366 
MINUTES OF PROCEEDINGS OF 
OB' = z 0 ; let tan 6 1 be tbe tangent of the angle which the curve makes 
with Oz at A, and tan 6% be the corresponding tangent at B. 
Then, from the definition of the parabolic twist, 
and 
But, from (21), 
d*l 
dz ‘ 3 
dz 
= constant = <?, suppose; 
= cz; .. 
( 21 ) 
.( 32 ) 
tan Oq = czq, and tan 0 X — cz 1 ; 
e = tan = -0047925. 
Comparing (22) with the form of this equation given in (4), z 3 = forty, 
2 
we have y' — rty and fo = - = 417*8. 
Hence the equation to the development of the parabolic rifling is 
«8 = 417‘8r0,.(23) 
and z 1 the distance of the origin from the commencement of the rifling 
_ tanA _ 6 . 555 ft 
e 
25. As in the last case, I place in the form of a table the results 
given by (15) for different values of z. The values of the constants 
are, r = *417 ft., k = 417*3, P = *312 ft., /q= *167, *00555. 
Table showing the 'pressure on the studs in a 10 -in. British service gun, rifled with a 
parabolic twist commencing at one turn in 100 calibres and terminating at one 
turn in 40 calibres , calculated from (15). 
Value of 0 , tlie 
distance from 
tlie origin. 
Corresponding 
travel of the shot 
in the bore. 
Corresponding 
velocity of shot. 
Total pressure 
on base of 'shot. 
Value of JR, or 
total pressure 
on studs. 
ft. 
ft. 
ft. 
tons. 
tons. 
6-555 
0-000 
0 
0 
0 
6-888 
0-333 
411 
1547 
31-2 
7-500 
0-945 
675 
1077 
28-7 
8-389 
1-834 
873 
781 
29-0 
9-278 
2-723 
992 
621 
30-2 
10-167 
3-612 
1078 
510 
31-4 
11-055 
4-500 
1146 
424 
32-3 
11-944 
5-389 
1200 
356 
33-0 
12-833 
6-278 
1245 
305 
33-8 
13-722 
7-167 
1282 
268 
34-5 
14-610 
8-055 
1311 
240 
35-2 
15-499 
8-944 
1333 
220 
35-8 
16-388 
9-833 
1349 
205 
36-3 
26. From an examination of the values of R given in this table, it 
will be seen that the total pressure on the driving-surface reaches about 
31 tons shortly after the commencement of motion, and the projectile 
quits the bore with a pressure of about 36 tons. With the view of 
