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POPULAR SCIENCE REVIEW. 
has enlarged the orbit of the moon, this body will move slower 
around the earth, the sun will have greater power over it and 
will be able to still further enlarge the orbit and cause the 
moon to revolve still slower around the earth. As this action 
will continue to accumulate for over one hundred years at a time, 
at the end of this period it may amount to a considerable 
retardation of the moon. From this effect of the attraction of 
the sun on the effect produced by the attraction of Venus, 
exactly similar inequalities will be produced to those arising 
from the action of the planet alone. From certain expressions on 
the part of Hansen it seems that he has not failed to take these 
circumstances into account, whilst Delaunay has entirely omitted 
to consider them in his investigations, so that his researches 
must be held to be imperfect. It is evident, therefore, that 
further research will be required to satisfactorily determine the 
value of these two terms of long period, and to decide whether 
Delaunay or Hansen is correct, or whether either is. And 
until this is done the theory of the terms of long period in the 
motion of the moon must be held to be in an unsatisfactory 
condition. 
It is well known that the mean motion of the moon is at 
present slowly increasing, so that there is a gradual acceleration 
in the velocity with which it moves around the earth. This 
secular acceleration was discovered by Halley, a celebrated 
English astronomer, and for many years the greatest mathe- 
maticians were unable to discover its cause. In 1787, however, 
Laplace discovered that from the slow change in the eccentricity 
of the orbit of the earth, the mean motion of the moon would 
have a gradual secular acceleration, and on calculating what it 
would be, he found it would amount to rather over 10" in a 
century. Now this was exactly the amount of the observed 
acceleration which had been discovered by Halley. Laplace’s 
discovery appeared, therefore, to completely account for this 
observed acceleration of the velocity of the moon’s revolution 
around the earth. Twenty-five years ago Professor Adams dis- 
covered that when the calculations were carried to a higher order 
of accuracy than had been considered necessary by Laplace, it 
very much reduced the value of the secular acceleration due to 
the decrease in the eccentricity of the orbit of the earth. At 
the time this discovery of Professor Adams gave rise to a very 
animated controversy, but it is now certain that the views of 
Professor Adams are perfectly correct, and that the secular 
acceleration in the mean motion of the moon which is due to 
the decrease in the eccentricity of the orbit of the earth, does 
not amount to more than 6*2" in a century. 
Professor Hansen, when he compared his tables with the 
ancient observations, found that they indicated a value of the 
