(504 PHILOSOPHICAL TRANSACTIONS. [aNNO 1780. 



3. To find now the attraction of the whole right-angled cuneus on a body at 

 a in the direction ab. — Since the force of each section is si by what is above 

 said, therefore the force of all the sections, the number of them being ab or «, 

 is ass = s . AB . — , the force of the whole cuneus abckda. 



AC 



4. To find the attraction of any rectangular part abcd on a in the direction 

 AB, fig. 1 1 ; abcd being one side of a cuneus, and ad its edge. And here, by 

 a like fluxionary process, it is found that * . bc X hyp. log. ^^^~ is the attrac- 

 tion of ABCD. 



5. To find the attraction of the right-angled part bcd of a cuneus whose edge 

 passes through a the place of the body attracted, fig. 12; he puts ab = a, bc 

 z= b, BD = c, T>A = d =:a — c, DC = e, AC = g, and dp = x; and then, by 



a like process, finds that -^ X {g — d x hyp. log. —T-^y—) expresses 



the force on a body at a in the direction ab. 



6. Lastly, to find the attraction of the right-angled part bcd on the point a, 

 fig. 13: using here again the same notation as in the last article, in a similar way, 

 he finds that the attraction in this case will be denoted by 



bcs , J , dc ^, , , ee + eg ~- dc, 



- X (,- - d + - X hyp. log. -H-^). 



7. To apply now these premises to find the place where the attraction of a 

 hill is greatest, it will be necessary to suppose the hill to have some certain figure. 

 That position is most convenient for observing the attraction, in which the hill 

 is most extended in the east and west direction. Supposing then such a position 

 of a hill, and that it is also of a uniform height and meridional section through- 

 out; the point of observation must evidently be equally distant from the 2 ends. 

 But instead of being only considerably extended. Dr. H. supposes the hill to be 

 indefinitely extended to the east and to the west of the point of observation, in 

 order that the investigation may be nearly mathematically true, and yet sufficiently 

 exact for the beforesaid limited extent also. It will also come nearest to the 

 practical experiment, to suppose the hill to be a long triangular prism, so that 

 all its meridional sections may be similar triangles. Let therefore the triangle 

 ABC, fig. 14, represent its section by a vertical plane passing through the meri- 

 dian, or one side of an indefinitely thin cuneus whose edge is in pg; or rather 

 PBCGP the side of one cuneus, and pag the side of another, their common edge 

 being the line pg perpendicular to the base ac; p being the required point in the 

 side AB where the attraction of the indefinitely thin cuneus shall be greatest, in 

 a direction parallel to the horizon AC. And then from tne foregoing suppositions, 

 it is evident that in whatever point of ab the attraction of abc is greatest, there 

 also will the attraction of the whole hill be the greatest, very nearly. 



8. Now drawing hpdef parallel to ac; and ah, pg, bi, cf, perpendicular to 

 the same. Then it is evident that at the point p, in the direction pf, the attrac- 



