April 29, 1 886] 



NA TURE 



605 



that " the resistance of the air may be considered to vary 

 roughly as the sixth power of the velocity for velocities 

 900-1100 f s., to vary as the thii-d power for velocities 

 1100-1350 f.s., and to vary as the second power for 

 velocities above 1350 f.s. {Proc. R.A. Inst., September 

 1871). 



Further experiments were made in 1878-80, which 

 furnished the values of K for velocities from 100 to 

 2800 fs., as published in Reports, 1879 and 1880. 



I now propose to express the resistance of the air to the 

 motion of ogival- headed shot (li diam.) in terms of ?/-, w^, 

 and v^, according to the values of v. The Newtonian 



) ; the cubic 



1000/ 



law of retardation is given by 



.f-^y.whe: 

 \iooo/ 



law by - — K( — — ) ; and the law of the 6th power by 

 w Viooo/ 



re //denotes the diameter of the shot 



in inches, and w its weight in pounds. The values of K-., 

 used in the tables given below (I. to V.) are those given 

 directly by experiment, as published in my Reports of 

 1870 and 1880, with the exception that the values of K,, 

 for velocities between loSo and 15S0 f.s. have been in- 

 creased by 0'6S per cent., to render the density of the air 

 uniform throughout. 



The points of division in these tables are some- 

 what arbitrary, and if they should be passed a little 

 either way the practical error will not be large. Capt. 

 Ingalls, of the U.S. First Artillery, has deduced very 

 similar coefficients from my experiments, which he has 

 published in his "Exterior Ballistics" (1S85). 



In another place I have shown {P>-oc.o{ X.h.e R.A. Inst., 

 1885) how K may be corrected : (i) for density of the air, 

 by the introduction of a factor t ; (2) for steadiness of the 

 shot by a factor a- ; and (3) for a different form of head, 

 by a factor k. The corrected value of A' thus becomes 

 Ktitk. And the same form of correction will apply to the 

 coefficients k and L. 



It must be remarked that the values of K for high 

 velocities were derived from the motion of shot fired at 

 low elevations. Consequently, in calculating ranges for 

 comparison with experimental ranges, S:c., the best agree- 

 ment may be expected for low elevations of 1° to 4" or 5°. 

 But when the muzzle velocity is high and the elevation 

 considerable, there are several disturbing causes to be 

 considered. 



The elongated projectile has a tendency to preserve the 

 parallelism of its axis, but this soon becomes inclined to 

 the direction of motion of its centre of gravity, and hence 

 arises a lateral pressure from below, which gives rise to a 

 gyratory motion of the shot. The effect of this upon the 

 shot is to increase the resistance of the air, to give a 

 lateral "drift," and probably a still greater vertical "drift," 

 because ihejirst lateral disturbing pressure is from below. 



When the projectile rises to a great height the density 

 of the air decreases, and the resistance of the air is 

 consequently diminished. 



The direction of the initial motion of a shot is com- 

 monly not that in which the gun is pointed, but is affected 

 by an error called the " jump." 



All these errors tend generally to increase the range, 

 except that, when the axis of the shot is oblique to the 

 direction of motion, the resistance is increased. But it 

 is evident that the direction of the axis of the shot does 

 not differ much from the direction of the tangent to the 

 trajectory, because the holes made in targets appear 

 practically circular. 



And, further, guns have different shooting qualities, and 

 t is said that two guns of the same type do not shoot 

 alike. One gun may be superior to another for one 

 charge and be inferior for a different charge, as our 

 experiments clearly showed. I mention these matters to 

 show that we cannot expect an exact agreement in all 

 cases between calculation and experiment. 



velocities under velocity 850 f.s. 



As it was impossible to carry out experiments for velo- 

 cities below 430 f.s. in the usual way, special experi- 

 ments were made with elevations of 45^ and muzzle 

 velocities 420-140 f.s. The ranges and times of flight 

 were calculated on the supposition that the above law 

 held for velocities below 430 f s. (Final Report, pp. 7, 

 48, 49). As the agreement between calculation and ex- 

 periment was satisfactory, it was concluded that the above 

 found law was good for velocities 100 to 850 f.s. 



Table II. — Resistance olv'. 



Mean value of A'= 74-4 between velocities 850 and 1040 feet 

 per second. 



f.s. 



1040 

 1060 

 loSo 

 1 100 



Mean value of L 



Experi- 

 mental 

 A't, 

 84-0 

 92-1 

 106 o 

 107-2 



79-2 between velocities 1040 and 1 100 feet 

 per second. 



Table IV.— Resistance 



IIOO 



1 1 20 

 1140 

 1160 

 1 180 

 1200 



Experi- 

 mental 



A':, 



107-2 

 io5-o 

 109-0 

 109-7 

 109-5 

 106-5 



-1-6 

 -2-8 



-hO-2 

 -I- 0-9 

 + 0-7 



-2-3 



1220 

 1240 

 1260 



1280 



Experi- 

 mental 



A":, 



U0-3 

 I0S-7 

 109-4 



III -2 



109-3 



+ 06 

 + 2-4 

 + 0-5 



Mean value of A'= 108-8 between velocities iloo and 130D feet 

 per second. 



