TRANSACTIONS OF SECTION A. 319 
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 gravitation by interposing matter, e.g. at the time of 
eclipses, has been examined by Bottlinger." For one reason alone, I believe this 
is very 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 amywhere near any period present in the moon’s 
motion or any probable combination of the moon’s periods. Indeed 
Dr. Bottlinger’s curve shows this: there is no trace of the fluctuation. 
Some four years 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 oné month in length, appeared to be the best of 
these hypotheses. The obvious objections to it are, first, that such an ellip- 
ticity, 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 
supposed to possess this elliptic shape in the sun’s equator is a quantity which 
is so doubtful that it furnishes no help from observation, 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 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 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 myself last summer, but rejected it because, although it 
explained the straight line appearance 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 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 an 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 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 impro- 
bability 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 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 purpose is rather scanty; it needs to be 
’ Diss., Freiburg i. Br., 1912. 8 Amer. Jour. -Sc., vol. 29. 
® Monthly Notices, December 1913. - 
