214 
THE VALUE OF A HIGH SITE FOR COAST ARTILLERY. 
I. The Probable Rectangle. 
The dimensions of the probable rectangle, as given in the Range 
Tables, have to be modified when the gun is raised above the level: 
the breadth zone is, of course, unaffected but the length zone must be 
reduced in the proportion of 
sin co : sin (co+0). 
For let a gun at 0, be fired at such a range that PT would represent 
the 50 per cent, length zone, on the level, the length zone due to the 
height, HO, will be given by PX. 
That is, if 
Now 
PT=l, PX=l'. 
PR=PT . 
and 
so that 
sin (w+0)’ 
PX is< PR. 
PX is<PT - 
sin («+0) ? 
but as a useful approximation we may write, 
sin co 
l' = l 
sin (&> + 0)' 
Therefore the higher a gun is placed above the sea-level, the more 
accurate weapon it becomes. 
