TRACT 27. PLACE OP GREATEST ATTRACTION.

75

by some small difference, in order to discover what part ofthe greatest attraction is wanting by observing at differentaltitudes.

IS. And first using the value of v, ('251999) as found inthe 14th article, the general formula in Art. 13, gives sax1*0763700, for the measure of the greatest attraction.

17. If 7i — JU, or .v — JL a; the same formula gives

(17 - v/79 + g h. 1. —- W - + £ hyp. log.

13 + 2 ^/ 79 .

zsa*

■ To)

•Slf

20 v I g I 3-,‘V 7

1'0702512 for the attraction at ^ of the altitude, which issomething less than the former,

18. If n = ^ B .=zX; the formula gives ^ x (16 — V76 -f*

8h. 1 . ^i^+31). 1 . ■ ' + V - fi ) — sax 1'0224233, for tlie at-traction at -j4 0 - or f of the altitude; less again than the lastwas,

19. If n=-~a — the formula gives \sa X [3 — ^/3 — 2h.1. 3 + Ah. 1.(3 +2 y/3)] = sa. X '9340963 for the attraction athalf way up the hill; still less again than the last.

20. If n zz -pj- = ■§; the formula gives ^ X (14 — 4-

12 h. 1. 3±|/ If + 2 h. 1. =: sa X '8109843, for the

attraction at ~ 0 - or -f of the altitude from the bottom; beingstill less than the last was. And thus the quantity of attrac-tion is continually less and less, the higher we ascend up thehill, above the '251999 part, or in round numbers '252 partof the altitude. Let us now descend, by trying the num-bers below '252; and first,

21, If 7i— • 25rri; the same formula in Art. 13, gives

jsax (7 — </13 + 2 h. 1. x h. 1. — - sa x

o o

1’0763589, for the attraction at y of the altitude; and isyery little less than the maximum.

22. If n — t 2 q- = ■§•; the formula gives sa X (9 — \/21

+ 2 h. 1. ■—-j- 2 h. 1. ’———) = -fc sa X (9-,/21+2h ^ 23 . f — sax 1'0684622, for the attraction at on

A