6 T. H. Havelock. 
We transform this as in the previous section, and also make use of the following 
evaluations 
7/2, 2 
| sec 0 cos (Koq, sec 0) d0 = — ale (Koq,)- 
0) 
[sec oan [* Salama see 6) gy, = (* Tolsafit) dm 
0 iL + m 2 J0 1 aa m 
J0 
= © {Hy (com) — Yocom) 8) 
Using, as before, g, for distance in front of the bow and q,’ for distance behind 
the bow, we find that the bow system is given by 
M 
C= — {Hy (Ko%1) — Yo (KoH)}3 G1 > 0 
U 
4M 
M , ’ 
Ps “= — Yo (kot) 5 qi > 9. (19) 
C= ; {Hp (kor) — Yo (Ko )} — 
There are similar expressions for the stern system with qg=« +l, all the 
signs bemg changed. These results are easily calculated from tables, and 
curves for the local disturbance and the waves for both bow and stern are 
shown in fig. 2. 
The complete disturbance is the sum of all the curves shown in the figure. 
The distribution of doublets is equivalent to a vertical line of sources at the bow 
and a vertical line of sinks at the stern. It may be noticed that the elevation 
os 
Fie. 2. 
becomes logarithmically infimite at bow and stern, and the discontinuities 
there arise as described in the previous section. The local disturbance is 
symmetrical fore and aft when taken as a whole, but is anti-symmetrical for 
bow or stern separately. If the complete disturbance associated with the bow 
is called a positive system, the stern generates an equal negative system. 
352 
