1863.] 



287 



[Chase. 



The approximate estimates of the solar distance are based on the 

 following hypothesis : 



Let e = effective ratio of daily rotation to gravity. 



a = arc described by force of rotation in a given time t. 

 r = radius of relative sphere of attraction, or distance through 

 which a body would fail by gravity, during the disturbance of its 

 equilibrium by rotation. 



A =area described by radius vector in time t. 

 Let e', a' , r' , a', represent corresponding elements of the annual 

 revolution. Then, 



A. : a! : : ar : a! r' : : e- : e'"'- 

 But the forces of rotation and revolution are so connected, that a 

 differs but slightly from a! 



e^ : e'^ : : r : /■' ^ 



^J^ r very nearly. 



t'= e' ) 



It may be interesting to observe how nearly r (22,738,900 m.) 



D 

 corresponds with Kirkwood's value of (. (24,932,000 m.). A more 



thorough comprehension of all the various effects of gravity and 

 rotation on the atmosphere, would probably lead to modifications of 

 our formulae that would show a still closer correspondence. 



There is a great discrepancy between the determinations of the 

 solar distance that are based on the records of 1844 and 1846; but 

 it is no greater than we might reasonably have anticipated. On the 

 other hand, it could hardly have been expected that any comparisons 

 based on the observations of so short a period as three years, would 

 have furnished so near an approximation to the most recent and 

 most accurate determination of the earth's mean radius vector. In 



