a, b, c, d, e denote the records made by the clock every second. 1, 2, 3, 4, 5, 6, 7, 8, 9, 10 denote the records obtained from the screens placed at intervals of 150 feet in the path of the projectile. (March 21, 1864.)"Soon after his appointment, Professor Bashforth, in his first letter to the Ordnance Select Committee, recommends the adoption of a kind of printing telegraph.... in order that we may have a check upon the measurements of striking velocities." It goes on to state, page 25: "As this suggestion did not appear to meet with approval, it devolved upon Mr. Bashforth to carry out his own plans, which have now been brought to a successful termination after four years of incessant labour." (July 23, 1868.) In the same page the Report further declares: "The state of our knowledge of the resistance of the air in 1865 was well expressed in Captain W. H. Noble's Report to the Ordnance Select Committee dated April 2, 1865:-"It is regretted that this subject cannot be fully treated in the present Report, but the difficulties in the way of a clear solution are so many and so great, that it would be difficult with our present experience to assign any new law representing with accuracy the resistance of the air to the motion of spherical and elongated projectiles"" (page 19). The scientific referees thus characterise the Bashforth instrument : "We do not think that any means before existed of recording a number of successive small intervals of time with the degree of precision and trustworthiness attained by Professor Bashforth's instrument." This instrument gives records in parallel spiral lines traced on a revolving cylinder :-(1) of every alternate beat of a half-seconds clock; (2) of the instants in 2,000ths of a second of the ball cutting threads in ten to fifteen screens placed 50-150 feet apart. The accompanying diagram is a reduced fac-simile of the record of an observed round of firing cannon-shot through the screens. Throughout the whole of these experiments, recorded permanently upon blue glazed paper, an elaborate system of testing minute working errors, by differences of a high order of scrutiny, approved by the first mathematicians of the age, has been put in practice. About 400 rounds have been tabulated: even corrections for the density of the air for observed readings, height of the barometer and thermometer, have been introduced. The precision and excellence of this mode of testing by successive differences may be illustrated in the following manner. If the velocity of the shot follows a particular law for certain limits, the successive differences will show its existence and any departure from it: just as a succession of squares and cubes tabulated with the slightest error can be thus detected : Nos. 1st differ. A1 2nd differ. A2 3rd differ. A3 Nos. 1 8 27 64 125 216 342 512 729 1st differ. A1 7 19 37 61 91 126 170 217 271 2nd differ. A2 3rd differ. A3 4th differ. A 18 24 30 35 12 44 47 54 1000 Now if the squares had been all multiplied by some constant coefficient, the last differences would have been equally reduced to zero. The same thing would have happened with the cubes. And, more complex still, if a new series were formed with terms consisting of squares and cubes, or their constant multiples, a series of differences would detect any deviation from a fixed law. Further, the law, being ascertained by a great number of experiments, slight errors of observation could be detected and rectified by the principles of interpolation.‡ The Bashforth chronograph, actuated by a fly-wheel of * An error of 1 is purposely introduced to show its exaggerated effect; the third differences, 0, 0, 0, 0, 0, 0, 0, being changed into 0, 0, 1, - 3. † An error of 1 only is introduced purposely, viz. 342 instead of 343, and great departure from regularity is shown in the third and fourth differences, in consequence of the above error. Even when a progressive law is unknown and implied, by which a series of results are obtained, still by successively differencing, by means of equidistant arguments, the existence of isolated errors can be speedily discovered and corrected. nearly uniform velocity, and recording clock-beats as well as screen-striking within the 2,000th of a second (the projectile cutting the threads of ten or fifteen successive screens, placed 50-150 feet apart), gives a permanent comparative record of the instants of the passage of the ball. The following example is expanded from "Trans. of the Royal Society," 1868, p. 425. Hemispherical-headed shot. Diameter 47 in.; weight 39-34 lbs. By interpolation* the instant of passing ten screens in succession, as marked by the spiral traced on the revolving drum, is thus given in decimals: : TIMES OF PASSING THE SCREENS. 3 4 5 6 7 8 9 10 Screen; 1 2 Times 24692 25956 27238 28539 2"-9858 3"-1196 3 2552 33925 35315 3" 6722 1264 1282 1301 1319 1338 1356 1373 The length of the spiral traced on the paper cylinder is about nine or ten inches for one second; thus by a vernier and It is hardly desirable to insert the formula of this process in an article on Popular Science. steel T-square and fine mark, the cylinder being removed from the machine and applied between centres as in the woodcut, the actual times of flight are compared with the instants of time measured on the paper, correctly, to the 200th of an inch. Next the velocities for the middle point of each interval between the screens are calculated. Data are then obtained for comparing the changes in velocity with those which ought to arise from a supposed law of resistance for every ten feet of the projectile's flight. The agreement of the calculated with the experimental results is then verified. From these researches, which, indeed, may be said to form a new era in gunnery, it appears as the result of chronographic experiments with some hundreds of rounds of every kind of shot used in the service That the diameter being the same, the shot preserves its velocity to a greater distance for hitting the mark, as the weight is greater. That the resistance is less for the same weight as the shot is elongated within certain limits. That the resistance also varies inversely as the square of the diameter. That the resistance of the air for velocities used in practice (900-1700 f. s.) cannot be expressed by any simple power, or The steel T-square slides along the plate L and the mark b upon it being placed accurately upon the successive records of seconds and screens, is read off by the vernier (a) to about the th of an inch, or 2,000ths of a second. The cylinder k is moved from the chronograph before the paper record is disturbed. simple function, of the velocity. The resistance of the air may be taken to vary as the SIXTH power of the velocity from 950-1050 f. s., as the THIRD power from 1070 to 1400 f. s., and as the SECOND power for higher velocities. Under these circumstances the cubic law, with a varying coefficient, has been adopted as the most convenient for calculation. That at 1,200 feet per second velocity this coefficient of resistance is the greatest for elongated projectiles, which rises in value rapidly at 1,000 f. s. to 1,100, and diminishes gradually as the velocity is increased beyond 1,200. But for spherical shot the coefficient of resistance rises more gradually to its maximum at the same velocity of 1,200 f. s., and diminishes gradually for greater velocities. DISSECTED TABLE. Chilled Shot Size and weight of shot 15-in. Initial velocity Distance from gun Rodman 150lb. 100lb. 68lb 32lb. 18lb. 12lb. 9lb. 6lb. 3lb. 2100 2100 2100 2100 2100 2100 210 2100 2100 7000 6000 5000 4000 3600 3100 2700 2300 1900 Corresponding ve locity at that distance 999 910 906 898 884 857 854 874 884 873 Such a table as this for every hundred feet is of high value, being the first ever trustily obtained.* It is remarkable that no Artillery Manuals hitherto extant give any reliable information upon the decrease of velocity at different ranges. The old difficulty, the unknown irrepressible stumbling-block, the resistance of the air, vitiated every attempt at scientific conclusions. Its great value may be at once seen from the solution of innumerable questions like the following: A 6-pr. and a 32-pr. are both about to be fired with the same initial velocity of 2,100 f. s. at what distance will the 32-pr. hit an object with the same velocity as the 6-pr. at 2,300 feet? By the table we see 4,000 feet distance has a velocity for the 32-pr. 884 f. s., and for the 6-pr. at 2,300 feet has a velocity of 884. Again, a 15-inch Rodman keeps up its velocity at 8,000 feet equal to that of a 68-pr. at 4,100 feet, target distance. Tables have also been ascertained for finding the velocity generated by different charges, so that the following complicated question can now be solved : A shot from a 9-inch gun (250 lbs.), fired at a target 200 yards' distance, is required to strike with the same velocity as it would strike at 1,000 yards, so as to compare perforating powers: what charges of powder must be used in each case? |