NATURE 
493 
THURSDAY, SEPTEMBER 1886 
22 
“33 
EXTERIOR BALLISTICS 
Exterior Ballistics in the Plane of Fire. By James M. 
Ingalls, Captain First Artillery, U.S. Army, Instructor. 
(New York: D. Van Nostrand, 1886.) 
APTAIN INGALLS has succeeded in presenting 
within the limits of 128 pages, for the most part a 
very good and complete account of the various methods 
now in use for calculating range tables and solving im- 
portant problems relating to trajectories of shot. The 
subject of ballistics is divided into three parts—interior 
ballistics, which treats of the motion of the shot within 
the bore of the gun, of which very little is known ; exterior 
ballistics, which deals with the motion of the shot after 
leaving the muzzle and till it strikes an object ; and the 
remaining part treats of the penetration into an object 
struck. The author confines his attention to exterior 
ballistics. His book is purely mathematical, but well 
adapted to the wants of the artillerist. It is in reality a 
second edition. 
In Chapter I. theoretical resistances are calculated for 
various forms of heads of elongated shot ; and Chapter II. 
is devoted to the consideration of experimental resist- 
ances, where reference is made to the experiments of 
Robins (1742); Hutton; Piobert, Morin, and Didion 
(1839-40) ; Virlet (1856-58). Then follows a brief notice 
of experiments made with the Bashforth chronograph at 
Shoeburyness. The dates of the publication of the first 
and final reports of these experiments are correctly given 
1870 and 1880 respectively, but there is no notice of an 
intermediate report (84/B/1879), printed by Government 
and circulated in 1879, giving coefficients of the resistance 
of the air for elongated shot for all velocities between 
430 and 2250 fis. (131 and 686 m.s.). But the first publi- 
cation of the results of these experiments will be found 
in the Zransactions of the Royal Society for 1868 for 
velocities 900 to 1600 f.s. (p. 441). Mention is then made 
of some rather meagre experiments said to have been 
made by Mayevski in 1868-69 with both spherical and 
elongated shot. In the latter case the assistance derived 
from the results of the English experiments is fully and 
candidly acknowledged by Mayevski, whose results it 
appears were not published till 1872, And lastly, 
“Mayevski’s and Hojel’s discussion of Krupp’s experi- 
ments made at Meppen (1881) are noticed. Some con- 
fusion is caused here from the intermixture of dates of 
experiments and dates of their publication, but it must be 
evident that the publication of Bashforth’s results was 
not anticipated by any experimenter here named for the 
whole range of velocities 100 to 2800 fs. for elongated 
shot, and for velocities 850 to 2150 f.s. for spherical shot, 
excepting in the latter case the results of Robins, Hutton, 
and Didion. 
Capt. Ingalls then proceeds to explain the methods of 
determining the coefficients of resistance. He passes 
over the ballistic pendulum, which is however not yet 
quite obsolete, and first deals with the case where veloci- 
ties of a shot are measured at two points a known distance 
apart. He gives a table of the 16 determinations of 
Didion’s p’ for spherical projectiles by Mayevski (pub- 
VOL. XXXIV.—No, 882 
lished 1872), and then he passes on to Mayevski’s and 
Hojel’s formulz for elongated shot (1882). It does not 
appear why priority is given to these recently published 
results. These being disposed of, the author gives a very 
good account of the manner in which Bashforth obtains 
his coefficients from the observed times occupied by the 
shot in passing over a succession of equal spaces (pp. 
31-35). Capt. Ingalls has expressed the law of resistance 
from these English results in terms of the powers of the 
velocity, upon which he remarked that the expressions 
deduced by Mayevski and Hojel from the Krupp experi- 
ments give a less resistance. He does not consider at 
all the nature of the experiments from which these con- 
tradictory results were obtained, but at once comes to the 
desired conclusion that “This is undoubtedly due to the 
superior centring of the projectiles in the Krupp guns 
over the English, &c.” But we very much doubt this 
statement. Further on, the experiments given in the 
“Annexe 4 la Table de Krupp” are calculated by (1) 
Krupp’s tables ; (2) by Ingalls’ tables (reduced by using 
¢ = ‘907, as had before been done in the Proceedings of 
the R. A. Institution, Woolwich, 1885); and (3) by 
Mayevski’s formule. The agreement between calcula- 
tion and experiment is apparently about equally satis- 
factory in all three cases. But the calculation by Ingalls’ 
tables supposes a reduction of over 9 per cent. in Bash- 
forth’s coefficients used in calculating these tables. We 
have not had an opportunity of examining the Krupp 
experiments of 1881, from which Mayevski’s formule of 
1882 are said to have been derived, unless they be those 
contained in Krupp’s Paper xxx., which gives the par- 
ticulars of a few “expériences pour déterminer la résist- 
ance de l’air aux grandes vitesses.” In that case we are 
informed that no less than szx chronoscopes were used 
in favs to measure velocities at 30, 130, and Iooo metres 
from the gun. This amounts to a confession that the 
particular instrument used was not to be relied upon. 
We have not space to pursue the question further, but we 
must direct particular attention to the group formed of 
rounds 7-10, fired July 5, 1881, stated as follows :— 
vat 30m. vat 130m. vat Iooo m. 
Round No. 301 No. 302 No. 292 No. 293 No. 114 No. 115 
7... 896'4 892°5 855°9 850°9 .. — 
8... 903°8 894°5 852°7' 862°7) =. — — 
9... 90774 1887-2 857°6 856°7 438°. — 
IO... 907°4 QII'4 854°t  $34°7 = oan 
Means... 903°8 89674 8551 851°3 438°. — 
goo'l m.s, 853°2 m.s. 438°I m.s. 
This is one of the six groups of rounds of which the 
experiment consists. It will be observed that there are 
large differences in some of the velocities measured at the 
same point by two different instruments, and that there is 
only a single velocity measured by one chronoscope at 
the distant station. It is quietly assumed that this one 
velocity of 438'1 m.s. determined from round 9 is perfectly 
correct and applies equally to all four rounds 7, 8, 9, and 
10! All the results deduced from this group depend 
entirely upon this szzg/e velocity. Chronoscope No. 115 
never came into action at all, and No. 114 only once. It 
is difficult to imagine a worse experiment. From all this 
it appears that it is necessary to be very cautious in 
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