TRACT 27. PLACE OF GREATEST ATTRACTION, %l

AB + AC

BC

J — bs x hyp. log. of * +v ^ + *- ~ s . bc x hyp. log.

:= the attraction of ABCD.

5. To find the attraction ofthe right-angled part BpD, of acuneuswhoseedge passes throughA, the place of the body at-tracted.—PutAB=tf, bc = 6,bd= Xc, da — d ~ a — c, DC = e, ac =g, and dp = x. Then,the force of any section pq being still as s s, the fluxion of the

. ra

bixi

force of the part DPa is/= swi = si x % = ^ +and the correct fluent, when x — c, is —

hyp. lqg. the force of a body at a in the

direction ab. C

6. To find the attraction of theright-angled part bcd, on the pointA—Using here again the same no-tation as in the last article, we have X

e e x>

/= =

. PQ: SX X — =

Isxi

a ft n/ (c*<£r + c'x*y

The correct fluent of

winch, when X — c, is/= hyp. log,

fC 4

ee + eg— dc^

' de-do '*

7, To apply now these premises, to the finding of theplace where the attraction of a hill is greatest, it will benecessary 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 di-rection. Supposing then such a position of a hill, andthat it is also of a uniform height and meridional sectionthroughout; the point of observation must evidently beequally distant from the two ends. But instead of beingonly considerably extended, I shall suppose the hill to be in-definitely extended to the east, and to the west of the pointof observation, iq order that the investigation may be nearly