60 A CALCULATION OF PROBABILITY OF FIRE. 
A.S, or the error in estimating the lateral movement of the objective, 
can be calculated in a similar way to AX, and is equal to 
da X oh v2, 
ty 
where da is the value of the error in reading the bearing of the objective 
by means of the arc and vernier and can be estimated at *2 per cent. of 
the range, 7’ the time of flight, and ¢, the time taken by the objective 
to traverse 1° of arc, and can be tabulated for various speeds if the 
direction and range are known. 
A B 
Thus the values of A, B, Mand WN can be tabulated. Mi and wy can 
be worked out and their values compared with a probability table, and 
the corresponding percentages p and p, found; then P ae will be 
the percentage of effective hits. 
Before proceeding to work out an example I will remark on the uses 
of all this rather elaborate calculation. 
Stated briefly they are 
(1) The interest in knowing what is the factor of efficiency we 
may expect from any particular gun at objectives moving under various 
conditions of speed, direction, range, Wc. 
(2) It might be of value to a Section C.R.A. in helping him to 
decide which of several objectives should be engaged, or at what range 
to open fire on any particular objective. 
(3) If a coast defence ‘Kriegsspiel’ was ever organized it would 
enable the umpires to form an idea of the probable results of any par- 
ticular period of the engagement. 
(4) It would assist one in comparing the results of different batteries 
firing at practice under different conditions. 
I will now proceed to work out the tables of values for A, B, M and 
N for a particular gun and objective, and then to show how these tables 
can be used to ascertain the probable percentage of effective hits. 
I will take as an example a 6” B.L. gun Mk IV or VI, 100 ft. above 
sea level for the gun, and a ship 100 yds. long by 20 yds. wide with a 
freeboard of 5 yds. for the objective. 
Lxt h 
As oF from (1 
JE cot G+L? sin? g tan ( (1); 
put 
SE COP CD ELSE DN ooosns0ivssvosonssaose4e0oonoa0or (7), 
Lxl h 
A — Hue tan 6 Peer cere errr ness sees rd esreeresdesees (8), 
2000, 5 
~ dd © tand 
1 Tf laying by Case II. 
