VOL. XL.] PHILOSOPHICAL TRANSACTIONS. 221 



*5^' "^ - — + ^^ ' — =^-=1 for the agsjregate of the centrifugal forces of the 



3 + px j +p 3 + 6x5+6 



column CN. And this being the same as the foregoing, shows that the columns 

 CB and CN are in equilibrio, supposing them to be homogeneous; nor are we 

 here obliged, as in art. 32, where we consider them as heterogeneous, to sup- 

 pose the coefficientsy, p, &c. to have any certain relation among one another. 



38. Perhaps it may be urged, that the foregoing calculus agrees only to a 

 canal, as bcn, which passes through the centre; and that we ought to prove 

 in the same manner, that the water included in any other canal pgr, would ob- 

 serve an equilibrium. But it appears to me, that this property may be derived 

 from the former; for it follows, from the foregoing calculation, that if we 

 might be allowed to make this hypothesis, viz. that independently of the attrac- 

 tion of any matter, the gravity at any distance cn from the centre, see fig. 15, 



would be proportional to -^ -|- - ^ = + - — , &c. it is plain 



3+;» 3+PX5+P 3-j-px5+p 



from thence, that a mass of the homogeneous fluid, which should turn about 

 the axis cb, would assume the same form as that of our heterogeneous fluids. 

 But if this spheroid should then put on a fixed state, except only some canal 

 pqr, the water in this canal would be in equilibrio; for without this, the sphe- 

 roid could not be esteemed as having arrived to its fixed state. But this suppo- 

 sition comes to the same as that of our heterogeneous spheroid, composed of 

 elliptical layers, in which should be found a canal pgr of a homogeneous fluid; 

 provided that the space, which this canal possesses in the globe, be not of so 

 large an extent, as to change the law of attraction. 



The only three planets, in which we can be assured of gravitation, and the 

 centrifugal force, are the sun, Jupiter, and the earth. As to the sun, the cen- 

 trifugal forc^ is there so small, in respect of its gravity, that his poles must be 

 very little depressed, so that we cannot be sensible of it by observation. Then 

 as to Jupiter, observations make him something less flat than according to Sir 

 Isaac Newton ; that is, than if he were composed of matter of a uniform den- 

 sity. Therefore by the foregoing theory, he must be a little more dense to- 

 wards the centre, than at the parts near the superficies. We might make a 

 thousand hypotheses about the manner of distributing the inequality of density, 

 proceeding from the centre towards the circumference, which would all agree 

 with the figure observed, and which are very easy to calculate by the principles 

 here laid down. 



As to what concerns the earth, I shall wait till we receive the observations 

 which must have been lately made in Peru; that by comparing those with what 



