238 
THE EFFECT OF THE ROTATION OF THE EARTH 
would be about 7^ inches either way. As the width of the 50 per cent 
rectangle at this range is over ten feet this divergence would not be 
noticeable. 
The following table gives a few examples. 
Time 
of 
flight 
sec. 
Divergence. 
Width 
50% 
rect. 
feet. 
Gun. 
M. V. 
f. s. 
Eleva¬ 
tion. 
Range 
yds. 
At Equator. 
Lat. 51°. 
min. 
ft. in. 
min. 
ft. 
in. 
12 pr. B. L. 
1710 
O > 
8 
4000 
11*8 
*19 
0 7* 
•12 
0 
5 
1014 
1960 
15 24 
6000 
20*6 
•75 
3 9 
•47 
2 
4 
.— 
6 in. B. L. 
12 42 
8000 
14-1 
•51 
3 5 
•39 
2 
7 
7-2 
900 (?) 
18 10 
10000 
28-0 
1*17 
9 9 
•74 
6 
2 
39 0 
^Howitzer 
60 0 
2000 (?) 
20*0 
6-28 
10 6 
3-95 
6 
7 
— 
The divergence here noted is that to the left when firing north, or 
to the right when firing south, if the sights are adjusted for east and 
west. It appears that the effect with the 6 inch gun ought to be 
noticeable at long ranges, on the average of a number of shots; for at 
the equator at 8000 yards it is very nearly half the 50 per cent, 
rectangle. In the case of the howitzer* defending a channel running 
north and south, if it were attacking the deck of a ship attempting to 
run the gauntlet, with high angle fire, it appears that the difference of 
deflection appropriate to the approaching and receding ship at 2000 
yards would amount to as much as 12 minutes, equivalent to an error 
of 20 feet at that range, which might be enough to prevent the shell 
striking the ship at all. 
The equations we have obtained also solve the problem of the 
deflection from the vertical of a stone dropped from a height, or 
projected vertically upwards. For the former we merely put zero for 
the initial velocities u, v, w y and equations (11—13) become 
x= - 6 > 2 .£( 7 sin$cos<^ 4 ) 
y = 0). J^rcos^ 3 > .(15). 
0 = - \gtf- - a 2 . | g cos 2 (pt 1 ) 
Hence it appears that the principal deflection is to the east but 
that there is also a deflection to the south (in north latitudes) if we go 
to a higher order in co. The easterly deflection for a fall of four 
seconds (about 250 feet) would be *57 cos </> inches, or about a third of 
an inch in England. The southerly deflection would be less than a 
thousandth part of this. The easterly deflection has been experi- 
Tlie details of the example about the Howitzer are not accurate. 
