400 
MINUTES OF PROCEEDINGS OF 
Let us take the practice at 1°. As there were 10 rounds fired, the 
sum of the differences of range will be 15*9 multiplied by 10 = 159, 
and the sum of the mean differences of deflection 0*4 multiplied by 
10 = 4. 
These respective figures must be divided by one less than the 
number of shots. 
P = 1 |® = 17-67.. 
8 = i = 0-44. 
9 
But for all ordinary comparisons we may discard the second place of 
decimals, and take 
ijp = 17'7. 
= 0'4. 
The length of the probable rectangle is then found from the table by 
taking the number corresponding to 17*7. The left-hand column 
gives 17, and, running the finger along, the horizontal line, the number 
46*68 will be found under *7 in the top column; 46*68yds. is therefore 
the length of the probable rectangle. Similarly, 1 *05 yds., corresponding 
to 0*4, is the breadth of the probable rectangle. 
But if it be wished to work with greater accuracy—that is, to a 
second or third place of decimals—it is easy to do so by proportional 
parts. Thus, let the numbers be as at first calculated—17*67 and 0*44. 
The value for 17*6 = 46*42, and the value for 17*7 = 46*68; it is 
evident, therefore, that the value for 17*67 lies somewhere between 
46*42 and 46*68. The difference between the two latter numbers is 
*26, and the proportional part to be added to the decimal part of 46*42 
will be found by multiplying this by *07 and dividing it by *10 ; or, in 
round numbers, by multiplying 26 by 7 and dividing by 10. 
and 
26 x 7 _ 182 _ 
10 10 “ 
46*42 
*18 
46*60 
Similarly, the value for 0*44 lies somewhere between the values for 
0*4 and 0*5—that is, between 1*05 and 1*32. The difference between 
the latter is *27, and the proportional part will be 
27 X 4 108 ,, 
