314

THEORY AND PRACTICE

TRACT St-

all the lengths and diameters of pieces that can be used. Inlike manner, the 2nd column shows all the correspondentlengths of the charge of pure powder, put in without anybag or wad, but set close up with the rammer, these beingthe charges to produce the greatest velocity of the ball ineach gun, and expressed in calibers of the gun also; allthose values of a, or length of the charge, being determinedby the foregoing theorem a 2 + (48 + b) a = 165, in art. 186,by using for the value of b the successive numbers 2, 4, 6,8, See, in the first column. The 3rd column exhibits thequotients of b divided by a, or the values of being theproportions of the length of the bore to the length of thecharge. The 4th column shows, in so many 100th parts ofthe weight of the bail, what is the weight of the severalcharges of powder whose lengths are contained in the 2d co-lumn, to produce the greatest velocity in the ball. Thus,for the first piece, of only 2 calibers long, the weight of thecharge to give the greatest velocity, is j 1 ^, or about ofthe weight of the shot; for the piece of 10 calibers, theweight of the charge is or just £ the weight of the

ball; for 26 calibers bore, the weight of the powder is 100,or just the weight of the ball; and so on to the last, of 60calibers bore, where the weight of the powder is of thatof the ball, or more than 1 £. And this column of the weightsof the powder is made out from that of the lengths of thecharges, in the following manner. In art. 184 it is shownthat the weight of the ball is *^cd 3 ounces, and that of thepowder -.5422 5acd*, which two quantities are to each otherin proportion as d to ’19a or | of a nearly, where d denotesthe diameter or 1 caliber, a the calibers in the length of pow-der ; therefore the values of a, in the 2d column, multipliedby '19, or divided by 5-26, will give the weight of the pow-der in 100th parts of the ball, as they are arranged in the 4thcolumn. Lastly, the 5th column contains the several great-est velocities by the same guns, with the foregoing chargesof powder, as computed from the formula 5875 V[~— X