September 5, 1901] 



NA TURE 



445 



many authors to two ; and in 1895 Sir George F. 

 Hampson, in vol. iii. of his "Moths of British India," 

 cut down Guenee's numerous famihes to si.\, in which he 

 has been followed by many writers since, including 

 Staudinger and Rebel in the catalogue just published. 

 We believe ourselves that, though Guenee may have 

 established more subdivisions than necessary, yet that 

 the modern reaction has gone too far, and that some of 

 his families which have been now abandoned will 

 subsequently be reinstated. 



Of the general execution of Mr. Barrett's work we 

 have spoken fully in our notices of previous volumes. 

 The present volume contains detailed notices of several 

 species of considerable interest, such as Nyssia zoimrin, 

 A/»-axasgrosstti<uia/aAx\A Hilh-niia defoliata. Mr. Barrett 

 does not seem to be aware that Nyssia zonaria, an 

 insect of our dry coast sand-hills, is said to be found in 

 marshy localities instead, in France. W. F. K. 



LETTERS TO THE EDITOR. 



[ The Editor does not Itold liiniseif responsible for opinions ex- 

 pressed by /lis correspondents. Neitlter can lie undertal;e 

 to return^ or to correspond witli tlie writers of, rejected 

 maniiscripts intended for tliis or any otiier part of NATURE. 

 No notice is talieti of anonvnioiis communications.'^ 



Testing of some Ballistic Experiments. 



When the Council of Militarj- Education directed my atten- 

 tion to the science of ballistics in 1S64, I came to the conclusion 

 that a thoroughly good chronograph would solve all practical 

 difficulties. The newly-invented mstrument was first tried in 

 1865 with ten screens 120 feet apart, by the use of a 12-pr. 

 Armstrong B. L. gun, when eleven satisfactory rounds were 

 obtained. (Report (84/6/1941), and (Proc. of the R.A. Inst., 

 1866.) Afterwards Ciovernment decided to have systematic 

 experiments made to determine the resistance of the air to 

 ogival headed projectiles (\'^d) fired from 3, 5, 7 and 9-incli 

 M.L. guns, which were carried out in 1867-68 for velocities 900 

 to 1700 f.s. The results then obtained are still in use. 



In 1871-72 I published general tables, S^ connecting range 

 and velocity, and T^ connecting time and velocity. These 

 tables were adapted to calculate the motion of a projectile when 

 moving in the direction of its axis and acted upon only by the 

 resistance of the air. These tables have now come into general 

 use. 



In order to test my first trial experiment of 1865, I will now 

 calculate, by the use of these general tables, S„ and T^., founded 

 on the results of experiments 1867-6S, the time in which the ex- 

 perimental projectile would travel from the first to each succeed- 

 ing screen, for comparison with the average times determined 

 by the trial experiments, and published 1S65-66. Here 

 w= 11-5625 lbs. ; (/= 3 inches; <!'=/«' = 077838 ; wld-= 1-28472 ; 

 .S„ = S,-frf-/ic' = 4i26i-883- «93-4o6, where n is to be taken o, 

 1,2. . . 9 in succession to obtain the velocity at each screen. 

 And (Ty- T„)7t//(^- gives the time in which the velocity of the 

 projectile falls from v to v. (Tables in " Text-book of Gun- 

 nery, 1897.") 



(a) 



Further, the mean velocity of the projectile, at every 10 feet 

 from the first screen, was calculated from the results of the first 

 trial experiment, and published in the Proceedings, l865. I will 

 now ccilcitlate the velocity of the projectile at every 100 feet for 

 comparison. HereS|,= S^, - J(^-/?«' = 4I254-I - »7-7838, where « 

 must be taken in succession o, 1,2, &c. , to find the velocity at 

 130, 140, 150, &c., feet from the gun. The following results 

 have been thus obtained : — 



NO. 1662, VOL. 64] 



These two examples (a) and (6), comparing the results of 

 experiment published in 1865-66, and of calculation in 1901, 

 conclusively show the remarkable accuracy 



( 1 ) of the trial experiment of 1865, 



(2) of the systematic experiments 1867-68, 



and (3) of the general tables, 1871, used to connect (i) and (2). 



This chronograph was used in all subsequent experiments. 



The experiments of 1867-6S were continued by the use of a 

 new 6-inch B.L. Armstrong gun in 1878-79 (Report 84/B/2853), 

 and further with a new 8-inch Armstrong gun in 1880 (Report 

 S4/B/2909). The coefficients of resistance to ogival headed 

 shot (1-5;/) for velocities too to 2S00 f.s. were thus determined. 

 At an early period it was decided to employ J. Bernoulli's 

 method of calculating trajectories. As opportunity offered, the 

 calculation of auxiliary tables (X), (Y), (T) and (Y) was pro- 

 ceeded with, of which 97 pages were published in 1873, and 

 48 pages in 1 881, for the cubic law of resistance. And 70 pages 

 were published in 1S90 for the Newtonian law. The ogival 

 form of head ( I -5^) chosen by Government was a very good 

 form for standard experiments, as such projectiles were steadier 

 than more acutely pointed projectiles, and the results obtained 

 were easily adapted to other useful forms by using Kd'-jw instead 

 of d'lw. Thus ogivals (2d) were found to encounter a resist- 

 ance 3 per cent, less than the ogivals (\''^d), which gives 

 ic = o-97, and I do not remember having had to use any smaller 

 value of K. I consider that a reduction of 5 per cent., or k = o-95, 

 would be the least value of k for projectiles of any practical use. 



The only difficulty in experimenting was when the velocity 

 was low, for then the trajectories were much curved. But the 

 results obtained were tested by the calculation of 32 rounds of 

 English 6-3-inch Howitzer, and 82 rounds of German 15 cm. 

 Kurze Kanone for velocities 330 to 750 f.s. and found satis- 

 factory. (Final Report, pp. 45-47,) The results for /n;^,^ veloci- 

 ties were tested by calculating, by the use of the general tables 

 (k = i) the times over given ranges of 1000, 2000, &c. , yards, 

 where the elevation of the gun was low, using horizontal muzzle 

 velocities for the 4-inch B.L. 1S84 ; the 6-inch Q.F. 1891 ; and 

 1893 ; the 9-2-inch B.L. 1898 ; and the 12-inch B.L. gun ; for 

 velocities 1000 to 2600 f.s. My coefficients of resistance 

 appeared to be slightly too low. (Second Supplement, p. 15.) 



When trajectories are calculated as tests of coefficients, it is 

 necessary that both the calculated range and time of flight agree 

 with experiment. But when an elongated shot was fired with a 

 high velocity, it was found that both the calculated ranges and 

 times of flight were shorter than those given by experiment. If 

 then the resistance was reduced so as to give the desired range, the 

 calculated time of flight was found to be too short. Hence it 

 was clear that the error could not be corrected by any change 

 of coefficient of resistance. 



When elongated shot came into use, it was well understood 



