474 



NA TURE 



[March 17, 1892 



his ballistic tables (1881 ). But Mayevski appears to have recently 

 become a disciple of Krupp, from the diagram in Nature, 

 August 28, 1890 (p. 411), where the dotted line (i) represents 

 roughly the resistance of the air to ogival-headed projectiles 

 given in my " Final Report," 1880 ; line (2) represents the law 

 of resistance deduced from these results by Major Ingalls, of the 

 United States Artillery, which is similar to the law deduced by 

 me (Nature, April 29, 1886, p. 605) ; and line (3) represents 

 the results Mayevski professes to have deduced from Krupp's 

 Meppen experiments. My law of resistance has been very 

 closely followed throughout by Mayevski, as is evident from the 

 diagram above referred to, which is suggestive of a free use of 

 the parallel ruler. The main object of these proceedings seems 

 to have been to persuade the world, and the Americans espe- 

 cially, that Krupp guns are far superior to English guns, regard 

 being had to the initial steadiness imparted by them to their 

 projectiles. But this claim is unworthy of notice so far as it 

 depends upon the Meppen experiments with chronoscopes, the 

 patent defects of some of which were pointed out in Nature, 

 April 29, 1886 (p. 606). If, however, Government consider this 

 matter worthy of investigation, there are simple practical methods 

 of determining the comparative steadiness of projectiles fired 

 from two or more guns. 



At present, my concern is with English guns only, and I wish 

 to point out, as briefly as possible, (1) that my results obtained 

 from English guns are quite correct ; (2) that the coefficients of 

 resistance for each round are expressed by such a short unit of 

 time that they are made to appear more irregular than they are 

 in reality, while the variation in their value is just what experi- 

 ment leads us to expect ; and (3) that when my mean coefficients 

 aSQ fairly used to calculate r&%\A\.%oi good experiments made with 

 recent English guns, in calm weather, the agreement between 

 calculation and experiment is perfectly satisfactory. 



My chronometric arrangements were made with a view to 

 guard against the errors cf remaining magnetism, which is the 

 chief source of error in the measurement of extremely short 

 intervals of time by the help of electro-magnetism. All the 

 time-records were made by one electro-magnet, whose galvanic 

 current was interrupted once a second by the swing of a half- 

 seconds clock pendulum ; and all the screen records were made 

 by another electro-magnet, whose galvanic current was being 

 rapidly interrupted by a self-acting contact-breaker, till the pull 

 of the lanyard turned off the contact-breaker, and then fired the 

 gun, after which the shot momentarily interrupted the galvanic 

 current as it passed each of ten or more equi-distant screens. 

 Also care was taken to reduce the strength of the galvanic cur- 

 rents, so as to leave each electro-magnet only just sufficient power 

 for the performance of its appointed work. Under these circum- 

 stances it may be safely assumed that, if there were any errors 

 arising from remaining magnetism, in either clock or screen 

 records, they would be cons/ant in each case, and therefore they 

 would have no injurious effect on the result obtained. The 

 records on a 4-inch cylinder were read off by a vernier to the 

 1/3000 of its circumference ; but as the scale of time was in 

 general only 9 or 10 inches to the second, it may be concluded 

 that the records were read off to the 1/2000 of a second at 

 least. 



The accuracy of the time and of the screen records was 

 tested by differencing, when slight adjustments were applied to 

 render the first and second order of differences regular to an 

 additional place of decimals. The following is a list of the 

 adjustments so applied in seven successive rounds, 146-152, 

 which are fair samples of those applied in the other rounds 

 (1867-68). They are expressed in decimals of the unit read off 

 by the vernier, or of the 1/2000 of a second. In round 258 an 

 example is given of the correction of an occasional erroneous 

 record at screen 6 : — 



+0-3 

 - 0-3 



+0-1 

 +0-3 



-ro-7 



152- i 258 



-O-I I - 0-6 

 4-0-7 - O-I 

 +0-3 i +32-9 

 -0-4 + 06 

 -fo-7 i + 0-2 



Here is conclusive evidence of the perfect trustworthiness of the 

 observations made, such as no other ballistic experiments have 

 afforded to my knowledge. When the readings of the screen 

 records required only such slight adjustments as those above 

 indicated, there could be no reasonable doubt about the perftct 

 accuracy of the experiment, and the round was accordingly- 

 adopted as good in all cases, unless there was some known 

 disturbing cause, as when the bronze gun expanded, or where 

 the gas check left the shot, &c. 



Although the records are read off only to the 1/20CO of a 

 second, we are able to express the coefficients of resistance 

 with much greater exactness through the employment of a long 

 range (1350 feet) where the only a*isolute errors in time possible 

 are at the two extremities of the range, and the accuracy of 

 each of these readings is tested by the differencing. Supposing 

 the retarding force of the air, acting upon an ogival-headed 

 projectile moving in the direction of its axis with a velocity z/ f. s. , 

 to be expressed by - 2b7^, the values of zooobwid" cor- 

 responding to all velocities from 900 to 1700 f.s. were found by 

 experiment in 1867-68, where w denotes the weight of the 

 projectile in pounds, and d its diameter in inches. Correspond- 

 ing to a velocity of 1200 f.s., the mean value of 200ol>7a/d^ 

 was found to be o'oooio89. But to avoid the use of so many 

 decimal places, K was subsequently employed to denote 

 (iooo)^2/^w/a'2 = {ioco)hvA^tld-r- = 108-9, where A-t is the 

 second difference of the times at which the shot passed successive 

 equi-distant screens / feet apart, with a velocity 1200 f.s, more 

 or less, and, in the case of the solid 5-inch shot it equals 

 o"-ooi24. From this it appears that for the specified shot the 

 time by which the unit of K is expressed is o"-ooooii2 in A^t. 

 Considering the shortness of this unit of time, it seems very 

 natural that some variations should have been found in the 

 experimental values of K for any specified velocity, derived as 

 they have been from both hollow and W?^ projectiles fired with 

 various charges from 3, 5, 7, and 9-inch guns. If we turn to 

 actual experiment, it is plain that the coefficients of resistance 

 for any given velocity cannot practically retain a constant value 

 for all rounds. For do not we frequently read that shot are 

 "noisy," or "unsteady" in their flight? There was much 

 unsteadiness in the Jubilee rounds; and Captain May, R.N., 

 in speaking of experiments with recent guns, remarked, "the 

 range of 500 yards is selected, because at this range shell which 

 start unsteadily will have steadied (that is if they ever do so), 

 &c." It is, therefore, quite natural that exact experiment should 

 afford evidence of this unsteadiness. 



It now remains to test the value of my mean results by making 

 use of them to calculate the ranges and times of flight of pro- 

 jectiles for comparison with the results of experiments made with 

 r^i;^«/guns. In 1879 some range tables of the 6-3-inch howitzer 

 were forwarded to me to show that my coefficients for low 

 velocities did not give satisfactory results. As the muzzle veloci- 

 ties in these tables were 332, 507, 628, 697, 740, and 751 f.s., 

 and the elevations varied from 5° to 40°, the trajectories were 

 much curved, so that my general tables were not applicable in 

 these cases. But when the ranges and times of flight were 

 properly calculated by Bernoulli's method, experiment and calcu- 

 lation were found to agree remarkably well. In the same way 

 numerous German range tables (Krupp guns ?) were calculated for 

 muzzle velocities varying from 380 to 774 f.s., which gave very 

 satisfactory results in general. Although there was no allow- 

 ance for jump or vertical drift in these calculations for low 

 muzzle velocities, the calculated often exceeded slightly the ex- 

 perimental ranges, showing that my resistances were perhaps a 

 little too low. The results of each of these comparisons— 32 

 English and 82 German— will be found in my " Final Report," 

 1880, pp. 45-47. For specimens of the best and worst results 

 of each kind, see Nature, April 29, 1886 (p. 606). Now 

 Mayevski proposes to reduce these coefficients of resistance, 

 already rather too low, by 20 per cent, more ! (Ingalls, 

 pp. 29, 36). 



In consequence of the Krupp scare, the authorities desired to 

 have the accuracy of my results tested by practice on a long 

 range, with a recent gun, and for this purpose they selected the 

 4-inch B. L. gun. Careful experiments were subsequently carried 

 out with this gun (1887), which showed that my coefficients of 

 resistance were perfectly satisfactory. But there was no real 

 necessity for any special experiments to be made with this gun, 

 as its own range table was afterwards found to be abundantly 

 sufficient for the purpose of testing my results. By calculating 

 trajectories carefully by Bernoulli's method, and then recalcu- 



NO. II 68, VOL. 45] 



