t

I

FIRED GUN-POWDER. 89

fluid generated during the proof, allowing for the proportionthat escapes by the vent, and the windage. Thus the shapeof a gun being known, the limits of the greatest velocity ofthe ball in each point of the length of the bore may be found

C ' 79 )*

181. The thickness of metal in each point of the lengthof the cylinder is determined by a ( Fig. 21) right line F D,drawn from the breech to the muzzle obliquely to the axis jthus the lengths BE, BH, and the corresponding thicknestesE F, H L of a gun A C B D being known, the inclinationof the right line MON which is the scale of the pressuresof the fluid against the sides of the gun may be determined,the ordinates E M, HO, B N, being in the ratio of the cor-responding thicknesses E F, H L, B D. If the right linesE B, F D be produced, they will meet at the point R, wherethe line MON will always terminate, even when F L Dand MON are curves. Thus E R = £ will be known and

considering p = E M, the value of n will be^j-: then po —

P X

— ~nx and m — § since M ? O is a triangle. Hence nmx *

p x % _

— ^ and consequently V—\/px — nmx %

which is an equation to the ellipsis to be constructed in themanner already pointed out (172).

Take p— then V = \/ i.bx — x ' 1 is an equation to acircle whose radius- 5 ; from the point R taken as centrewith a radius RE —L describe the arch EGK, then theordinates HG, BK, will express the relative velocities whichthe.bullet would have at the points H, B, if the line MONwere the scale of pressures of the fluid. It should be remarked;

1. That on diminishing the charge of powder in thesebarrels without weakening the resistance,of the shot andwads, the pressure of the fluid at the point E will remainthe fame, but it will be weaker at the points H andB, (152) ; the velocity therefore of the bullet at thefame points will be less.

2. That on diminishing both the charge and the re-sistance, either by using smaller wads or by rammingthem down with less force, the pressure of the fluidwill be less at the point E, as well as at H and B.

3. That

It