071 several Astronomical and Philosophical Suljecls. 83 



tion of the plummet made on both sides of the hill. These ope- 

 rations employed the years 177-t, 177^ and 177C ; and the me- 

 thod of performing them was stated by Dr. M. in the Philoso- 

 phical Transactions for the year 1775. 



*' Thus then the problem was performed, so far as showed expe- 

 rimentally that there is a mutual attraction in all matler ; and 

 that the sum of the two attractions on both sides of the hill in 

 particular, amounted to 11 '6 seconds. The Society were very 

 Well pleased with the operations. They also conferred on what 

 further use might be made of these measurements ; and it was per- 

 ceived that by their means, after due calculations made, the mean 

 density of the whole earth might be determined : for there were 

 now obtained these data; viz. the mass and attraction of the hill, 

 with the magnitude and attraction of the earth, to determine its 

 density and mass. This was of course a grand and most im- 

 portant object. But the question was, Who was to perform 

 the immense calculation that was requisite ? wlio would do it ? 

 and indeed who could do it ? There might be one or two per- 

 sons who were thought capable of undertaking the task ; but 

 those and all the other members of the Society stood aghast at 

 the prospect of the number and magnitude of the calculations, 

 and shrank with dread from the mighty labour. I was then looked 

 to, and asked by the President and Council to undertake the 

 task ; to which I was also strongly solicited by Dr. Maskelyne. 

 Being then a young member of the Society, and anxious to di- 

 stinguish myself, I undertook the operation and became respon- 

 sible for the result ; which, after the daily labour of nearly two 

 years, I produced to the Society, with a minute detail of the par- 

 ticulars of the calculations, accompanied with the appropriate 

 drawings. The Society were so well pleased with this work that 

 ■they awarded me a liberal premium, and printed my memoir in 

 the Philosophical Transactions for the year 1778, exactly in the 

 form in which I had delivered it. 



" It is to be observed, that in this operation, being the first of the 

 kind that was ever made, all the modes of calculation were to be 

 devised or invented ; and that, without several plans which 1 con- 

 trived, it might be doubted whether the labour could ever have 

 been accurately accomplished. To the ingenuity of these con- 

 trivances the most honourable testimony has lately been borne 

 by one of the best mathematicians in this kingdom, Professor 

 Playfair. The result of that calculation was, that the mean den- 

 sity of the earth is to that of the hill, in the ratio of 9 to 5. What 

 was the density of the hill, was then not known, and therefore 

 the density of the earth, as compared to water, could not then 

 be detcrnjincd. But to show the mode of making the coujpari- 



F 2 son. 



