TRANSACTIONS OF SECTION A. 315 
moon from its theoretical orbit, in which, of course, errors of observation are 
included. The first two slides exhibit the average deviation of the moon from 
its computed place for the past century and a half in longitude.? The averages 
are taken over periods of 414 days and each point of the continuous line 
shows one such average. The dots are the results obtained by Newcomb from 
occultations; the averages for the first century are taken over periods of 
several years, and in the last sixty years over every year. In both cases the 
same theory and the same values of the constants have been used. Only 
one empirical term has been taken out—the long-period fluctuation found by 
Newcomb having a period of 270 years and a co-efficient of 13/. I shall show 
the deviations with this term included, in a moment. 
The first point to which attention should be drawn is the agreement of the 
results deduced from the Greenwich meridian observations and those deduced 
from occultations gathered from observatories all over the world. There can be 
no doubt that the fluctuations are real and not due to errors of observation. 
A considerable difference appears about 1820, for which I have not been able to 
account, but I have reasons for thinking that the difference is mainly due to 
errors in the occultations rather than in the meridian values. In the last sixty 
years the differences become comparatively small, and the character of the 
deviation of the moon from its theoretical orbit is well marked. This deviation 
is obviously of a periodic character, but attempts to analyse it into one or two 
periodic terms have not met with success; the number of terms required for 
the purpose is too great to allow one to feel that they have a real existence, 
and that they would combine to represent the motion in the future. The 
straight line character of the deviations is a rather marked peculiarity of the 
curves. 
The actual deviations on a smaller scale are shown in the next slide; the 
great empirical term has here been restored and is shown by a broken line. 
The continuous line represents the Greenwich meridian observations; the dots 
are Newcomb’s results for the occultations before 1750, the date at which the 
meridian observations begin. With a very slight amount of smoothing, 
especially since 1850, this diagram may be considered to show the actual 
deviations of the moon from its theoretical orbit. 
The next slide shows the average values of the eccentricity and of the 
position of the perigee.? The deviations are those from the values which I have 
obtained. It is obvious at once that there is little or nothing systematic about 
them; they may be put down almost entirely to errors of observation. The 
diminishing magnitude of the deviations as time goes on is good evidence for 
this; the accuracy of the observations has steadily increased. The coefficient 
of the term on which the eccentricity depends is found with a probable error of 
0/-02, and the portion from 1750 to 1850 gives a value for it which agrees with 
that deduced from the portion 1850 to 1901 within 0/-01. The eccentricity is 
the constant which is now known with the highest degree of accuracy of any 
of those in the moon’s motion. For the perigee there was a difference from 
the theoretical motion which would have caused the horizontal average in the 
curve to be tilted up one end over 2” above that at the other end. I have taken 
this out, ascribing it to a wrong value for the earth’s ellipticity; the point will 
be again referred to later. The actual value obtained from the observations 
themselves has been used in the diagram, so that the deviations shown are 
deviations from the observed value. 
The next slide shows the deviations of the mean inclination and the motion 
of the node, as well as of the mean latitude from the values deduced from 
the observations.* In these cases the observations only run from 1847 to 1901. 
Tt did not seem worth while to extend them back to 1750 for it is evident 
that the errors are mainly accidental, and the mean results agreed so closely 
with those obtained by Newcomb from occultations that little would have been 
1 Monthly Notices R.A.S., vol. 73, plate 22. 
* Tables II., III. of a Paper on ‘The Perigee and Eccentricity of the 
Moon,’ Monthly Notices R.A.S., March 1914. 
° «The Mean Latitudes of the Sun and Moon,’ Monthly Notices R.A.S. 
Jan. 1914; ‘The Determination of the Constants of the Node, the Inclination, 
the Earth’s Ellipticity, and the Obliquity of the Ecliptic, id. June 1914. 
