416 On the Ventilation of Coal-Mines. [Dse. 
of bodies, B, F, G, &c., which are in contact; the momentam 
of A will be instantaneously transferred to the furthest body, G, 
without any change of place in F and B. This is evident from the . 
proposition. 
Prop. 2.—If a body, A, moving in the direction C D with the 
momentum M, meet another, B, moving in the direction D C with i 
the momentum R, these bodies will interchange their directions ‘ 
and momenta; for the force acting upon A in the direction DC, 1 
in consequence of B’s re-action to A’s motion, and the exertion 
of its own momentum, will be M + R; but A’s momentum if ‘ 
C D is M; and the excess of these forces, viz. R, gives A’s 
momentum in D C after collision: in like manner B is urged in 
CD with the same force, M + R, and in D C with the force R. 
Therefore M is B’s momentum in C D after impact. Q. E. D. . 
Cor.—Two perfectly hard bodies, whose centre of gravity is ; 
stationary, are not-reduced toa state of rest by collision. | 
Prop. 3.—If a perfectly hard body, A, moving with the momen- 
tum M in the line C D, impinge upon another, B, also moving in 
C D with the momentum R, no change of direction will take place 
in either; but A’s momentum after impact = A R= B, and that 
of B= M+R—AR=B. For the relative velocity of A and 
B before collision = M-~ A — R + B; therefore momentum of 
collision = M — A R = B = re-aetion of B or A in direction 
D C; which subtracted from the greater magnitude M, or A’s 
momentum in C D, gives AR + B= A’s momentum in that 
direction after collision. Again, the action of A upon B’s momen- 
tum, R, in the same direction C D gives B’s momentum after im- 
pact=M+R—AM+B. Q.E.D. 
Cor.—A and B cannot in any case move together after impact ; 
for supposing they can, A’s velocity, R+ B=M+B+R— 
B—AR+=BB. HenceM +A = R-—+B, which is impos- 
sible by the proposition. Tam, yours, &c. 
Fowl-Ing, Kendal, Oct. 9, 1815. JoHn GouGH. 
ARTICLE V. R 
Queries respecting the Ventilation of Coal-Mines. 
(To Dr. Thomson.) 
SIR, 
Tre various accidents that have recently happened to miners are: 
calculated forcibly to excite the attention of every friend to huma- 
nity; and the interest which these events have awakened, will, 1 
have no doubt, induce many persons to exercise their minds upon 
the means of averting such fatal mischiefs from so useful a portion of 
the community. 
