438 
PROFESSOR F. BASHFORTH ON THE RESISTANCE OF THE 
where £=150 feet, and the mean value of bl 2 so determined from each round may be 
taken to correspond to the mean velocity of that round. 
Since the retarding force is f= — 2bv 3 , acting upon an experimental shot of weight 
W' lbs., the resistance of the air measured in pounds 
W' 
= -2 bv 3 ~; 
and the resistance will always be the same against a shot of the same external form 
when moving with the velocity v. If W be the weight of a different shot, then the 
retarding force 
/<=- 2 ^x4=- 2 (4y, 
or b varies inversely as the weight of a shot of given external form. If we vary the 
diameter of the shot, it is usual to assume that the resistance of the air varies as the 
square of the diameter for similar forms of heads of shot. The values of 2 b are given 
below in terms of E, the radius of the shot in feet, and W, its weight in pounds. But 
inasmuch as the diameters of shot are generally given in inches, the same values of 2 b 
have been expressed in terms of d, the diameter of the shot in inches. Unfortunately 
there are only three successful rounds for each of the solid ogivals, and one value of bl 2 
in each case is manifestly too large. This must have arisen from unsteadiness of the 
shot in its flight. If we reject these two, the values of bl 2 derived from the solid ogivals 
agree very well with those derived from the hollow shot of the like forms. 
For the hemispherical head we have bl 2 = '00084 for shot of mean weight 39*34 lbs., 
and 4*7 inches in diameter. To find the value of 2 b adapted for hemispherical-headed 
shot of weight W lbs., and diameter =d inches = 2 B. feet, we have 
2 x *00084 / d \ 2 /39*34\ 
25 =TT5or x (l7) (w-) : =-0000001329 
W’ 
2 x *00084 , 
124R' 
150 ! 
< 4 ' 7 ; 
^=•000077 
and so on for the rest. 
Table of values of 2 b for differently formed heads adapted for elongated shot 
of weight W lbs. and radius B, feet, or diameter d inches. 
Form of head. 
Experimental 
value of bl 2 . 
Mean weight of 
experimental 
shot. 
Value of 2 b when 
diameter =2R feet. 
Value of 2 b when 
diameter ~d inches. 
(!) Hemispherical 
(2) Hemispheroidal 
(3) Ogival (1 diameter) 
(4) Ogival (2 diameters) 
(5) Ogival (1 diameter) 
(6) Ogival (2 diameters) 
•00067 
•00070 
•00070 
•00125 
•00118 
lbs. 
39-34 
38- 70 
39- 56 
38-52 
21-81 
21-94 
•000077?" 
w 
>?! 
w 
•000064?" 
w 
,w 
' w 
,R 2 
•000060 . 
•000062 
,K 2 
•0000001329 . 
W 
•0000001085 ^ 
w 
■0000001097— y 
w 
•0000001042 J! 
w 
