Manchester Memoirs, Vol. xlvii. (1903), No. 13. n 



To satisfy these equations for all values of n requires 

 Mi^N^ = M{ = N; = o, and then M^, A//, N^, N; are deter- 

 minate and we obtain for the stress on the middle section 



7-, ^ T^ ( . til . nl 



wBAdE sinh — h sm— 



/= — , I 2 2 



■' ElAw' w'v'l I + ; ; 



^ ' ^ Hi nl , nl . til 



Z* g sinh— cos — hcosh— sin— 



22 22 



*-"VCS7^-?0 



(8) 



The statical stress in the plates of the middle section, 

 when the vessel is supported as shown in Diagram 2, is 



^ Md zivBAdD zwdD , , „ ,, 



ft =• -~T = rj — = rr ["'^ = ^^a\. 



•" I Af-K I 47rV '- -■ 



Appendix II. 



When the vessel is proceeding across the waves at an 

 angle (90 — 0), then 



. 27r 



X = LcosH and li = li„ + ^sin— cos0(jt: 4- vf) IV = wBdL 



as before . . (9) 



and, by integrating, we find that the pressure per unit 

 leneth of boat is 



where 



P= wB\ {h„ -yA-d)^ Asm -Ax + vt) \dx, 



^, AZcos'^e . 27r B sin6 , , 



A = -jT — ^— sin-7- — — . . . (10) 



B-rrSmd L 2 COS^e ^ ' 



Hence, if we replace A hy A', the preceding investiga- 

 tion will hold as before, and normal stress at centre 



A' 

 = (normal stress = o) X —p- 

 ^ ^ A 



