292

THEORY AND PRACTICE

TRACT 37.

simple state, v the velocity, and n the first force of the in-flamed powder, being the unknown quantities to be deter-mined. But, several circumstances are omitted in this so-lution, which would diminish the velocity of the ball; andthough, when taken separately, they may amount to but little,yet, when taken all together, they may be too considerable,to be entirely neglected. The first of these, that may be no-ticed, is the counter pressure of the atmosphere or externalair, which ought to be taken into the account y for, so longas the ball continues in the cavity ae, it is pressed back, andits motion retarded, by the pressure of the incumbent air onthe forepart of the ball. This pressure is equal to that of acolumn of mercury 30 inches high, or equal to mcd z as foundabove-, which retarding force is to the weight of the ball w,

as to I. Therefore, instead of the first fluxional equa-tion, it will now be vv = 2 . ?mcd x (— — *), the correct flu-ent of which gives v 1 = X (an X hyp. log. — ;

and when x = ae= i, then v — X an x hyp. log. i

+ a — b) is the velocity with which the ball issues at the muz-zle of the gun.

■o . , Ixmcd* . 6gm ,96m , 96 .

But,/-- =V /-L- =V /— = ,/_

230.144

de

1783 v

therefore the theorem is v = —(an x hyp. log. --f-a — b)~

1783

*/(le

163. By taking the same example as before, and com-puting it by this rule, the result comes out only the 366thpart less than before, or about 8 feet less, being too incon-siderable to be regarded. Should we also take into the ac-count the effect of the air before the ball, which is condensedthere by the resistance from the pressure of the atmosphere,it will probably amount to about an equal quantity, or littlemore. So that the two together may be estimated at aboutthe 180 th part of the whole.

164. There are also several other causes of the diminu-tion of the velocity, besides the two above-mentioned. One'of these is the friction of the ball in moving along the cylin-