranteed by a professional lecturer in bee- 

 keeping to be suffering at the time from the "Isle of 

 Wight disease." In all cases the examination under 

 the 1/12 immersion was conducted within five minutes 

 after the bees had been killed. In no case did I find 

 a trace of Nosema apis. In some there was a pre- 

 dominance of wild yeasts in the affected parts ; in 

 others again bacterial multiplication was very far ad- 

 vanced. It may, of course, be advanced that these 

 particular bees were not suffering from the " Isle of 

 Wight disease," but in view of the conclusion adopted 

 by several competent biologists that Nosema apis has 

 no causal connection with the " Isle of Wight disease," 

 and also of the importance of the subject, further 

 investigation is urgently needed. The impression left 

 on the present writer was that Nosema apis, when 

 found, was an accessory, and not a causal agent; and 

 the fact that in practically all the observations of this 

 disease that have been made in Scotland Nosema apis 

 has been conspicuous by its absence supports this 

 impression. It would appear that different causative 

 agents produce the same symptoms ; from the practical 

 point of view, as the agents may be protozoa, or yeasts. 



