VOL. XLVIII,] PHILOSOPHICAL TRANSACTIONS. 331 



Supposing, for example, that the difference between the degrees of Paris and 

 Tornea has been found too great by 80 toises, the difference between the two 

 diameters will come out about -^i-o, which, subtracted from -rW, gives -j-Lj,. for 

 the diminution of the gravity from the pole to the equator. And such a con- 

 clusion would agree pretty well with the observations made in France and Lap- 

 land with the excellent clock of Mr. Graham. 



However, though the errors to be supposed in the operations, to reconcile 

 them with my theory, be in themselves small enough, I shall abstain from as- 

 serting that they have been committed. It is a fact not to be decided, till after 

 the result of the observations which are expected from Peru. For the great 

 difference which is to be found between the degrees of Quito and Tornea, is 

 the only means of knowing whether the diameters be less or greater than 230 

 to 23 1 . 



Were the question only, to demonstrate the flatness of the earth, the mea- 

 sures of the degree of Paris and Tornea would be full sufficient; but to discover 

 the true ratio of diameters, is what can be performed only by the comparison be- 

 tween the degrees whose mutual distance is the greatest. 



Such a ratio once fixed, if it happen to be less than 230 to 231, it will be 

 very easy, by the preceding theory, to imagine some hypothesis for the inside of 

 the earth, which shall agree with both theory and observation, whether admitting 

 the supposition of the original fluidity of the globe, or not. 



But if the diameters were found undoubtedly in a greater ratio to one another 

 than 230 to 231, I own, that not only the theory established in this second part 

 of my book must be abandoned, but it would be very difficult to reconcile the 

 measures of the pendulums with those of the degrees on Sir Isaac's system. 

 And I dare say, that the success in tliat case would hardly depend on any na- 

 tural hypothesis. 



The subsequent 70th article containing only a proof, that the preceding theory 

 agrees with any ratio between -^ and -^j for the quantity which expresses the ex- 

 cess of Jupiter's equator above its axis, there is no necessity for the translation of 

 the arguments leading to a result so answering to the observations ; and I pass to 

 the conclusion of that article, which ends my book. 



The preceding theory agreeing with all the measures of the pendulum, and 

 observations of Jupiter's diameters, if besides it happen, that the measures ex- 

 pected from Peru give, when compared with those of Lapland, a difference of 

 diameters less than -^-^-u-, this theory will have all possible confirmation, and the 

 universal gravitation so well agreeing with the motions of the planets, will also 

 agree with their figures. 



Now I beg every candid reader to examine, whether, in that chapter quoted 



u u 2 



