230 
ON SOME RECENT CONTRIBUTIONS TO THE THEORY 
OF THE MOTION OF THE MOON. 
By E. NEISON, F.R.A.S. 
A QUARTER of a century has now elapsed since the late Pro- 
fessor Hansen, of Seeberg, near Gfotha, completed his 
elaborate researches on the motion of the moon, and he was 
enabled to announce that the lunar theory as developed by him 
fully represented the motion of the moon during the preceding 
century 1750-1850. Professor Hansen had then been at work 
on this recondite subject for nearly thirty years, and had won a 
high reputation, not only from the ingenious and powerful 
methods he had devised for attacking the most difficult problems 
of gravitational astronomy, but also from the entire mastery 
over the minutest details of the lunar theory which he had shown 
by his discovery of two inequalities of long period in the motion 
of the moon due to the attraction of the planet Venus. This 
announcement of Professor Hansen’s coming from so high an 
authority was most gratifying to astronomers, for it showed that 
after one hundred years’ work science had at last gained com- 
plete mastery over one of the most difficult problems of astronomy. 
The discovery by Professor Hansen of the existence of these 
two terms of long period was a step of the greatest importance, 
for it appeared to completely remove the last great difficulty in 
the lunar theory, a difficulty which had been puzzling astrono- 
mers for many years ; and it has been termed by Sir Gr. Airy 
“ one of the greatest steps — perhaps the greatest step — in gravi- 
tational astronomy.” For years it had been known that the 
moon was at times before, and at other times behind, the place 
in its orbit which it should have theoretically occupied. It had 
further been shown that this alternate retardation and accelera- 
tion was periodical in its character, and that it required about 
ninety years to proceed from one extreme to the other. This 
difference, moreover, was not unimportant, for at one time the 
moon would reach any fixed point in its orbit more than half a 
minute before its theoretical time, and at some other period it 
would he over half a minute later than the time fixed by theory. 
And what rendered this inequality the more perplexing to 
astronomers was the fact that they could not imagine any source 
from which it was even possible that there could arise such an 
