88 TH£ FORCE OF

and it may be considered as the limit of the greatest Velocityof the shot.

iyy. In fire-arms of all calibres fired with large chargesand wadded, so that only the necessary interstices for thepropagation of fire reynain between the grains, the thicknessof metal must be increased gradually from the muzzle to thebreech, that the gun may be enabled in every point to resistthe actual pressure of the elastic fluid : wherefore the scale ofpressures against the sides converges toward the mouth of thegun, and the greatest ordinate of the scale is very near theplace occupied by the soot. Then,

Fig. XV. In order to find the equation of the scaleof pressures, draw the“right line K I parallel to the di-rectrix E G, considered as the axis to which the ordi-nates are perpendicular: let the pressure K E ---p andthe abscissa EL = KI=cv. As the ordinate I H of thesegment KHy appertains to the abscissa KI, J H maybe expressed by nx , and multiplying n x by the abscissa,— x and by m denoting the fraction that squares the sur-face KI H the product n m x z will express the surfaceKIH: now the rectangle E K 1 L — px, therefore thesuperficies EKH L =p x—nm x*; and call the velocityL B that answers to this superficies V, then V =

\/ px — tnnx *.

180. Since mufquet barrels were first made in Piedmont,none have been received at the Arsenal before they had beenproved in the presence of some officers of artillery. Morethan a hundred thousand barrels have been proved in thefollowing manner: they are charged with 17 drachms ofcommon cannon powder; over which is put a very highwad of hard tow, that is with difficulty pressed into the bar-rel, and is afterwards rammed down with all the force thatthe armourer can exert: a leaden bullet weighing i8£drachms is then put in and wadded as before. The barrelsthus loaded, are placed horizontally with the breech against astrong beam of wood, and each of them is fired twice. Atevery proof some of the barrels have burst, and the crack issometimes at the breech, at other times at the middle of thebore, or near the muzzle: but as it is not found to have hap-pened more frequently in one part than another, the officers andmanufacturers have deemed it unnecessary to make any alte-ration in the thicknesses of metal; so that they may be rea-sonably regarded as proportionate to the pressures of the elastic

fluid