Z8 THE PROPERTIES

well wadded, with the addition of a soot and wad over it jthe length of the recoil will be again increased. At length,with similar charges and wads, and, instead of one, puttingtwo or three shot into the gun, the recoil will increase in pro-portion to the number of shot, and the range will diminish.

92. We may easily apply this fact to the experiments of1746.

It has been proved (71 75), that only a limited quantityof cannon powder takes fire : thus, till the charge be so pro-portioned as to be all fired in the piece, a greater quantity ofelastic fluid is generated in proportion to the largeness of thecharge. Now considering the gun and its carriage taken to-gether as a constant quantity termed C, and the substancesimpelled towards the mouth of the gun, viz. the two wadsand the shot, as P ; the length of the range ought to be tothe length of the recoil as C : P-, without making allow-ance for friction and the resistance of the air to the motionof the shot. But as the space that the shot should movethrough in the piece is diminished in proportion as thecharge is increased, and the vis matrix consequently acts up-on it for a shorter time ; the decrease of impulsion must bededucted from the action of the elastic fluid generated ingreater quantity as the charge is larger : Hence it results, thatthe ranges are proportionally shorter than the recoil, thoughthey both increase as the charge is augmented.

But if the charge be so augmented, that a part I arrivesat the mouth of the piece without taking fire, then the sub-stances to be impelled being in greater quantity, the famecircumstance that occurs when several soot are put into thepiece will in part occur here. As no more grains will befired, than if the charge were smaller and all ignited, the sootwill acquire less velocity; but the reaction against C increasingat the fame time, the recoil will be greater than before.The substances P + I forced towards the mouth of the piece,presenting to the explosion of the elastic fluid a greater re-sistance than P alone, and the number of ignited grains and thequantity of fluid generated during the time that the soot ismoving along the bore being more considerable, the absoluteincrease of fire acting against the gun and carriage must alsoaugment the recoil; while the range may be shorter, equal,or longer, than that produced by a charge that is entirelyconsumed in the gun, in the ratio that the increase of fluidbears to the substances P + I, and to the space that the soot

has