TRACT 37.
OF GUNNERY.
213
respondent degrees of resistance to the same ball, as com-puted from the known theory of such resistances, viz, con-sidered as being proportional to the square of the velocity.The theorem for this purpose is investigated in prob. 20,pa. 367, vol. 2 of my Course of Mathematics, and is this,
prid* i i . , . t
v = 7' the resistance, where p is = 3’14-1G, 71 = the spe-cific gravity of the medium, g — 16, d — the ball’s diameter,and v = its velocity, both expressed in feet. Now, for ourball of 2 inches or £ of a foot in diameter, that is, d = J.,and the value of n = I t ounces, the mean specific gravity
of air, the theorem becomes or TT—r-td = the re-
4888 44000
sistance. Hence all the series of resistances will be easilyfound, by dividing the squares of the velocities by the constant number 4S88 ; or, still easier, by dividing the squaresof the triple velocities by 44000. In this manner then wereeasily found the theoretical resistances, as placed in the 3rdcolumn of the table.
19. Then, to form a comparison between these two co-lumns, of the experimental and theoretical resistances, eachnumber in the former is divided by the correspondent num-ber in the latter, and the ratios or quotients are set oppositethem in the next or 4th column ; where it is seen that, nearthe beginning, or with the slowest motions, the experimentalor real resistance, exceeds the theoretical one, by about the5th part, or in the ratio of 6 to 5; that as the velocity is in-creased, the former gains more and more over the latter, allalong, till at the velocity of 1G0O feet per second, where thedifference is at the greatest, the former being more thandouble the latter, or in the ratio of 2'08 to 1 ; after which,as the velocity is further increased, the ratio slowly decreasesagain, and terminates at 2000 feet velocity, in the ratio of 2to 1 very nearly.
2Q. To the former 4 columns a 5th is added, to showaccording to what power of the velocity, at every point, theresistance increases, being the indices of those powers, bycomparing constantly a first number, for instance that of