TRACT 37.

OF GUNNERY.

277

grees; the 2nd column shows the distances, in yards, towhich the ball would go, in vacuo, on a horizontal plane;the 3rd column contains the distances to which it will rangethrough the air, considered all of the same density as at theearth’s surface; the 4th column shows the same ranges cor-rected for the diminution of the air’s density as the ball as-cends, being therefore called the corrected range; and the5th, or last column, shows the height to which the ball risesin the air, or the height of the vertex of the curve above theplane.

130. By this table it appears what an immense differencethere is between the motions through the air and in a void,especially with the large velocities. It is seen that the rangesthrough the air, instead of increasing in the duplicate ratioof the initial velocities, as in unresisting space, really in-crease slowmr than those velocities, in all the actual cases ofmilitary service ; and in the most useful cases, viz, from 800to 1600 feet, they increase nearly as the square-roots of thevelocities. A set of similar tables, made with the same shot,at other elevations, w r ould nearly complete what might bedone by theory, as well as useful and necessary for practice.

To use the foregoing Table.

131. Suppose it were required to find the dimensions ofthe path described by a 12-pound shot, discharged with 1G00feet velocity, and at an elevation of 45 degrees.

Here, recollecting that the curves are similar, and theircorresponding lines proportional to the diameters of the shot,when these are discharged wdth velocities that are to oneanother as the square-roots of the same diameters; v'e musttherefore first find what velocity of the. 24lb, or tabular ball,corresponds to the 1600 velocity of the 12 -pounder, in thismanner. The diameters of the two balls being 4-403 and5*546, it will be, as ^4*403 : V5-546 : : 1600 : 1796 thecorrespondent velocity of the 24 -pounder; which beingsought in the table, the range and height answering to it, are