VOL. XLVIII.] PHILOSOPHICAL TRANSACTIONS. 333 



while I have not given room to know them on that point ? How can he know 

 whether, since the examination of all the measures, I have not found any way to 

 reconcile them with the theory ? Which I say in no manner as a hint I intend to 

 make any corrections in those measures, but merely to show the little foundation 

 which F. Frisi had to represent me as he has done. 



However difficult it may be to account for F. Frisi's expressions, I shall hazard 

 yet another conjecture. His great zeal for Sir Isaac, for which he is certainly to 

 be commended (if not blinded by that zeal) has hindered him from distinguish- 

 ing between the different ways of opposing that great man's sentiments. Per- 

 ceiving then, that my calculations (§ 50, part 2) had led me to a result quite 

 different from Sir Isaac's assertion, (Prop. 20, lib. 3), he was offended at my 

 boldness to such a degree, that he was unable to examine impartially what I 

 said ; and instead of discussing a mathematical question quite independent of any 

 actual measure, wherein if I were mistaken, he would have forced every geome- 

 trician to condemn me, he has supposed that I have built my argument on an 

 operation which was not performed at the time when I wrote. 



Tliis conjecture would appear to me the true cause of F. Frisi's error, if it 

 were not inconsistent with a proceeding of his towards Sir Isaac, which I will 

 venture to relate. After F. Frisi has examined himself the IQth problem of the 

 third book of the Principia, which is much less complicated than that I spoke 

 of, the truth of which is incontestable, he finds, by his own mistake, a disagree- 

 ment with the result of that proposition, and charges that illustrious author, 

 without the least apology, with an error, which, says he, (quite from the pur- 

 pose) is the 6th, that has been found in the same work, and also gives an enu- 

 meration of the 5 others, though they are not at all concerned in the question. ^ 



I cannot forbear saying, that the manner in which I have proposed my re- 

 marks on the 20th proposition of Sir Isaac, has nothing of that slight way of 

 treating so great a man ; and as my utmost wish is to be judged on that account 

 by the Royal Society, I shall relate what were my objections ; which I cannot 

 effect in a more concise and clear method, than by giving the translation of the 

 article which contains it. 



^ 51. Of the 2d part of the theorj', 8ec. ' In which is seen what had induced 

 Sir Isaac Newton to think, that the planets, when denser at the centre than at 

 the surface, ought to be flatter than in case of homogeneity.' 



' Some years ago I gave, in the Philos. Trans. N° 449, the theorem of the 

 preceding article ; and on this occasion I mentioned a passage of Sir Isaac con- 

 trary to it. Not having at that time looked into the 2d edition of his Principia, 

 I could not know what had engaged that illustrious philosopher to think so ; and 

 far from suspecting any mistake in his proposition, I was contented to think, 

 that the difference between our conclusions arose from a different way of con- 



