99

Mechanics.

LAW III. Re-a5lion is always equal andcontrary to ASlion ; or the Actions of two

Bodies

any given Velocity, it shall lose all its Motion, or bequiescent after the Stroke; the Body B which receivesit will communicate it to C, and C to D, and D to E,and E to F; and because Action and Re-action betweenthe Bodies B, C, D, E, are equal, as they were quies-cent before, they must continue so ; but the Body Ehaving no other Body to re-act upon it, has nothing toObstruct its Motidn, it will therefore move on with thesame Velocity which A had at first, because it has allthe Motion of A, and the same Quantity of Matter byHypothesis.

20. Let there be three Bodies A, B, C ; and let Astrike B at rest; the Velocity generated in B by the Stroke2 QV

will be y = ■ ■ —— , and so the Momentum of B will be'4.1 *c

2 Q v &

■ . — g - " - ' — E?' With this Momentum B will strike C

“ 4 .

at rest and contiguous to it; the Velocity generated in

2 £9 y 2 $ y C

C will be ~~~; and its Momentum will be , =s

4 i+ C G

2 ac x 2 qv

4 Q_V 9 C

that is,

Eig, in

ELC

21. If now we suppose B a variable Quantity, whileA and C remain the same, we shall find what Propor-tion it must have to each of them in order that the Mo-mentum of C may be a Maximum t or the greatest pos-sible, by putting the Fluxion thereof equal to nothing j

4Q.-OVE-4Q.CEE

0 ; whence we

<ECst-QEI-EC-hE!-

get Q_C —EE — o, and so Q_C — EE- conse-quently Q_: E'-E-C, orA:B::B:C; that is,the Body B is a Geometrical Mean between A and C.

22. Hence if there be any Number (n) of Bodies ista Geometrical Ratio (r) to each other; and the first be

H 2 A.