560 proceedings: philosophical society 



or 3 terms of an infinite series. An expression in closed form may be 

 derived, if it is assumed that the surface of the earth is an equipotential 

 surface having the form of an elhpsoid of revolution. The expression 

 for the surface gravity g is: 



Vl - e" sin^ <p + mef (e) , ~ ^ =^ siir <p 



Vl-e sin% 



In this equation cjo is the force of gravity at the equator, e is the eccen- 

 tricity of a meridian ellipse, (p is the geographic latitude, m is ratio 

 of the centrifugal force at the equator to gravity there, and 



the Q's being zonal harmonics of the second kind. An expression was 



also derived for — , the rate of decrease of gravity with elevation above 



the earth's surface, the results agreeing with those derived from a for- 

 mula given by Helmert. Attention was drawn to the fact that Hel- 

 mert's formula is really a geometrical interpretation of Laplace's equation 

 and hence is more general than might appear from Helmert's proof of 

 it. The paper was discussed by Messrs. Swann and L. J. Beiggs. 



J. A. Fleming, 



Secretary. 



