ELECTRICAL UNITS OF MEASUREMENT. 101 



The semi-period of an infinitesimal satellite 

 revolving round the earth, close to its surface, 1 

 is equal to the semi-period of an ideal simple 

 pendulum of length equal to the earth's radius, 

 and having its weighted end infinitely near to 

 the earth's surface ; and therefore, when reckoned 

 in seconds, is approximately equal to the square 

 root of the number of metres (6,370,000) in the 

 earth's radius ; because the length of a seconds 

 pendulum (or the pendulum whose semi-period 

 is a second) is very approximately one metre. 

 Thus we find 2,524 mean solar seconds for the 

 semi-period of the satellite, and its angular velocity 

 in radians per second is therefore (77/2524=) 

 0*001244: hence the earth's mean density, reck- 

 oned on the universal-gravitation system, with the 

 mean solar second for the unit of time, is 

 [(0-001244)2 X 3/(47r) = ] 370 X io~ 7 ; and, if we 

 take (from Bailey's repetition of Cavendish's 

 experiment), 2 the earth's mean density as 5-67 



1 Thomson and Tait's Natural Philosophy, 2nd edition, vol. i., 

 parti., 223. 



2 M. Cornu has criticised Bailey's method of reducing his observa- 

 tions, in respect to allowance for viscous diminution of the oscilla- 



