DESCRIPTION OF A CHRONOGRAPH, ADAPTED FOR MEASURING THE VARYING VELOCITY OF A BODY IN MOTION THROUGH THE AIR, AND FOR OTHER PURPOSES. BY FRANCIS BASHFORTH, B.D., PROFESSOR OF APPLIED MATHEMATICS TO THE ADVANCED CLASS OF AND LATE FELLOW OF ST JOHN'S COLLEGE, CAMBRIDGE. [An Extract from the Proceedings of the Royal Artillery Institution, Woolwich.] LONDON: BELL AND DALDY. M.DCCC.LXVI. 186. h. 13. 31 DESCRIPTION OF A CHRONOGRAPH. THE resistance of fluids to the motion of solids is a problem of great practical and theoretical interest, because sometimes this resistance becomes a source of power, whilst at other times it is a large consumer of power which would otherwise be usefully applied. Thus the action of the wind upon sails is made to drive a mill or a ship. The wind acting upon the sails tends to drive the ship, and the resistance of the water is opposed to the progress of the ship. The resistance of the water to the motion of the oar, the paddle, or the screw, enables the rowers or the steam engine to drive the vessel. A very large part of the power developed in the locomotive is employed in overcoming the resistance of the air to the motion of the train. And quite recently it has been found that the friction of the tidal wave is probably slowly diminishing the velocity of the earth's rotation about its axis. We are dependent upon the resistance of fluids for our power to cross the ocean, for without that property we should not be able to use sail or oar, paddle or screw. Still little is known with accuracy respecting the laws of the resistance of fluids. It is extremely difficult to make satisfactory experiments on account of the great disturbance produced in the surrounding fluid, and as the mathematician knows neither the nature of this disturbance, nor the amount of resistance to be accounted for in particular cases, he is not able to find ground on which to base a satisfactory theory. For a history of what has been done, it will suffice to refer to the articles, "Ballistik" and "Widerstand," in Gehler's Physikalisches Wörterbuch, 1825 and 1842. The resistance of the air to spherical balls, moving with high velocities, has been a subject of special interest for more than a century, because it was of practical importance to the science of gunnery, and because it offered a simple yet striking instance of the great resistance which a very rare medium would offer to a solid moving in it with a high velocity. Thus Robins1 states that Dr Halley thought it reasonable to believe that the opposition of the air to large metal shot is scarcely discernible, although in small and light shot, he acknowledged that it ought and must be accounted for. 2 Robins further states, that a musket-ball, fired with a charge of half its own weight of powder, would leave the gun with a velocity of 1700 f.s., and that, with an elevation of 45°, its range would be 17 miles in a vacuum; whilst practical writers on the subject say that the range in air is Gunnery. Preface, p. 48. 2 p. 145. 1 |