TRACT 37.

OP GUNNERY.

221

succeeding velocities 200, 300, 400, &c, the continual quo-tients of each of these velocities 200, 300, 400, See, di-vided by the first 100, give the successive numbers 2, 3, 4,&c, the logs, of which therefore are the correspondent di-visors to the difference between the logs, of the first resist-ance and that of each of the following ones, to give the re-spective numbers denoting the indices of the powers, as ar-ranged in the 5th column of the table.

22. The circumstance of the variable and increasing ex-ponent in the ratio of the resistance, is owing chiefly to theincreasing degree of vacuity left behind the ball, in its flightthrough the air, and to the condensation of the air before it.It is well known, that air can only rush into a vacuum witha certain degree of velocity, viz, about 1200 or 1400 feet ina second of time; therefore, as the ball moves through theair, there is always left behind a kind of vacuum, either par-tial or complete ; that as the velocity is greater, the degreeof vacuity behind goes on increasing, till at length, whenthe ball moves as rapidly as the air can rush in and followit, the vacuum behind the ball is complete, and so continuescomplete ever after, as the ball continues to move with allgreater degrees of velocity. Now the resistance, which theball suffers in its flight, is of a triple nature; one part of itbeing in consequence of the vis inertia of the particles of air,which the ball strikes in its course; another part from theaccumulation of the elastic air before the ball; and the thirdpart arises from the continued pressure of the air on theforepart of the ball, when the velocity of this is such as toleave a vacuum behind it in its flight, either wholly or inpart: for, while the ball is at rest, it is manifest that thispressure of the whole atmosphere is the same or equal on allsides of the ball; but, as soon as the ball begins to move, itis also manifest that the pressure behind will be less than theconstant degree of pressure in front, and the difference mustbe the greater as the motion of the ball is the more rapid,being in fact proportional nearly as the velocity of the ball;