264 SHIP CALCULATIONS; 
We are now prepared to assemble in Table III, the results found by 
applying the formule to the quantities found in the Tables I and II. “The 
areas of sections to the fifth water-line are found and the columns contain 
the signs which indicate all the operations performed. 
TABLE II].—To Finp S, A, V, D, anp T FROM TaBLEs I AND II: 
w=2 feet; s=9.17 feet. 
ee 
T 
Functions of Ss Functions of A Values of V D D' tons 
sections to | sq.ft. | water-line sq. ft. Ly cu. ft.| tons | fresh | per 
fifth water-line areas, from Vv water | inch 
Table I. 2WLy Table I. 2sxZy Table II. 2swzLy 35 =0.9722D A 
420 
I 2 3 4 5 6 7 8 9 10 II 12 
21 O69) 30.8 Z4| 74.8 | 1,371.8 224 167.6 6148 | 175.6 170.7 3-3 
Ze 18.6 74.4. 23] 65.7 | 1,204.9 223 97-35 3571 | 102.6 99.2 2.9 
23 28.4 | 113.6 De | 51.6 946.3 D227) 38.70 1420 | 40.6 39-5 2.2 
Za | 33-3 | 133.2 | () 21] 12.9 473.2 | 221 0.00 fo) 0.0 0.0 1.1 
Zs | 29.1 | 116.4 = = = _— — — — = = 
Zg | 18.6] 74.4 = = — — —_— = — = mae 
(4) Zo | 1. 
(oe) 
14.4 = = = = = = = = = 
The Additive Method.—Instead of finding first the volume at the upper 
water-line and working downward, it is the custom in the United States 
method to commence at the lower water-line, and work upward in successive 
functions, which is just the reverse of the subtractive method. Thus, the 
functions of the areas of sections to the lowest water-line is found first, 
and then the function of that to the next higher water-line is found by 
adding the half sum of the upper ordinates, andsoon. Thus, having found 
y= dy, + vot ys +3 
we have 
B= Dap 
a 
