208 PHILOSOPHICAL TRANSACTIONS. [aNNO 1738. 



Isaac's spheroid ; and if he himself had not pointed at the causes, which 

 might make Jupiter not quite so flat as by his theory, and the earth some- 

 thing more. 



As to Jupiter, he says, (Page 4l6 of the 3d edition of Phil. Nat. Prin. 

 Math.) that its equator consists of denser parts than the rest of its body, be- 

 cause its moisture is more dried up by the heat of the sun. But as to the 

 earth, he suspects its flatness to be a small matter greater than what arises by 

 his calculation. He insinuates, that it may possibly be more dense towards 

 the centre than at the superficies. I am something surprised that Sir Isaac 

 should imagine, that the sun's heat can be so great at Jupiter's equator, when 

 it has no such eff^ect at that of the earth ; and that he does not ascribe each 

 to a like cause, by supposing that Jupiter also may be of a different density at 

 the centre from that at the superficies. 



But whatever reason he might have for introducing two difl^erent causes, I 

 give the preference to the hypothesis which supposes unequal densities at the 

 centre and at the circumference. I have inquired, by the assistance of this 

 theory, what would be the figure of the earth, and of the other planets which 

 revolve about an axe, on supposition that they are composed of similar strata, 

 or layers, at the surface ; but that their variable density, from the centre to- 

 wards the circumference, may be expounded by any algebraical equation what- 

 soever. 



And though my hypothesis should not be conformable to the laws of nature, 

 or even though it should be of no real use ; which would be the case, if the 

 observations made by the mathematicians now in Peru, compared with ours in 

 the north, should require that proportion of the axes, which is derived from 

 Sir Isaac's spheroid ; I thought however that geometricians would be pleased 

 with the speculations contained in this paper, as being, if not useful, yet 

 curious problems at least. 



Part I. In which are found the Laws of Attraction, which are exerted on 

 Bodies at a Distance, by a Spheroid composed of Orbs of different Degrees 

 of Density. 



Problem I. — To find the Attraction which a homogeneous Spheroid BNEbe, 

 fig. 9, pi. 6, differing hut very little from a Sphere, exerts on a Corpuscle 



placed at a in the Axis of Revolution. 1. We may conceive the space 



BNEiDMB, included between the spheroid and the sphere, to be divided into 

 an infinite number of sections perpendicular to the axe Kcb. Supposing then 

 that every one of the particles, which are contained in one of these elements 

 or moments snmu, exerts the same quantity of attraction on the body at a. 



