108 PROCEEDINGS OF THE AMERICAN ACADEMY 



37£ times greater than at present. It can never, therefore, have been 

 reduced to so great an extent by the moon's action on the tides. But 

 since, when the oblateness is small, the rotation area is nearly, propor- 

 tional to the velocity, and the excess of the square of the equatorial 

 above that of the polar axis is nearly proportional to the square of 

 the velocity, this excess may have been originally nearly 18 times as 

 great as at present, or about 15£ per cent of the square of the polar 

 axis. This would correspond to a figure of the earth in which the 

 equatorial radius would have been about 2^- per cent greater than 

 at present ; so that it is sufficient to account for the observed phe- 

 nomenon. 



This peculiar form of shrinkage would produce the highest moun- 

 tains at the equator, and the tendency of the mountain ranges would 

 then be to assume the direction of the meridian. But nearer the poles 

 the mountains would be less elevated, and would rather tend towards 

 the direction of the parallels of latitude. 



It is, next, expedient to consider the mechanical question of the loss 

 of living force in the case of the moon's action upon the waters of the 

 earth, and its effect upon their different motions. In this connection 

 there are problems worthy of the attention of Geometers ; such as the 

 relative motions of bodies rotating above the same vertical axis, towards 

 which they are drawn by weights, and acting upon each other through 

 the friction on the axis. For one of the bodies a rotating wheel may 

 be substituted. There is also the case of two planets revolving about 

 a primary, and acting upon each other through some form of friction. 



In this way, it will be seen that the planet or satellite once formed 

 is constantly removed from the primary, and that planets tend to 

 approach each other. It is interesting to consider whether this may 

 not be one of the actual problems of nature. 



Six hundred and ninth Meeting. 



May 25, 1869. — Annual Meeting. 



In the absence of the regular presiding officers, Hon. Robert 

 C. Winthrop was chosen to take the chair. 



The Chairman called the attention of the Academy to the 

 recent decease of Hon. William Mitchell and of Dr. William 

 Allen, both of them Resident Fellows. 



