p
r
84 THE FORCE OF
tial velocity DF corresponding with this trapezium is ex-pressed by the square root of the same superficies :
For example, Let A D be - s of a foot, D R will be 4 feet
6 inches or which
6
substituted in the theorem,
will
give DF = « =
1479 26 x L
84
Zb
729' 36 '
/--
V' i479*6xg =
475 feet for the initial velocity.
173. This method of finding the scale of velocities in thespaces, may be' practised when the wad is strongly rammedon the powder; for then the greatest ordinate of the corre-sponding scale of pressures is at, or very near to the placeoccupied by the shot, in the bore of the gun : and there isno difficulty in reducing by approximation the line of the ve-locities to a regular curve, from which, expressed geometri-cally may be deduced the scale of pressures. But when thegreatest ordinate is distant from the part occupied by the shot,as with weak powder or low wads; then to find the curveline of velocities, it is not only necessary to make experi-ments with the guns mentioned in the preceding paragraph,but with others in which the shot has a very small space topass through, as 2 or 3 calibres: thus the curve line may bedescribed from its origin, and any irregularity corrected byapproximation.
174: If the scale of pressure only be sought; as the velo-cities are in the fub-duplicate ratio of the sum of the pres-sures, whenever the proportion of two velocities C E, D F isless than the fub-duplicate ratio of the spaces A C, A D, orof the length of the part of the bore from the shot to themuzzle, then the corresponding part SMN of the scale ofpressures will converge towards the mouth of the gun : whenthe ratio of the velocities is equal to the fub-duplicate ratioof the corresponding lengths, the scale SMN will be parallelto the directrix AD; and when greater, it will divergefrom it.
175. Having ascertained the initial velocity —« and thescale of pressures, the value of n, which expresses how muchthe greatest elasticity of the fluid acting on the shot exceedsthe elasticity of the atmospheric air, may be found by means
of
1
>
I
>