determination of the

tract 27.

Te

*. of the altitude ; and is something less than at of the al-titude.

23. If «'=■!%•; the formula gives** X (19 — 91 +

2h.l. +| h.,1. -sax -9986188, for the

attraction at T r T of the altitude; still less than the last was.And, lastly,

24. If n — 0, or the point be at the bottom of the hill;the formula gives 3 set x (2 + fi. 1. 3) = set X ‘1146531, forthe attraction at the bottom of the hill; which is between| and | of the greatest attraction, being something greaterthan y but less than ^ of it.

25. The annexed table exhi-bits a summary of the calcula-tions made in the preceding arti-cles ; where the first columnshows at what part of the altitudeof the hill the observation ismade; the second column con-tains the corresponding numberswhich are proportional to the at-traction ; and the third columnshows what part of the greatest attraction is lost at each re-spective place of observation, or how much each is lessthan the greatest.

26. Having now so fully illustrated the case of the firstextreme, or limit, let us search what is the limit for theother extreme, that is, when the hill is very low or flat. Inthis casei b is nearly equal to d, and they are both very greatjn respect of a t consequently the formula for the attraction

in Art. 10, will become barely s X [a 1 X h. 1.. + 2(a~x)

6

Ter

8109843

I

T

s

Ty

9340963

z

YT

4

10224232

X

T3-

TP?

10702512

7T5-

Z 5 Z

t o-'Sf^r

10763100

0

z

T

10163589

■3TFTT

z

7 -ST

10684622

•TJ4

I

TU

9986188

i

IT

0

7146531

z

7

X h. 1. ; the fluxion of which being put 0, we ob-

tam o = h. 1.-— 2 n. J.-. = b. 1.-h. I. t-) J =

x a—x sc - a—x

If. I.

Q— *>

x{ c la — x)

; hence therefore ( a — x)

x (2 a — x), and