of long period in the mean motion of the Moon. 193 
anomalies of mean motion cannot be accounted for by a devia- 
tion from the received law of gravitation inversely as the 
square of the distance, because the anomalies produced by such 
deviation would be regularly progressive, and would be most 
sensible in the secular motion of the moon’s perigee. The com- 
parison of the theoretical and observed values of this motion is, 
ser passage of bodies could scarcely escape detection. Still, 
this explanation does not admit of being mathematically dis- 
proved. If we attribute the deviation to the impact of mete- 
oric matter, we must suppose the moon to have encountered 
such matter in quantities nearly incredible. 
These three causes exhaust those on which we can base the 
first explanation, unless we invalidate the third law of motion. 
For, by that law; matter moves only by the influence of other 
matter. er matter can affect the motion of the moon only 
by impact and gravitation. The gravitation of known bodies. 
the gravitation of unknown bodies, and the impact of matter is 
therefore an exhaustive enumeration. 
_ We pass now to the second explanation of the first hypothe- 
sis, namely, errors'or omissions in the theoretical computation 
of the effect of gravitation. The wide difference between the 
from the tables during the past ten years, without discordance 
? 
s 
ite close. 
hardly worth while to dwell upon this explanation until we 
in the quantity of ice accumulated around the poles has, I be- 
