THEORY and practice

TRACT 37.

in

empty; the 4th when the hollow part is filled with powder:the diameter of the hollow is usually ^ of that of the mor-tar. On account of the vacuity of the shell being filled onlywith gunpowder, the weight of the whole so filled, and con-tained in column 4, is much less than the weight of the samesize of solid iron, and the corresponding weights of-suchequal solid balls are contained in col. 5. The ratio of theseweights, or the latter divided by the former, occupies the6th column.

123. Now, because the loaded or filled shells are of lessspecific gravity, or less heavy, than the equal solid iron balls,in the ratio of l to 1*42, as in column 6, the former will haveless power or force to oppose the resistance of the air, inthat same proportion, and the terminal or greatest velocity,as determined in the 10th problem, will be correspondencyless. Therefore, instead of the rule there given, viz,

for that velocity, the rule must now be 178v'^^= 149 , 4v'<tf= v, the diameter of the shell being d; that is, the terminalvelocities will he all less in the ratio of 149*4 to 178. Now,computing these several velocities by this rule, to all the dif-ferent diameters, they are found as placed in the 7th column;and in the Sth or last column arc set the altitudes whichwould produce these velocities in vacuo, as computed fromthis theorem

G4

124. Having now obtained these terminal velocities, andtheir producing altitudes, for the shells, we can, from themand the former table of ranges and elevations, easily computethe greatest range, and the corresponding angle of elevation,for any mortar and shell, in the same way as was done forthe balls in this problem. Thus, for example, to find thegreatest range and elevation, for the 13 inch shell, whenprojected with the velocity of 2000 feet per second, beingnearly the greatest velocity that shells can be discharged with.Now, by the method before used, = 3*746 ; opposite tothis, found in the first column of the table of ranges, corrc-