262 SHIP CALCULATIONS; 
water-line. It remains for us to find the similar functions of the fourth, 
third, second, and first water-lines from 225. 
TasiEe I.—To Finp FuNCcTIONS OF AREAS OF WATER-LINES AND SECTIONS, 
AND OF DISPLACEMENT, FROM THE ORDINATES; OR, GIVEN THE VALUES 
OF y, TO FIND 2, AND 225. 
Nambers Numbers of water-lines. Functoncor 
of sections to 
sections. 5 4 2 3 , fifth water-line. 
Once sense iee (4) o.1 (4) o.1 (4) o.1 (4) 0.0 (;) 0.0 0.3 (4) Zo 
either cee neha (G)) 27 2.8 2.0 1.1 (4) 0.1 7-7 Z1 
Die be eek (&) Bo2 6.1 5.0 Bes, (3) 0.6 18.6 Ze 
Cees rear (4) 5 8.6 RoW 6.1 (4) 1.5 28.4 Z3 
Ai aeons pe a (4) 5.1 9.9 8.3 7.9 (4) 2.1 33-3 D4 
ona oP (4) 5.2 10.4 10.0 8.6 @) 2.4 36.6 Z5 
Baise amends es (4) 5.2 10.4 10.1 8.7 (4) 2.5 36.9 Ze 
Rei Ouie Sir orA ea (4) 5.1 10.1 9.6 7.9 (4) 2.1 34.8 Z7 
ee Mace bee (4) 4.9 9-3 8.2 5-5 (4) 1.2 29.1 Zs 
Cleo eb sees (4) 4.1 Foi 4-7 Ao (4) 0.4 18.6 Z9 
HOooccccv0a0e. (Z) 1.8 (2) (2) (2) (2) 1.8 (2) Zio 
HGncuons sot 41.1 74.8 65.7 51.6 12.9 246.1 2210 
of areas of 
water-lines. @) oe D4 =3 Ze @) Drs Check. re 
Likewise, in column 7, we have found the functions of sectional areas 
up to the highest, or fifth water-line, and we may desire to know these 
functions to each water-line; and must subtract the half sum of the two 
upper ordinates to get the function of the sectional area to the next lower line. 
We have 
Qs = 3V1 + Yo + 3+ Ya + 35. 
To get from this the similar function to the fourth water-line, we must 
Ys Vs 
2) 
subtract or one-half the two upper ordinates; thus 
B= B,— = dy, + ye toe dos 
and so on, for the functions of the lower water-lines. 
