ON STEAMSHIP PERFORMANCE. 121 
3. By the coefficient of fineness of ends, and 
4, By the actual length as found by the lines. 
For the afterbody the length would be 2 of the above quantities, with the 
exception of 4, where it is given by the lines. 1, 2, 3, 4 worked out for the 
‘ Atrato’ would give a length of bow as computed by 
1. 70:16 feet * 
a 80, 
. 7S _—_—_ 
ASNEG' |, 
quantities which differ immensely. But whatever the length of forebody, 
afterbody, and middlebody may be as computed above, the three together 
must form the given displacement with the given draught of water. The 
wave-line method supplies formule by means of which the exact length of 
bow answering both conditions may be found; and in order to prove which of 
the four quantities is correct we proceed as follows :— 
Let p denote the coefficient of fineness of midship section, 
q the coefficient of fineness of body, 
r the coefficient of fineness of ends equal to g+p ; then 
volume of forebody equal to ‘5 Bldp =:51x @® 
»  afterbody ,, °5 Bi'dp +:19635 Bedp=(‘5 Il’ +-19635 B)® 
a middlebody ,, Bl'dp=l' x ® 
total displacement - ‘5 Bldp +:5 Bldp+:19635 Bedp+ Bl'dp. 
Dividing this by the parallelopiped, BLd, will give the coefficient of fineness of 
body, or qg, 
51 4°50 +19635B—U'=?LarL; but 7+ 7=L—l'; 
hence -5L+°5/" +-19635B=rL, 
from which equation 7’, or the length of the middlebody, may be determined; 
and haying the length of the middlebody deducted from the total length of 
the ship, six-tenths of the remainder will give the length for the-forebody, 
and four-tenths of the remainder will give the length of the afterbody. 
Working the above formula out for the ‘ Atrato’ we shall get 
‘5 x 3365 + 51 4+ -19635 x 40-92 = 6339 x 336-5, 
“Sl =37-02, or 1’ =74:04 equal to length of middlebody. 
hence length of forebody equal to :6(336-5— 74-04) = 157-476, 
and length of afterbody __,, *4(336°5 — 74:04) = 104-984. 
It will be seen from these quantities that already twice as long a bow has 
been obtained as is necessary for a speed of 11:22 knots. 
Let us now test these quantities for the displacement. 
* A curve is appended at the end of this Report, by which for any given speed in statute 
miles the length of bow and stern might be measured. 
