40 Prof. J. H. Pointing. Determination of Mean [June 4, 



II. "On a Determination of the Mean Density of the Earth 

 and the Gravitation Constant by means of the Common 

 Balance." By J. H. POYNTING, D.Sc., F.R.S., Professor of 

 Physics, Mason College, Birmingham. Received May 13, 

 1891. 



(Abstract.) 



In a paper printed in the ' Proceedings of the Royal Society,' 

 No. 190, 1878, an account was given of some experiments undertaken 

 in order to test the possibility of using the common balance in place 

 of the torsion balance in the Cavendish experiment. The success 

 obtained seemed to justify the continuation of the work, and this 

 paper contains an account of an experiment carried out with a large 

 .bullion balance, in place of the chemical balance used in the pre- 

 liminary trials. The work has been carried out at the Mason College, 

 Birmingham. 



The Principle of the Experiment. The immediate object of the 

 experiment may be regarded as the determination of the attraction of 

 one known mass on another. If two spheres, of masses M and M', 

 have their centres a distance d apart, the attraction is, according to 

 the law of gravitation, GMM'/d 2 , where G is the gravitation constant. 

 Astronomy justifies the law in certain cases as regards M'/d 2 , but 

 does not give the value of G or M, except in the product GM. To 

 find G we mast measure GMM'/d 2 in some case in which both M and 

 M' are known. Having found G, we may determine the mean 

 density of the earth, for, assuming that it is a sphere of radius R, the 

 weight of any mass M' at its surface is 



Gx|7rR 3 AM'/R 2 



But if g is the acceleration of gravity the weight of M' may be 

 expressed as M'gr. Equating these values, we get 



Method of Using the Common 'Balance. With the length of beam 

 used (about 123 cm.) a differential method was applicable, in which 

 the attraction on the beam was eliminated. Two spherical masses of 

 lead and antimony, about 21 kilos, each, were hung from the two 

 arms of the balance, so that their centres in the first position 

 were about 30 cm. above the centre of a large attracting mass, a 

 sphere of lead and antimony about 153 kilos., placed on a turntable, 



