244 NOTICES OF THE MEETINGS [ Feb. 4, 
upon the moon tending to draw it towards the earth is not simply the 
attraction of the earth, but consists of that attraction diminished by 
a disturbing force which is produced by the sun’s attraction. The 
sun sometimes attracts the moon towards the earth or the earth to- 
wards the moon, sometimes it produces the opposite effect ; but on 
the whole it tends to pull the moon away from the earth. And this 
diminution of the earth’s attraction is greater as the sun is nearer ; 
and therefore, in an elliptic orbit such as the earth describes about 
the sun (or such as the sun appears to describe about the earth), 
the diminution of the earth’s attraction is greater when the earth 
is nearest to the sun than when the earth is farthest from the 
sun. It might be supposed that one of these effects exceeds that 
which would happen when the earth is at its mean distance from 
the sun, as much as the other falls short of it; but in reality 
the excess is greater than the deficiency, and therefore the more 
excentric the earth’s orbit is, the greater is this disturbing force. 
So long as these circumstances remain the same, the magnitude of 
the moon’s orbit will not be sensibly altered. But the fact is, 
that, in consequence of the perturbations produced by the planets, 
though the earth’s mean distance from the sun remains unaltered 
from age to age, yet the excentricity of its orbit is diminishing 
from age to age; the sun’s disturbing force is therefore diminishing 
from age to age: and the real force which acts upon the moon as 
tending to draw it towards the earth is therefore increasing from 
age to age; and, from age to age, the moon approaches a little 
nearer to the earth and performs her revolutions alittle quicker. This 
effect is extremely small. Between one lunation and the next 
(taken one with another) the moon’s distance from the earth is 
diminished by about ;, of an inch; it would seem at first that 
this could produce no discoverable effect in the moon’s motion: but 
one of the most wonderful things in the application of the laws of 
mechanics generally, and the law of gravitation in particular (where 
the magnitude of the force varies with the variation of distance), is, 
that the effect of a variation of a small fraction of an inch is as 
certain, in proportion to its magnitude, as that of a thousand miles. 
Still the effect produced in the moon’s apparent motion is very 
small: in a century it amounts to only ten seconds ; an angle which, 
when expressed in the usual way by the breadth of a known object 
as seen at a known distance, is less than the angle subtended by the 
human hand as seen at the distance of a mile. Yet in the course of 
twenty-four centuries the effect of this becomes so important as, in 
the case of eclipses, completely to change the face of the heavens ; 
an eclipse might happen in Asia or Africa which, but for this consi- 
deration, we might expect to occur at that time in America. 
Shortly after the discovery of this secular change, the French lunar 
tables (Biirg’s) were constructed, the first which introduced this ele- 
ment. The late Mr. Francis Baily soon made use of these in an in- 
vestigation of the date of the eclipse of Thales, which deserves to be 
