809 
The idea of explaining these fluctuations by an absorption of the 
gravitational attraction of the sun upon the moon by the earth 
during lunar eclipses, has for the first time been publicly worked 
out by Mr. Borrninerr’), the investigation having been proposed as 
the subject of a prize essay by the philosophical faculty of the 
University of Munich. I had also towards the end of 1909 com- 
menced a similar investigation, which was however ofa preliminary 
character and, as it did not lead to positive results, was discontinued 
and not published. The publication of Mr. Borriincmr’s dissertation 
led me to resume the investigation. . 
The decrease of the attraction of the sun upon the moon can be 
taken into account by adding to the forces considered in the ordinary 
lunar ‘theory a perturbing force acting in the direction of the line 
joining the sun and the moon, in tke direction away from the sun. 
If the sun and moon are treated as material points, this force is 
| EN PA 
m nh, ma 
en : ee (ee Ot ae ee = RL) 
: 
The meaning of the letters is: 
m’ == mass of the sun, 
n’, a’ = mean motion and mean distance of the earth, 
n, a= the same elements of the moon (osculating values), 
n,,@, — the mean values of these elements, 
A, r/ = distance of sun from moon and earth, 
B did nen 
The effect on the elements of the moon’s orbit can be computed 
by the ordinary formulas. The perturbing forces are: 
radial force H cos B cos &—'), 
transversal dt. H cos B sin (6—$’), 
orthogonal » —H sins, 
where $ and 8 are the selenocentric longitudes of the earth and sun, 
and 8 is the selenocentric latitude of the sun, the moon’s orbital 
plane being taken as fundamental plane. For the instant of central 
eclipse we have $—S’=0. The transversal force therefore changes 
its sign during the eclipse, and its total effect is very nearly zero. 
The effect of the orthogonal force is entirely negligible. In the 
expression of the radial force, we can put cos ($—$’) = 1. We have 
further with sufficient accuracy | 
A =, Se Bice EE 
1) K. F. BorrunceR. Die Gravitationstheorie und die Bewegung des*Mondes. 
Inaugural-Dissertation (München). 1912. 
See also “The Observatory” November 1912. 
