For the curves of constant d/L, the substitution of L 2 /T 2 was made for C 2 

 in equation (1); thus, 



— t— 5 — tanh 



T 2 2TT L (6) 



Multiplying both sides of equation (6) by d/L ; 



d V g , 2TTd 



— 7T~ — d/L tanh 



^277 L (7) 



Thus, for a given value of d/L, d and T may be calculatedo 



Plate 8 has the same axes as Plate 7 and shows curves of constant 

 wave length and constant d/Lo The curves of constant d/L are plotted in 

 the same manner as those on Plate 7. The equation for plotting the 

 vertical asymptotes of the curves for constant wave length is derived from 

 equation (2). To change the wave length from feet per second to knots, 

 and the period from seconds to minutes: 



L = 33°78 CT (8) 



Then from equation (3) J 



2 7T C =. 2TT d 



tanh (9) 



gT CT 



In deep water 2 d is very large, and the hyperbolic tangent approaches 



CT 

 one. Thens 



J3L 



2TT 



or 



C =» T (10) 



0o 0054-8 



where C is in knots and T is in minutes. Since the vertical asymptote 

 for the curves of constant wave length is in the deep water region of the 

 graph, the value of C in equation (10) may be substituted in equation (8), 



T = 0.01275 /L7 (11) 



The equation for the diagonal asymptotes is derived by; 



L = CT = yid T 



dT 2 = L 2 



77280 (12) 



