NATURE 



409 



THURSDAY, AUGUST 28, 1890. 



THEORETICAL BALLISTICS. 

 A Revised Account of the Experiments made with the 

 Bashforth Chronograph, to find the Resistance of the 

 Air to the Motion of Projectiles, Ssr'c. By Francis 

 Bashforth, B.D., late Professor of Applied Mathe- 

 matics to the Advanced Class of R.A. Officers, 

 Woolwich, and formerly Fellow of St. John's Col- 

 lege, Cambridge. (Cambridge : University Pressj 

 1890.) 

 O OB INS, in the last century, revolutionized the science 

 -■-^ of artillery by his invention of the ballistic pen- 

 dulum ; and in our own times Mr. Bashforth has accom- 

 plished the same thing for modern rifled artillery, by the 

 aid of electricity and by his own chronograph. 



Previous to Robins's experiments, the vaguest ideas 

 prevailed as to the velocity of cannon shot and musket 

 bullets : it was never supposed that such a light medium 

 as the air could offer the enormous resistance it does ; 

 and the resistance of the air being supposed almost 

 insensible, and Galileo's parabolic theory being applied, 

 the velocity of projectiles was very much underestimated. 

 At the same time, to reconcile Galileo's theory with the 

 observed ranges in practice, it was usual to suppose the 

 first part of the trajectory to be a finite straight line, the 

 point-blank range, and to add the parabola at the end of 

 the straight line. 



The ballistic pendulum of Robins enables us to dilute 

 the velocity of the bullet so as to make it easily measur- 

 able ; and by firing at the pendulum from different dis- 

 tances, and calculating the loss of velocity through the air, 

 we are able to obtain a fair estimate of the resistance. 

 Robins found in this manner that the resistance of the air 

 to a bullet, three-quarters of an inch in diameter, weighing 

 one-twelfth of a pound, is about 10 pounds, or 120 times 

 the weight of the bullet at a velocity of about 1600 feet 

 per second. By firing with a charge of powder half the 

 weight of the ball at the ballistic pendulum at ranges of 

 25, 75, and 125 feet, he found that the mean velocities of 

 impact were respectively 1670, 1550, and 1425 f.s. 



Now denoting by R the average resistance in pounds 

 over the first 50 feet, in which the velocity fell from 1670 

 to 1550, the principle of energy gives, in foot-pounds, 



1670''^ 



50R 



10. 



i51°,orR 



2 X 322 X 12 



Robins proceeds to theorize by the principle of me- 

 chanical similitude, and shows that a 24-pound cannon- 

 ball fired with a charge of 16 pounds of powder, should 

 acquire a velocity of 1650 f.s., and that the resistance of 

 the air would then amount to 540 pounds, or nearly 

 twenty-three times the weight of the shot. He is now 

 able to clear up the difficulty of the supposed point-blank 

 range, the distance during which the shot is conceived to 

 fly in a straight line. To reconcile the parabolic theory 

 of Galileo with the observed very small curvature of the 

 trajectory at the outset, ancient writers on ballistics were 

 in the habit of making a concession to the vulgar opinion 

 (an opinion not yet extinct, although Tartaglia pointed 

 out its fallacy) that the path of a shot was a straight line 

 for a certain distance, called the point-blank range, 

 NO. 1087, VOL. 42] 



during which the shot " flyeth violently," the motus 

 violentus of old writers. 



But now Robins is able to show that, in consequence of 

 the much higher velocity of the shot, and the much 

 greater resistance of the air than was ever considered, a 

 24- pound shot fired with two-thirds of its weight of powder, 

 will, at a distance of 500 yards from the piece, be separ- 

 ated from the line of its original direction by an angle of 

 little more than half a degree, so small an aberration as not 

 to be noticeable with crude artillery appliances ; and 

 generally that the track of the shot departs greatly from the 

 parabola, and is much more closely imitated by the com- 

 bination of motus violentus in a straight line, fnotus 

 mixtus in a curve or circular arc, and motus naturalis in 

 a vertical line, the vertical asymptote of the true path, as 

 taught by the old writers on artillery. 



The treatise of Robins, " New Principles of Gunnery," 

 1742, attracted immediate attention, and was translated 

 with a commentary by Euler. 



The ballistic pendulum employed by Robins weighed 

 about 56 pounds, and was used only with musket bullets ; 

 and to this day it will probably be found the most efficient 

 instrument for measuring the velocity and retardation of 

 small-arm projectiles ; the threads or wires of the electric 

 screens being easily missed by bullets, or, if struck, being 

 apt to deflect them. 



Experiments were made at Woolwich by Hutton in 

 1775 and by Gregory in 181 5, and by Piobert, at Metz, in 

 1839, to apply the ballistic pendulum to cannon-balls ; and 

 although not such an accurate instrument on a large 

 scale, in consequence of elasticity and vibration, still it 

 was the only means at hand till the invention of the 

 electric telegraph. The application of electricity to the 

 measurement of the time of flight of the cannon-ball im- 

 mediately suggested itself to various minds — Wheatstone, 

 Konstantinoff, and Brdguet — and a chronograph was soon 

 produced, capable of registering two instants of time, and 

 thence one velocity ; as performed at present by the 

 Boulengd chronograph, now in universal use for the deter- 

 mination of muzzle velocities and the proof of powder. 



Notwithstanding the obvious advantages of electricity 

 so late as 1855 a monster ballistic pendulum was con- 

 structed to the order of the Government, and first set up 

 at Shoeburyness, then at Woolwich, and finally dis- 

 mantled without ever having been used in any course of 

 experiments. The model alone of this instrument, shown 

 at the Exhibition of 1862, is reported to have cost ^800; 

 but for all practical purposes the pendulum could have 

 been replaced by a large box rammed with sand, and 

 suspended by chains about 6 or 8 feet long, and the 

 indications would probably have been more accurate. 

 The experimenters who followed Robins would have suc- 

 ceeded better if they had expended all their care and 

 ingenuity upon experiments on a small scale ; and really 

 with all their trouble it is found that, when checked by 

 electric records, their results are not so accurate as the 

 original observations carried out by Robins. 



The problem of the electric chronograph was occupying 

 Mr. Bashforth's mind when he received the appointment 

 of Professor of Mathematics to the newly instituted Ad- 

 vanced Class of Artillery Officers in 1864; where he was 

 well placed for carrying out his experimental ideas, with 

 the assistance of his enthusiastic pupils. 



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