August 28, 1890] 



NATURE 



411 



ance, and to tabulate the other factor, as a slowly varying 

 quantity. 



Practically, we find that A^/ is about one-thousandth of 

 a second when / = 150, the distance between the screens 

 in feet, so that dHlds^ is a decimal beginning with six or 

 seven zeros. Mr. Bashforth avoids this inconvenience by 

 writing the retardation — 



ds'^xioooj' 



equivalent to reckoning the velocity in thousands of feet 

 per second. 



We have explained this notation at some length, as 

 Mr. Bashforth has taken this and all other notation for 

 granted as known, which is already given in his " Motion 

 of Projectiles." The numerical values of K from the ex- 

 periments are given in Table XI. for spherical and in 

 Table XII. for ogival-headed projectiles ; these two tables 

 containing the complete theoretical deduction of all the 

 author's numerous experiments. 



But as for very high or very low velocities the New- 

 tonian law of resistance, varying as the square of the 

 velocity, is more likely to be near the truth, the author 

 has converted his coefficients K for the cubic law into 

 coefficients k for the Newtonian quadratic law, tabulated 

 in Tables I.-VI. ; here, again, he has omitted to explain 

 the formula required in the use of Jt ; but it is easily 

 inferred to mean that the resistance of the air is 



d-M -—] poundals, or d- ~{ JL\ pounds, 

 \ioooy £^\lOOO/ ^ ' 



so that the relation connecting i and K is 1000^ = vK. 



In the practical use of the tables, we choose the one in 

 which ^ or K is the more nearly constant and changes 

 the slower. 



The value of k for ogival-headed projectiles has been 

 plotted graphically in the following diagram by Mr. A. 

 G. Hadcock, quoted by Mr. Bashforth on p. 149 ; curve 

 I being drawn from the result of Mr. Bashforth's experi- 

 ments ; curve 2 from the empirical laws of General 

 Mayevski deduced from Bashforth's experiments; and 

 curve 3 from the empirical laws of Captain Ingalls, drawn 

 up to represent the resistance of the air according to 

 Krupp. 



790 990 mo 1330 



787 9C8 IZ30 I37S 



The diagram is interesting as showing how far the 

 Newtonian law is true for very low and very high 

 velocities, and it confirms in a remarkable way the 

 change in the value of & as we pass through the velocity 

 of sound, so that its final value is about three times its 

 initial value, as found out by Robins ; insomuch that the 

 resistance of the air to a 12-pound shot moving at 

 NO, 1087. VOL. 42] 



1700 f.s., which, according to the experiments of Newton 

 on slow motions (" Principia," lib. ii.. Props. 38-40), 

 ought to have been 144 pounds, was found by Robins to 

 be 433 pounds, or three times as much. 



At velocities less than that of sound the projectile is 

 always moving among its own waves ; at greater veloci- 

 ties the point is supposed to be cleaving undisturbed 

 air, like a swift steamer on the water ; and now the chief 

 element of resistance arises in the energy drawn off- in the 

 waves in the wake, waves which have been photographed 

 by Mach and Salcher, according to an article signed 

 " B." in Nature. 



Recently it has been discovered that with high veloci- 

 ties the shot carries the sound of the gun along with it, 

 while backwards and sideways the sound is propagated 

 at its ordinary rate ; this phenomenon is sufficient to 

 destroy the utility of range- finders based upon the obser- 

 vation of the velocity of sound. 



Curve 3 indicates that the resistance of the air to 

 Krupp's projectiles is about 10 per cent, less than to 

 ours ; this may be attributed to the sharper point, better 

 centering obtainable with breech-loading, and a slightly 

 less standard density of air ; but Mr. Bashforth points 

 out, with some justice, that the resemblance of Krupp's 

 curve 3 to his own is rather suspicious, considering the 

 small number of published experiments upon which 

 Krupp's experiments are based. 



Mr. Bashforth honestly prints all the values of K 

 derived from his experiments, values often exhibiting great 

 discrepancies among each other, and takes their mean 

 as the true value ; whether more delicate chronographs 

 and improved electrical manipulation will enable us to 

 refine on Bashforth's results remains to be seen, as a 

 correction in the first decimal place of the value of K, 

 depends upon the millionth of a second — a refinement we 

 are very far off from having attained. Mr. F. J. Smith has 

 given an account of a chronograph of his own invention, 

 and in the August FAt7. Mag. a description of a method 

 of eliminating the latency in electro-magnetic records in 

 chronographs, which may prove very useful. A chrono- 

 graph to read directly to one ten-thousandth of a second 

 is now the great desideratum : when chronographs were 

 first brought out, the millionth of a second was glibly 

 talked about, but so far, the thousandth is very good work 

 indeed. 



The experimental part of work is concluded when the 

 value of K is obtained ; but on these experiments Mr. 

 Bashforth is able to build up his tables of T and S 

 (XXIII.-XXXIII.), which enable us to calculate before- 

 hand the performance of any gun, and save thousands of 

 pounds in gunpowder at the price of a little ink. 



Knowing C, the ballistic coefficient of the gun, then 

 the formulas 



/ = C(Tv - T^), s = C(Sv - S^), 

 connect the distance s in feet and the time t in seconds* 

 for any initial velocity V, and final velocity v. 



An additional table, for D, invented by Mr. W. D. 

 Niven, is not given by Mr. Bashforth, but is found of 

 great practical use ; it gives 8, the deviation in degrees in 

 a vertical plane for a flat trajectory, by the formula — 

 S = C(Dv - D-.). 



Colonel Siacci, of the Italian artillery, has converted 



