A CALCULATION OF PROBABILITY OF FIRE. 61 
» will vary with the value of ¢ or the inclination of Z the length of 
the ship to the line of fire. 
@ with this particular gun at this particular height above sea level 
will vary with the range. 
Now when ¢=0 the ship is advancing or retiring directly. The 
value of A is obviously the length of the ship Z+ the horizontal equiva- 
lent of the angle of arrival @ due to the height / of the freeboard. 
But 
Ll h Ih 
A= + Bap ay ee) and A=L. 
Similarly when 6=90°; that is, when the ship is moving across at 
right angles to the line of fire, 
,. & 
ASG and A=l+——. 
But for intermediate values of ¢, e.g. 15°, 30°, 45°, 60°, 75°, X must 
be calculated by working out the value of the expression 
VE cos? 6+ L? sin? f 
for the different values of ; these values work out to 
O20 15° 30° 45° 60° 715° 90° 
It. A= 20 3299 5291 7211 8718 9672 100 
Ll=100 x 20 
Ll 
TV, 92= 100 2 37-8 27-7 22:9 20°6 20 
me must be worked out for successive ranges 1000, 2000, 3000, 
tan 0 
4000, 5000, 6000 yds. @ being equal to the angle of descent + depression 
angle must be found by working out the depression angle at these 
ranges due to the height of the gun, and adding the result to the D.A. 
given in the range tables. h the freeboard =5 yds. 
Ranges 
yds. 1000 2000 3000 4000 5000 6000 
ie =O 94°88 64:73 43°11 30°04. 22°04 
tan 6 
Calculation of A. 
From IV. 
~=0 g=15° g=30° g=45° g=60° g=75° =90° 
Ll 
SC 100 62 378 27°7 229 20°6 20 
