Abstract
IN my experiments made to determine the resistance of the air to the motion of projectiles, it was assumed that this resistance followed some law producing gradual change in the velocity, and consequently that the times occupied by the shot in passing over a succession of equal spaces would admit of being differenced. This method of proceeding gave the required result in the form of a coefficient Kv of v3, in terms of the second and higher differences of time above referred to, when the time was expressed in seconds to five places of decimals. So long as this value of K remains constant, the resistance of the air varies as the cube of the velocity The first results obtained were published in a note in the Phil. Trans. for 1868, p. 441. The experiments were afterwards more carefully calculated, and given in detail in the Reports published by Government in 1870. In using these results to calculate general tables for space and time, for cases where the projectile could be supposed to move approximately in a straight line, and free from the action of gravity, the corrected mean values of Kv were used, and made to vary with the corresponding velocity v. And in my “Treatise on the Motion of Projectiles”(1873), the cubic law of resistance was used for the purposes of calculation, so that for those velocities where K varied was necessary to divide the trajectory into such small arcs that, throughout each arc, the average value of K could be used without sensible error. This treatment of the question rendered it unnecessary for me to attempt to express the law of resistance according to powers of v for all practical velocities. But from the results of my experiments for velocities between 900 and 1700 f. s., I remarked that “the resistance of the air may be considered to vary roughly as the sixth power of the velocity for velocities 900–100 f.s., to vary as the third power for velocities 100–1350 f.s., and to vary as the second power for velocities above 1350 f.s. (Proc. R.A. Inst., September 1871).
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BASHFORTH, F. On the Law of the Resistance of the Air to the Motion of Projectiles . Nature 33, 604–607 (1886). https://doi.org/10.1038/033604e0
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DOI: https://doi.org/10.1038/033604e0