VOL. LXVin.] PHILOSOPHICAL TRANSACTIONS. 4ip 



all the measures of degrees there set down, that mean being 37038 toises. Dr. 

 H. therefore uses the round number 57030 as probably nearer the truth. This 

 number being multiplied by 6, the product 342180 shows the number of French 

 feet in one degree ; but, by p. 326 of the same volume, the lengths of the 

 Paris and London feet are as 76.734 to 72, that is, as 4.263 to 4 ; therefore, as 

 4 : 4.263 :: 342180 : 364678 = the English feet in one degree ; and this being 

 multiplied by 36o the whole number of degrees, there results 131284080 feet 

 for the whole circumference, which are equal to 248644- miles, making 69-^4- to 

 a degree in the mean latitude. Lastly, -§- of 13 1 284080 give 87522720 for the 

 measure of the attraction of the whole earth. 



Consequently, the whole attraction of the earth is to the sum of the two 

 contrary attractions of the hill, as the number 87522720 to 881 1-S-, that is, as 

 9933 to 1 very nearly, on supposition that the density of the matter in the hill is 

 equal to the mean density of that in the whole earth. 



But the Astronomer Royal found, by his observations, that the sum of the 

 deviations of the plumb-line, produced by the two contrary attractions, was 11.6 

 seconds. Hence then it is to be inferred, that the attraction of the earth is 

 actually to the sum of the attractions of the hill, nearly as radius to the tangent 

 of 11.6 seconds, that is, as 1 to .000056239, or as 17781 to 1 ; or as 178O4 to 

 1 nearly, after allowing for the centrifugal force arising from the rotation of the 

 earth about its axis. 



Having now obtained the 2 results, namely, that which arises from the actual 

 observations, and that belonging to the computation on the supposition of an 

 equal density in the two bodies, the two proportions compared must give the 

 ratio of their densities, which is that of 17804 to 9933, or 1434 to 800 nearly, 

 or almost as 9 to 5. And so much does the mean density of the earth exceed 

 that of the hill. 



Thus then we have at length obtained the object which we have been in quest 

 of through the very laborious calculations that have been described in this paper, 

 and in the survey and measurements from which these computations were made ; 

 namely, the ratio of the mean density of all the matter in the earth, in com- 

 parison with the density of the matter of which the hill is composed. And that 

 ratio we have found to be equal to the ratio of 9 to 5. And, for the reasons 

 beforementioned, it seems we may rest satisfied, that this proportion is obtained 

 to a considerable degree of proximity, probably to within the 50th part, if not 

 the 100th part of its true magnitude. Another question however still arises, 

 namely, what is the density of the matter in the hill ? Is its mean density 

 equal to that of water, of sand, of clay, of chalk, of stone, or of some of the 

 metals ? For, according to the matter, or different sorts of matter, of which 

 it is formed, and according as it is constituted with or without large vacuities, its 



3 H 2 



