Septembee 18, 1914] 



SCIENCE 



399 



combined with a rotation period very nearly 

 one month in length, appeared to be the 

 best of these hypotheses. The obvious ob- 

 jections to it are, first, that such an eUip- 

 tieity, small as it can be (about 1/20,000), 

 is difficult to understand on physical 

 grounds, and, second, that the rotation 

 period of the nucleus which might be sup- 

 posed to possess this elliptic shape in the 

 sun's equator is a quantity which is so 

 doubtful that it furnishes no help from ob- 

 servation, although the observed 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, of non-uniform strength, and 

 rotating with the sun, is mathematically 

 exactly equivalent to an equatorial ellip- 

 ticity of the sun's mass, so that the hypoth- 

 esis 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 

 Professor Turner,^" who assumes that the 

 Leonids have finite mass and that a big 

 swarm of them periodically disturbs the 

 moon as the orbits of the earth and the 

 swarm intersect. I had examined this my- 

 self last summer, but rejected it because, 

 although it explained the straight line ap- 

 pearance of the curve of fluctuations, 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 

 the swarm with this idea should be a late 

 arrival and its periodic effect on the moon's 

 motion of diminishing amplitude; with re- 

 spect to the latter, the observed amplitude 

 seems rather to have increased. 



The main objection to all these ideas con- 

 sists in the fact that they stand alone: 

 there is as yet little or no collateral evi- 



10 Monthly Notices, December, 1913. 



dence 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 favor. 



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 portions 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 im- 

 probability 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 communi- 

 cated to the other bodies of the solar sys- 

 tem, we should expect fluctuations having 

 the same period and of the same or oppo- 

 site phase but differing in magnitude. It 

 therefore becomes 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 pur- 

 pose 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 re- 

 sults for Mercury, given for another pur- 

 pose, can also be extracted from the same 

 place. For Venus and Mars, Newcomb un- 

 fortunately only printed the normal equa- 

 tions from which he deduces the constants 

 of the orbit. 



On the screen is shown a slide which ex- 

 hibits the results for the earth and Mer- 

 cury compared with those for the moon. 

 In the uppermost curve are reproduced the 

 minor fluctuations of the moon shown 



