ON THE MOTION OF PROJECTILES. 
237 
Then, neglecting co z the above equations give 
But 
v * 
- = tan a. 
u 
Hence, to the order adopted, 
1 +tan a tan a 
tan a - tan a 
iJuL + v* f w gt \ 
sin (j)cot - cos 2 a cos $ - 1 -/ 9 - o / « , 9 <ot 
u \\fu 2 + v 2 6 \u 2 + v 2 / 
The first term is the one we anticipated, depending only on the 
latitude and time of flight. But the second term involves the azimuth 
of the line of fire also, and would be of importance if it were large 
enough. 
We may write 8 for tan 8, and measuring 8 and co in minutes and 
minutes per second, co — \ and 
,(14). 
For example, the 12 pr. B.L. field-gun with 8° elevation (no 
jump) and a muzzle velocity 1710 f.s., time of flight 11*8 sec. 
b' = 2*95 sin $ - • 19 cos cj) cos a. 
In England, say latitude 51°, this would give 
S'= 2*29- *12 cos a, 
that is a deflection of 2'T7 to the right when firing north and 2 '‘41 
when firing south. The range of the gun with this elevation is 
4000 yds, so that the shot would (on the average) fall about 5 inches to 
the left when firing north, and five to the right when firing south, 
if the sights were adjusted to the mean direction when firing east or 
west. Under the same circumstances at the equator the divergence 
