1866. | Adams’ Recent Astronomical Discovery. 513 
irregularity altogether. It is somewhat singular that in 1783 
Lagrange, after discussing the effects of perturbig forces on the 
mean motions of the planets, stated it “as a truth rigorously 
demonstrated, that the mutual attraction of the principal planets 
cannot produce any sensible alteration in their mean motions.” 
Had it occurred to him to apply his formule to the moon, to 
determine whether a similar freedom from secular inequalities 
exists among the secondary planets, he would not have had the 
mortification of seeing his gifted rival, Laplace, reap the honour 
of solving a problem which for ninety years had baffled the 
mathematical world. 
Laplace first convinced himself that the records of ancient 
eclipses fully proved the existence of the secular inequality in the 
moon’s mean motion. He then suggested three possible solutions, 
viz. that the phenomenon is due (1) to a continual retardation of 
the earth’s diurnal motion, or (ii) to the existence of a resisting 
medium, or (ii) to the non-instantaneous transmission of gravity. 
Not satisfied with any of these solutions, he sought again and 
again to detect in the sun’s disturbing action the source of the 
moon’s secular acceleration; but unsuccessfully, until 1787, when 
he was able to announce that the true cause of the phenomenon 
lies in the secular variation of the eccentricity of the earth’s orbit. 
To show how this happens it will be necessary to discuss briefly the 
important inequality called the annual equation, with which the 
minor inequality we are considering is most intimately connected. 
Remembering that the sun’s disturbing effect on the moon’s 
motion is measured by the difference of his effects on the earth and 
moon, it will be evident that when the moon is in syzygy (that is, 
“new” or “ full”), the attraction between the earth and moon is 
diminished, since the attraction of the sun on the nearer of the 
two bodies is greater than his attraction on the farther; but that 
when the moon is at or near either quadrature the attraction 
between the earth and moon is increased, since lines drawn from 
the sun to the earth and moon are nearly equal, but inclined at an 
appreciable angle. Now of these two disturbing effects the former 
is much the more powerful, since it is due to inequality of distance, 
while the other is exercised only through the effect of a minute 
obliquity of pull. And estimating the disturbing effects through a 
complete lunar revolution, it appears from similar considerations, 
that, on the whole, the effect of the swn’s action is to diminish the 
earth’s attractive influence over the moon. 
Now any diminution of the central force which retains a body 
in its orbit is necessarily accompanied by an increase in the major 
axis of the orbit of the disturbed body. Accordingly the moon 
takes a longer period in accomplishing each revolution around her 
primary than she would but for the sun’s disturbing influence. If 
