VOL. XL.] PHILOSOPHICAL TRANSACTIONS. 21 I 



cording to the Direction nx ; supposing the point h, which answers perpendicu- 

 larly below t/ie Point n, to be at a very small Distance from the Point y. — 

 8. Let there be drawn riHTr perpendicular to the diameter RYr, and let the 

 space RllTr be transferred to ttIIz. Then the space Trzllr will be the only part 

 of RflrTr, which will attract the body n according to hy. 



To find the attraction of this little space, we will suppose it to be divided 

 into the elements tIss, the attractions of which, according to hy, will be 



TtSS X QT 2HV X Q? X QT . , n . c . • 1 2HY X HQTZ . , . 



-— , or , , the fluent or which j is the attraction 



NT* ' Nt' ' NT' 



of Tzrs, according to hy. In which if we put llTr for Ha, we shall have 

 nH.Hx2HY ^^ j HY X riH' X c ^^^ ^j^^ attraction required. 



NT' NT' ' 



Q, It is easy to perceive, that if, instead of a circle, the curve Rllr were an 

 ellipsis, or any other curve whose axes were but very little different from one 

 another, the foregoing solution would be still the same. 



Problem V. To find the Attraction which an Elliptical Spheroid klIi (fig. 1 3) 

 exerts on a Corpuscle placed without its Surface at n, according to the Direction 

 ciL perpendicular to cs. — 10. To perform this, we will begin by drawing the 

 diameter CfAv, which bisects the lines Rr perpendicular to cn; and the ratio of 

 CH to HY shall be called n. Then accounting the ellipsis Rr as a circle, see the 

 foregoing article, we shall have, by the foregoing problem, t^'^xrh xch ^^^ 

 its attraction, according to hy ; which being multiplied by the fluxion of mh, 

 the fluent of this will be the attraction of the segment of the spheroid RMr. 



This calculation being made, and not being substituted for nr, we shall have 

 -—J- for the attraction of the spheroid in n, according to the direction ex. 



Problem VI. To find the Attraction of a Corpuscle n, according to ex, 

 towards an Ellipsoid BNEbe, composed of Strata, the Densities of which are 

 defined by the Equation D = fr"" + gf^- — H- Take the fluxion of the quantity 

 — -, which expresses the attraction of the homogeneous ellipsoid klA, and 



you will have — ;— for the attraction of an infinitely little elliptic orb; which, 



being multiplied by the density d, gives -^^ ^ -^ — ^^ '-, the fluent of 



which -i^ 1- —f^I i— !, is the attraction of the spheroid kl/^, according to 



5 + jJXe^ 5+yxe* ^ 



ex. Therefore the total attraction of the spheroid sNE/jie on the corpuscle n, 



according to the direction ex, will be ^^f U ?^— . 



^ 5+7' ^ 3 + 9 



£ B 2 



