VOT. XLVIII.] PHILOSOPHICAL TRANSACTIONS. 30/ 



the magnitude and figure of the earth, down to the present times; and the pre- 

 ference is justly given to the measurements of Mr. Lat. Toises 



Norwood in England, a. d. i635, and of the mem- O" O' 56753 



bers of the French Academy of Sciences since that 45 57100 



time. From these he gathers, that within less than 4Q 11 57183 



60 or 70 toises, the lengths of a degree of the meri- 53 57300 



dian are as annexed. &^ 20 57400 



Chap. 1 contains an account of the principles on which this theory is founded, 

 viz. the universal gravitation of matter, and the diurnal rotation of the earth. 

 Our author mentions also the hypothesis of the earth's being originally in a fluid 

 state; but rejects it as precarious and improbable. He allows however, that with 

 regard to the present question, it is all one whether it was first a fluid or not, 

 seeing the ocean is circumfused just in the same manner, and to the same alti- 

 tude, as if the whole was still a fluid. Chap. 3 and 4 are employed in the doc- 

 trine of centrifugal forces, and their effect in changing a fluid sphere into the 

 form of an oblate spheroid. In the former of these chapters, the author resolves, 

 as usual, the centrifugal force of a particle into two others; one, that acts directly 

 contrary to the gravitation of the particle; and the other a force in a direction 

 perpendicular to it. And this last he considers again as acting laterally on the 

 contiguous particles impelling them towards the equator. But the quantity of 

 this force, when greatest at the octant, he computes to be only j^^, ^.^ of the 

 force of gravity; and therefore, says he, it may be safely neglected. In fact, 

 after the spheroid is come to be in a permanent state, and all its parts in equili- 

 brio, there is no longer any such- lateral force at all ; it being now entirely satis- 

 fied by the gradual contraction of the earth's axis. 



The general contents of the following chapters are sufficiently expressed in 

 their titles already given. Nor can we be more particular, without entering into 

 a detail of algebraical operations, which would be improper for this place; and 

 which is the less necessary, as the same things have been treated of by several 

 other authors. This does not however in the least detract from the merit of 

 Frisi, who discovers throughout this work much acuteness and skill, joined with 

 all the candour and ingenuity that become a philosopher. And as he has not 

 yet exceeded his 23d year, it may be expected, that the sciences will one day be 

 greatly indebted to him ; especially as we find him actually engaged in composing 

 a complete body of physico-mathematical learning. 



But there is in his 6th chapter, a criticism on one of Sir Isaac Newton's de- 

 monstrations, in which we cannot agree with him. And as this demonstration 

 has proved a stumbling-block, not only to Frisi, but to many other learned men, 

 we shall be obliged to consider that part of it, which has been mistaken, at some 

 length, by the help of the scheme, fig. 1, pi. 8. In which let the ellipsis a/>boa, 



rr2 



