174 MINUTES OF PROCEEDINGS OF 
expressed in terms of the differences of the times, which, it has been 
shown, can be ascertained by means of Mr. BashfortlTs chronograph 
and screens. 
9. Application to Practical Examples. 
(Article 55). 
Mr. Bashforth describes how— 
1st. The screens were placed 150 ft. apart. .\ l = 150. 
2nd. The readings of the clock were taken for five consecutive 
seconds, during which time the gun was fired. 
3rd. These readings were corrected by differencing, 
4th. They were interpolated for half-seconds. 
5th. n n tenths of seconds, when the differ¬ 
ences appeared nearly constant; so that for smaller fractions 
of seconds simple proportion could be used in place of further 
interpolation. 
6th. The gun was fired about the third second, and the readings 
were taken for the time of the projectile passing through each 
screen. 
7th. These readings, were corrected by differencing. 
8th. They were compared with the former interpolated readings; 
thus the time of each screen being passed was very accurately 
obtained, viz.— 
Time 
Screen, in secs. 
1 3-0526 
2 3-1616 
3 3-2730 
4 3-3868 
5 3-5031 
6 3-6219 
7 3-7432 
8 3-8669 
9 3-9930 
10 4-1216 
At AH 
1090 
1114 
1138 
1163 
1188 
1213 
1237* 
1261 
1286 
24 
24 
25 
25 
25 = 
34 
24 
25 
Suppose the velocity and retardation to be required at the fifth screen 
—namely, v 5 and,/ 5 . 
Here A4 = T188; A 2 4 = -0025; A 3 4, &c., vanish in the first four 
places of decimals. 
Also A 2 4= ‘0025 j which is required for substitution in (2), since 
“s l” brings us to the fourth screen* 
