October 15, 1914] 



NATURE 



189 



a variety of cases of intramercurial planets, and 

 arrives at the conclusion that such matter, if it exists, 

 must have a mass comparable with that of Mercury. 

 Some time ago I examined the same hypothesis, and 

 arrived at similar results. The smallest planet with 

 density four times that of water, which would produce 

 the long inequality, must have a disc of nearly 2" 

 in its transit across the sun, and a still larger planet 

 would be necessary to produce the shorter period 

 terms. But obsersational attempts, particularly those 

 made by Perrine and Campbell, have always failed to 

 detect any such planet, and Prof. Campbell is of the 

 opinion that a body with so large a disc could scarcely 

 have been overlooked. If we fall back on a swarm 

 instead of a single body, we replace one difficulty 

 by two. The light from such a swarm would be 

 greater than that from a single body, and would 

 therefore make detection more likely. If the swarm 

 were more diffused we encounter the difficulty that 

 it would not be held together by its own attraction, 

 and would therefore soon scatter into a ring; such 

 a ring cannot give periodic changes of the kind 

 required. 



The shading of gra\-itation by interposing matter, 

 e.g. at the time of eclipses, has been examined bv 

 Bottlinger.' For one reason alone. I believe this 

 is ver>- doubtful. It is difficult to see how new 

 periodicities can be produced; the periods should be 

 combinations of those already present in the moon's 

 motion. The sixty to seventy years' fluctuation stands 

 out in this respect because its period is not anvwhere 

 near any period present in the moon's motion or 

 any probable combination of the moon's periods. 

 Indeed, Dr. Bottlinger 's cur\-e shows this : there is 

 no trace of the fluctuation. 



Some four vears ago I examined ' a number of 

 hypotheses. The motions of the magnetic field of 

 the earth and of postulated fields on the~moon had to 

 be rejected, mainly because they caused impossible 

 increases in the mean motion of the perigee. An 

 equatorial ellipticity of the sun's mass, combined with 

 a rotation period very nearly one month in length, 

 appeared to be the best of these hypotheses. The 

 bvious objections to it are, first, that such an 

 llipticity, small as it can be (about i /2o,ooo), is diffi- 

 ult to understand on physical grounds, and, secondlv, 

 that the rotation period of the nucleus which might 

 be supposed to possess this elliptic shape in the sun's 

 equator is a quantitv'^ which is so doubtful that it 

 furnishes no help from observation, although the 

 obser\'ed periods are well within the required limits. 

 Dr. Hale's discovery- of the magnetic field of the sun 

 is of interest in this connection. Such a field. ' f 

 non-uniform strength, and rotating with the sun. is 

 mathematicallv exactly equivalent to an equatorial 

 ellipticity of the sun's mass, so that the hypothesis 

 might stand from the mathematical point of view, 

 the expression of the symbols in words being alone 

 different. 



The last published hypothesis is that of Prof. 

 Turner,' who assumes that the Leonids have finite 

 mass, and that a big swarm of them periodicallv dis- 

 turbs the moon as the orbits of the earth and the 

 swarm intersect. I had examined this myself last 

 summer, but rejected it because, although it explained 

 the straight line appearance of the cur\'e of fluctua- 

 tions, one of the most important of the changes of 

 direction in this curve was not accounted for. We 

 have the further difficulty that continual encounters 

 with the earth will spread the swarm along its orbit, 

 so that with this idea the swarm should be a late 



" Diss., Fr'ibure i., Br.. 1912. 



8 Anier. Jour. Sc, vol. xxix. 



9 Monthly Notices, December, 1913. 



NO. 2346, VOL. 94] 



arrival, and its periodic effect on the moon's motion 

 of diminishing amplitude; with respect to the latter, 

 the observed amplitude seems rather to have 

 increased. 



The main objection to all these ideas consists in the 

 fact that they stand alone : there is as yet little or no 

 collateral evidence from other sources. The difficulty, 

 in fact, is not that of finding a hypothesis to fit the 

 facts, but of selecting one out of many. The last 

 hypothesis which I shall mention is one which is less 

 definite than the others, but which does appear to have 

 some other evidence in its favour. 



The magnetic forces, mentioned above, were 

 changes in the directions of assumed magnetic fields. 

 If we assume changes in the intensities of the fields 

 themselves, we avoid the difficulties of altering por- 

 tions of the moon's motion other than that of the 

 mean motion. We know that the earth's magnetic 

 field varies and that the sun has such a field, and 

 there is no inherent improbability in attributing 

 similar fields to the moon and the planets. If we 

 assume that variations in the strength of these fields 

 arise in the sun and are communicated to the other 

 bodies of the solar system, we should expect fluctua- 

 tions having the same period and of the same or 

 opposite phase but differing in magnitude. It there- 

 fore beconies of interest to search for fluctuations in 

 the motions of the planets similar to that found in the 

 moon's orbit. The material in available form for this 

 purpose is rather scanty; it needs to be a long series 

 of observations reduced on a uniform plan. The best 

 I know is in Newcomb's '* Astronomical Constants." 

 He gives there the material for the earth arranged in 

 groups of a few years at a time. The results for 

 Mercury, given for another purpose, can also be ex- 

 tracted from the same place. For Venus and Mars, 

 Newcomb unfortunately only printed the normal 

 equations from which he deduces the constants of 

 the orbit. 



On the screen is shown a slide (see p. 190) which 

 exhibits the results for the Earth and Mercury com- 

 pared with those for the moon. In the uppermost 

 curve are reproduced the minor fluctuations of the 

 moon shown earlier; the second cur\e contains those 

 of the earth's longitude; the third, those of Mercury's 

 longitude. (By accident the mean motion correcticHi 

 has been left ' in the Earth curve ; the zero line is 

 therefore inclined instead of being horizontal.) It 

 will be noticed that the scales are different and that 

 the Earth cur\-e is reversed. In spite of the fact that 

 the probable errors of the results in the second and 

 third curves are not much less than their divergences 

 from a straight line, I think that the correlation ex- 

 hibited is of some significance. If it is, we have here 

 a force the period of which, if period in the strict sense 

 it has, is the same as that of the effect : the latter is 

 not then a resonance from combination with another 

 period. We must therefore look for some kind of a 

 surge spreading through the solar system and affect- 

 ing planets and satellites the same way but to 

 different degrees. 



The lowest curve is an old friend, that of Wolf's 

 sunspot frequency, put there, not for that reason, but 

 because the known connection for the last sixty years 

 between sunspot frequency and prevalence of magnetic 

 disturbance enables us with fair probability- to extend 

 the latter back to 1750. With some change of phase 

 the periods of high and low maxima corresf>ond nearly 

 with the fluctuations above. The eleven-year oscilla- 

 tion is naturally eliminated from the group results for 

 the Earth and Mercury. One might expect it to be 

 present in the lunar cur\'e, but owing to its shorter 

 period we should probably not obtain a coefficient of 

 more than half a second. Notwithstanding this fact, it 



