Royal Society. 149 



spherical shell of uniform density (v), there will be no change in 

 the attraction which it exerts on any point external to both. Thus 

 suppose A B to be a section of the earth made by the plane of any 

 meridian, and suppose its matter to be solid and arranged in any 



manner. Take any point O, and with centre O and any radii O C 

 and O D describe spherical shells ; suppose a uniformly distributed 

 portion of the matter composing the former shell to be removed and 

 to be uniformly distributed on the latter shell. This can be done 

 without disturbing the attraction of the whole mass on any external 

 point. 



Since the point O may be taken anywhere within the earth, and 

 since the radii O C and O D are subject to no condition except that 

 the spheres whereof they are radii must fall wholly within A B, and 

 since the density of the transferred matter may have any value not 

 exceeding the least density of the part from which it is removed, it 

 is clear that the number of particular cases included in the proof is 

 indefinitely great. 



XX. Proceedings of Learned Societies. 



ROYAL SOCIETY. 



[Continued from vol. xxx. p. 318.] 



December 21, 1865. — Sir Henry Holland, Bart., Vice-President, in 

 the Chair. 



HP HE following communications were read : — 

 ■*■ " On the Expansion of Water and Mercury." By A. Mat- 

 thiessen, F.R.S. 



Before commencing a research into the expansion of the metals and 

 their alloys, it was necessary to prove that the method I intended 

 to employ, namely that of weighing the metal or alloy in water at 

 different temperatures, would yield good and reliable results. 

 Phil. Mag. S. 4. Vol. 31. No. 207. Feb. 1866. M 



