516 Adams’ Recent Astronomical Discovery. [ Oct., 
acceleration equal to the mean of these values as to leave nothing 
to be desired. On the other hand, a change of 2” or 3” in the 
assumed value of the acceleration introduces difficulties into the 
explanation of most of the eclipses, and renders the occurrence of 
some of them physically impossible. 
Despite this accordance, which would have deterred most men 
from the labour attending the re-investigation of a subject of such 
difficulty, Adams subjected the problem several years ago to strict 
and rigid scrutiny. In a memoir read before the Royal Society of 
London in 1858, he pointed out a cause of disturbance which 
Laplace and those who had followed him in the calculation of the 
acceleration had overlooked. We have seen that Laplace had 
investigated the effect of the central disturbing force only, assuming 
that the tangential disturbing force would give rise to no perma- 
nent alteration of the moon’s mean angular velocity ; or, in other 
words, Laplace had assumed that the area described by the moon 
about the earth in a given time undergoes no permanent alteration. 
Now, Adams pointed out that when the variability of the eccen- 
tricity of the earth’s orbit is taken imto account, in integrating the 
differential equations involved in the problem of the lunar motions 
(in other words, when the eccentricity is made a function of the 
time), non-periodic or secular terms appear in the expression for 
the moon’s mean motion, and that their effect is to dimimish con- 
siderably the co-efficient of the lunar acceleration. 
In 1856 M. Plana published a paper, in which he expressed 
his acquiescence with Adams’ views, but later he retracted this 
admission. In 1859 M. Delaunay deduced the same result as 
Adams, who then published the results of a new investigation, im 
which he had calculated terms even of the seventh order. The 
value thus calculated was 5’:7. Three months later M. Delaunay 
had carried the calculation to terms of the eighth order, and 
assigned 6:11 as the value of the co-efficient. 
At this stage the views of Adams became the subject of con- 
troversy, which for a long time occupied much attention among 
astronomers. In May, 1859, Pontécoulant entered the field. He 
objected energetically to the “new terms” developed by Adams, 
whose processes he characterized as “une véritable supercherie 
analytique.” Hansen pointed out the remarkable coincidence be- 
tween the value he had obtained and the records of ancient eclipses. 
Mr. Main examined the question, and came to the conclusion that 
Adams and Delaunay were in the right, but that Hansen’s larger 
value was needed to satisfy the records of ancient eclipses. Levyerrier, 
on the other hand, declared unreservedly against Adams and 
Delaunay: ‘‘ Nous conservons des doutes et plus que des doutes,” 
he said, “sur les formules de M. Delaunay—trés-certainement la 
vérité est du coté de M. Hansen.” 
