THE VALUE OF A HIGH SITE FOR COAST ARTILLERY. 
225 
First let the mistake be such as would cause an ‘ over.’ 
Suppose a gun placed at 0 and aimed at P, elevated in such a way 
that an error PT would result on the level; then the error from the 
high site would be PX , where 
PX —PT . s ^ - g> - , approximately, 
sin (/3 + o>) ^ J 
From this we see that the flatter the trajectory, the less will be the 
longitudinal error from the high site. 
The low site, however, reaps some advantage from the fact that co is 
less than the angle of arrival at X, but this is more than compensated 
for, by the smallness of PX as compared with PT, as will be seen by 
considering the virtual targets. 
In this investigation the angle of arrival at X will be taken as equal 
to /3 + a), though this is manifestly more than its true value, for the 
tangent to the trajectory, at the apex, is inclined at /3 to HH' and its 
inclination gradually increases to T, where it would have its maximum 
value ft + co. 
Let v be the height of the virtual target at any range, due to a 
level site, and let v be that of the virtual target due to a site h! high, 
at the same range. 
