DERIVATION AND ANALYSIS OF METHODS. 267 
All the additional explanations needed are given in the columns of 
Table IV, and the signs have been added to indicate the values therein 
contained. ‘Table V is taken directly from Table IV, and the even numbered 
columns of Table IV are multiplied by w for the values of S. 
TABLE V.—AREAS OF SECTIONS AND VOLUMES OF DISPLACEMENT FROM 
TABLE IV. 
Numbers of water-lines. 
Areas of Areas of Areas of Areas of 
ee ets sections. sections. sections. sections. 
sections. 
Column 6, Column 8, Column 10, | Column 12, 
Table IV. Table IV. Table IV. Table IV. 
Xw. Xw. Xw. xXw. 
I 2 3 4 5 
S = 2wdy. 
V = s3S. fo} (3) 0.0 (4) 0.2 @) 0.6 GG) 68 
w = 2 feet 
S = 9.17 feet I 2.6 8.8 18.4 30.8 
2 9.4 26.4 48.6 74.4 
3 18.2 45.8 78.4 113.6 
4 24.2 56.6 93.0 133.2 
5 26.8 64.0 104.8 146.4 
6 27.4. 65.0 106.0 147.6 
7 24.2 59.2 98.6 139.2 
8 15.8 43.2 78.2 116.4 
9 6.2 20.2 43.8 74.4 
10 (t) 0.0 | G) 0.0 | () oo | G) 7.2 
1. Sums of columns........... _ 154.8 389.4 670.4 984.4 
2. Volumes in cubic feet to each 
water-line............... _— 1420 3571 6148 9027 
RMIMINIE TOK S)tce, scenes Siecckoce soles = Ve V3 V4 V5 
We are now in position to compare the subtractive with the additive 
method. ‘The latter, as we have seen, requires a far greater number of 
additions, extending over three columns as in Table IV, and the sources 
of error are thus increased. Furthermore, the large figures handled in the 
even columns of the same table, due to the summing of the double functions, 
$ 22, furnish an additional source of error in adding, to say nothing of the 
+ 
