3 2 ?\ -

Hydrostatic s,

the Medium d, and the Resistance r as — Then

at

(by Art. 14.) r j ~ — iv, wherefore -~r— — iv$ and'

U H

so ds ZZ: (F-vv 1 —

56. Whence if the Density be uniform, as of Wa-ter, then d—i. And if «;= 2, then J — a'dv— J , —

>— Now s is the Fluent of the Fluxion j, and the

' ■ “U

Fluent 1 of — is (T—«'L<v, where Q_ is some con-

stant Quantity, to sind the V alue of which, suppose s =zQ^—s, then Q=ra 1 L'y, but whxn s—o,v~ =V;therefore Q=«’LV. Wherefore i-c'LV —a Lv—

0 -iT.

V

57. The Time t is found by the Formula in Art. 12.

■where we had t — —, but because when d is given,v . ■

, . . , . • 's a n <v wJ—a

3 ~ a n w 1 —” (Art. 55.} therefore t — — — — - -

•v v

— a n iv — n. Whence taking the Fluents we have tQ-— a n v l — n .

—-— ; and putting t ~o, we. have v—V, where-fore Q=aa»Vi—» ; consequently substituting for Q_ its

\r 1 u aW 1 —»— a’‘v'— n TT

Value, we have t — —----. Hence, if « = 2.

1 —n

<7‘V— a’v V —v

= a 1 X

V v “ ' v Vv58. We had above s — a*-w ' l ~ n ; and taking the

Q —a n v' 1 — n __

Fluents on both Sides, we have s —

1 1 — a”v z — n

Let 2 •

■ m\ tiien 1115— a n V

m

2 —n

' V ”; hence a n V M — ms — a» v m ; therefore v —1

«r?V« — ms m

Which Theorem therefore gives the

Velocity when the Space s is known,