476 



NATURE 



[March 17, 1892 



too small to be appreciable, to one of a degree of arc or even 

 more. . . . It also varies somewhat with the angle of elevation." 

 In one of his examples he supposed the jump to be 22 to 23 

 minutes. Although the jump and vertical drift are uncertain in 

 amount, they have considerable influence on the range and time 

 of flight, and on this account the calculation of trajectories is a 

 decidedly unsatisfactory method of testing the coefficients of 

 resistance of the air to elongated projectiles. 



In the early days of elongated projectiles the vertical drift 

 caused by the "kite-like action "of the shot was duly recognized, 

 but of late this disturbing force has been commonly ignored. 

 For now, when a calculated range is shorter than the experi- 

 mental range, it is at once assumed that the theoretical resistance 

 is too high. This resistance is forthwith reduced so as to make 

 the calculated agree with the experimental ranges, but seldom 

 is any care taken to compare the time of flight calculated with 

 this reduced resistance with the experimental time. It ought, 

 however, to be remembered that, while a reduction of resistance 

 increases the range it diminishes the time of flight over a given 

 range. Major Ingalls has given a complete example of this 

 method of correcting my resistance (Problems, &c., p. 151). 

 For elevations of 



2°, 4°, 6°, 8°, and 10°, 



he found it necessary to reduce my coefficients by 



4"5 2-3 5-2 8-1 9.7 per cent., 



in order to obtain the experimental ranges by calculation ; and 

 these reduced resistances gave the calculated times of flight too 

 short by 



o"*o9 o""i2 o""i3 o""26 and o"'42, 



which proves clearly that the theoretical resistances had been 

 too much reduced throughout. Also, if the method of cor- 

 rection pursued in the above example was correct, it would 

 follow that the coefficient of resistance is a function of the 

 elevation, which is simply absurd. 



On the other hand, suppose we correct the elevation so as to 

 make the calculated agree with the experimental range, which 

 seems to me to be a satisfactory approximate correction in such 

 cases. A careful calculation of the trajectory of an ogival- 

 headed shot (two diameters) fired from the 4-inch B.L. gun, at 

 an elevation of 1 5°, gave a range of 6448 y ards ( 1 85 yards too short 

 by the range table), and time of flight 2o"'46 (i"'io too short), 

 the density of the air having been supposed to vary with the 

 height of the shot. Now, corresponding to an elevation of 

 14° 16', the range table gives a range of 6448 yards, and time 

 of flight 20" '53. If we suppose that the elevation of the gun, 

 14" 16', was practically increased by 44' by jump and vertical 

 <Jrift, we obtain an elevation of 15" for the initial direction of 

 the shot. But, according to calculation, for an elevation of 15° 

 •we have found the range 6448 yards exactly, and the time of 

 flight 2o"'46, which is only -o"*o7 in error, and the calculated 

 horizontal striking velocity is 646 f.s. This, I maintain, is the 

 proper method of correction, because it corrects both range and 

 time of flight, when there is no wind. Using the general tables 

 and the horizontal muzzle velocity, the calculated time over 

 6448 yards is found to be 20" 53, and horizontal striking velo- 

 city 647 f.s., where t = 0'967, the mean density of the air, as 

 the projectile would rise to a height of 1800 feet. 



If the above be a correct view of what takes place, it follows 

 that the axis of the shot during its flight is inclined at such a 

 small angle to the direction of its motion, that the resistance of 

 the air to its forward motion is not sensibly greater than when 

 it moves in the direction of its axis. But small as this angle 

 must be, we find evidence of the marked effect of the lateral 

 action of the air in causing the shot to drift to the right towards 

 the end of the range. It is therefore to be expected that the 

 resistance of the air, acting from below on the shot, soon after it 

 Jeaves the gun will raise the shot upwards, and cause it to 

 move as if it had been fired at an elevation a little greater than 

 that at which the gun was laid. 



The Ordnance Committee fired some ogival-headed projectiles 

 from a 9 •2-inch wire gun at high elevations in 1888, professedly 

 to try whether calculations of trajectories at very long ranges are 

 trustworthy. But before experimenting they invited calculators 

 to furnish them with the calculated range and time of flight of a 

 380-pound elongated shot fired at an elevation of 40° with a 

 muzzle velocity of 2360 f.s. My calculations for an ogival head, 

 struck with a radius of one diameter and a half, gave a range of 

 19,436 yards, and time of flight 62"-i5, which were sent in in 



NO. II 68, VOL. 45] 



March 1888, Allowing 300 yards for jump and vertical drift, I ob- 

 tained a range of 19,736 yards. In April two rounds were fired 

 with a velocity of 2375 f.s. at an elevation of 40", which gave 

 ranges of 21,048 and 21,358 yards. My reply to this announce- 

 ment, by return of post, was that the ranges were about 1500 

 yards too great. In July the experiment was repeated, which 

 gave ranges of 20,236 and 20,210 yards, being a reduction of 

 near 1000 yards. Two rounds fired at an elevation of 30° gave 

 ranges of 17,500 and 18,344 yards ; two at 35° gave ranges of 

 19,420 and 18,963 yards ; and one at 45° gave a range of 21,800 

 yards. The times of flight have not been published. These 

 great variations in range were due in part to unsteadiness in the 

 motion of the shot, but chiefly to the prevalence of high favour- 

 able winds. 



In order to test guns or coefficients 01 resistance in a satisfac- 

 tory manner, calm weather is absolutely necessary. And if the 

 shot is expected to rise to a height of two or three miles, trial 

 balloons ought to be sent up to test the state of the currents in 

 the higher regions. Afterwards, when good mean results of 

 experiments have been obtained, then, and not till then, may 

 these mean results be used to test the results of calculation. 

 Experiments ought not to be made at all unless precautions 

 necessary to secure a correct result can be taken. 



I have calculated a complete range table for the 9*2 inch gun 

 for elevations 1° to 45°, according to the original programme 

 of the Ordnance Committee (Nature, September 13, 1888, 

 p. 468), where the net results of calculation have been given. 

 These ranges will require an addition perhaps of about 2 per 

 cent, for jump, vertical drift, &c., and a further i percent, if 

 the ogival head be struck with a radius of two diameters instead 

 of one and a half, and the increment of time must be ruled by 

 this increment of range. 



My sole object having been to obtain the correct law of re- 

 sistance of the air to the motion of projectiles, I was always 

 ready to consider any proposed correction. But my results, 

 obtained from numerous and most exact experiments, could be 

 changed only on perfectly satisfactory evidence. That evidence 

 I have failed to obtain in any single case, so that my results 

 remain practically the same as they were given in my original 

 reports, 1868-80. I have recently published a revised account 

 of all my experiments, accompanied by newly calculated general 

 tables, for both English and French measures, and other tables 

 required in the calculation of trajectories, according to the 

 results "of modern analysis. With these helps I have now 

 thoroughly tested my final results by the use of range tables of 

 the 4-inch, 6'3-inch, and 12-inch guns, with the most gratifying 

 results. And Major McClintock, R.A., has tested my coeffi- 

 cients for small-arm bullets, with very satisfactory results (Proc. 

 R.A. Inst., xii. 569). This evidence of the accuracy of my 

 results is the more valuable because it is derived from Govern- 

 ment experiments, made for other purposes, which have mani- 

 festly been carried out with great care and ability. Anyone so 

 disposed has the means to reexamine the whole matter for 

 himself. If there be not some error in my calculations, it 

 appears that my results do not admit of any real improvement, 

 and consequently my labours in this matter may be considered 

 to have reached a satisfactory conclusion. 



F. Bash FORTH. 



FORTHCOMING SCIENTIFIC BOOKS. 

 '"PHE following is a list of scientific works which will be 

 -'- issued by various publishers in the course of the spring : — 

 Messrs. Macmillan and Co.: — "Essays on some Contro- 

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 "The Beauties of Nature," by Sir John Lubbock, F. R. S., 

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 of Co-Planar Vectors and Trigonometry," by R. B. Hayward, 

 F.R.S., Assistant Master at Harrow; "Key and Students* 



