VOL. XLVIII.] PHILOSOPHICAL TRANSACTIONS. 329 



The expressions of Frisi, referred to by Mr. Short, are as follow: 



" Quia tamen plerique omnes hucusque, aut nihil pro figura telluris determi- 

 nanda ex iis observ^ationibus deduci posse cum geoinetra celeberrimo Ruggero 

 Boscovik autumarunt, aut exinde cum ill. Clairaut, Bouguer, aliisque, contra 

 incomparabilem virum ac prope divinum Isaacum Newton insurgentes, admira- 

 bilem ipsius theoriam facto minus respondentem dixeruiit, assignatamque in prop, 

 jg, lib. 3, Princip. Mathem. terrestrium axium proportionem a vera absonam 

 omnino esse, alios mihi observationibus parum, alios nimis tribuere visum est, 

 omnes ferme oppositis erroribus pecc^sse, ubi res neque aurificis lance, neque 

 molitoris, ut aiunt, statera librandas sunt." 



This, when compared with the propositions of my theory, which they relate 

 to, will appear, I hope, quite incoherent; Hnd I cannot show it more clearly 

 than by translating the last chapter of my book, to which Frisi refers the reader. 

 For the better understanding of that chapter, it is proper to know, that the 

 chief results of the precedent inquiries are these theorems: 



1. Supposing the earth in its former state composed of several fluids of dif- 

 ferent densities, and settled all in equilibrium by the laws of gravity and centri- 

 fugal forces, the surfaces separating the different mediums will always affect the 

 form of a curve, which is so near to the ellipsis, that it may be supposed so, 

 without any error of the least moment. 2. That, in the case of the denser 

 fluids being nearer to the centre, as hydrostatics require, the spheroid will always 

 be less flat than in the homogeneous one, and vice versa. 3. And as to the 

 diminution of the gravity from the pole to the equator, it will always follow the 

 opposite rule, viz. if the spheroid be denser towards the centre, the gravity will 

 decrease in a less ratio than in the homogeneous spheroid, and vice versa. 4. 

 That if (? represent the fraction found out for the difference of diameters, , ■ , 

 — S will express the total diminution of the gravity from the pole to the equator, 

 not only in the case of the spheroid supposed originally fluid, but in any suppo- 

 sition of variation for the densities and proportion of the diameters of the beds, 

 provided they be elliptical. 



These premised, let us proceed to the last chapter of the theory of the earth's 

 figure; in which the principles laid down in the preceding chapters are compared 

 with the observations. 



^ 68. For the diminution of the gravity from the north to the south. 



It has been seen in the preceding chapter, that when a spheroid is not sup- 

 posed homogeneous, the diminution of the gravity from the pole to the equator 

 will be greater than in the case of homogeneity. Hence, if my theory holds in 

 our globe, the whole decreasing of the gravity will be equal to -^-^ or greater, 

 and never less; since the ratio of 230 to 231 will (§21) express the ratio of the 

 action of gravity at the equator and [X)le, when the spheroid is homogeneous. 



VOL. X. ' U u 



