334 PHILOSOPHICAL TRANSACTIONS. [anNO 1753. 



ceiving the inside of the earth ; and I imagined, that he had happened to fall on 

 such a disposition of parts, as would answer to his assertion. I then followed 

 only his commentators, and especially Dr. Gregory, showing, that his explana- 

 tion of Sir Isaac's conclusion was wrong, as grounded on a proposition which 

 did not hold in the present case. For that proposition (which is, that the gra- 

 vity at any point of the earth is inversedly as the distance from the centre) only 

 holds when the earth is homogeneous ; and consequently ought not to be made 

 use of, when the density is greater towards the centre than at the superficies.' 



' Since I have discovered that the theorem, the demonstration of which I had 

 given in the Philos. Trans, for the case of beds supposed of the same ellipticity, 

 holds in an infinity of other suppositions, I have taken greater care to discover 

 what could have induced Sir Isaac to think, that the earth is flatter, as the gravity 

 is more decreasing from the pole towards the equator ; and I believe I have found 

 it out in the second edition of the Principia, and it is, for having built on the 

 same argument as Dr. Gregory.* 



' In p. 386, after having observed, that the experiments gave a diminution of 

 two lines to the second pendulum from the pole to the equator, he argues thus : 

 Since, says he, the case of homogeneity afforded only 1 yg^.„ to 4, the difference 

 7-^ miles between the two diameters (which followed from the same hypothesis) 

 is to be magnified in the ratio of 1 1 g ^ „ to 2, and it will come out 31-tV miles 

 for the real difference. For, pursues he, the retardation of the pendulum at the 

 equator denotes the diminution of the gravity in that place ; and the lighter the 

 matter is there, the higher will it rise to be equiponderant with that of the pole.' 



' Further, p. 387, examining the measures of the degrees of latitude made in 

 France by M. Cassini, by which the earth is higher at the pole than at the 

 equator by about 95 miles, he pretends, that accordingly the pendulum should 

 be longer at the equator than at the pole by about half an inch. And all that 

 shows the opinion which Sir Isaac was of, that in any case whatever, the equili- 

 brium requires a gravity inversely proportional to the length of the columns, 

 which proportion, as I hope to have evinced, is only demonstrated in the case of 

 homogeneity, and is not true in general. Thus, what I argued in the Phil. 

 Trans, against Dr. Gregory, holds also against Sir Isaac' 



By all that I have said, every body may judge, whether differing from Sir 

 Isaac's sentiments on a point, which I had for so long a time examined, I did 

 not express my disagreement with him in as decent a manner as any one should, 

 when speaking of so great a man. And in case the r. s. thought some alterations 

 were to be made in the form of my remarks, I declare that I shall execute it, as 

 may be prescribed to me by that illustrious company. But I cannot help think- 

 ing, that unless those, who would examine my demonstrations, find some error 

 in them, no alteration is requisite to be made in my expressions. I desire then 



