f 60 ] 



VI . On the Density of the Earth, deduced from the Experiments 

 of the Astronomer Royal, in Harton Coal-pit. By the Rev. 

 Samuel Haughton, M.A.j Fellow of Trinity College, Dublin^. 



SOME time ago the following density of the earth was de- 

 duced by me, by the aid of very simple considerations, from 

 the pendulum observations of the Astronomer Royal in Harton 

 Coal-pit, South Shields, as reported in the newspapers. 



The method of deducing the density is rough, and cannot be 

 considered as having the same value as the more precise and 

 detailed considerations on which Mr. Airy has based his own 

 calculations ; yet as it is simple, and easily understood, it may 

 prove of some interest to the readers of the Philosophical Maga- 

 zine. It is based on the following facts : — 



1st. From the fact that the seconds^ pendulum gains 2^ 

 seconds per day at the bottom of the coal-pit, I infer that gra- 

 vity at the surface is to gravity at the bottom of the pit as 19200 

 to 39201. 



2nd. If a spheroidal shell be drawn through the bottom of the 

 coal-pit similar to the spheroid forming the surface of the sea, 

 the mass of the whole earth is equal to the mass of this spheroid, 

 plus the matter exterior to it, including sea and land. 



The two foregoing propositions, being facts, will easily be ad- 

 mitted ; I now add to them an hypothesis which very probably 

 does not deviate far from the truth ; it is as follows : — 



That the attraction of the sea and land, external to the sphe- 

 roid through the bottom of the coal-pit, does not differ sensibly from 

 the attraction of a shell bounded externally by a similar surface, 

 and having a mean density the same as the mean density of the sea 

 and land external to the spheroid. 



If this be admitted, we can state the two facts already given 

 as follows:— 19201 A . h\ ^ 



^=T9200(l-^r)^' W 



A= (1+1^)8+?,% (2) 



In these equations — 



A is the mean density of the whole earth ; 



h is the mean density of the portion included by the sphe- 

 roid passing through the bottom of the coal-pit ; 



p is the mean density of the land and water above the bot- 

 tom of the coal-pit ; 



- is the ratio of the depth of the coal-pit to the radius of 



the earth. 



* Communicated by the Author. 



