124 



value is used in the preparation of the table. The value of g is taken 

 as 32.16. By entering table IX with the computed value of PjS or 

 of its logarithm, the value of ^ for a simple tidal fluctuation mth a 

 speed of m2, is readily determined by interpolation. 

 The value of B is then, from equation (155): 



B=P^ cos (p (16Uj 



247. If the tidal fluctuation has a speed, a, differing from that of 

 the principal lunar semidiurnal component, m2, on which table IX is 

 constructed, equation (159) may be written: 



{g/m2)'\lsin 4> tan 0= {(1/1112) P/S (161 



To determine the value of ^, table IX is then entered with the 

 computed value of (a/m2)P/»S'. It may be noted that the speeds, a 

 and m2, may be expressed in any common units. 



248. Value of (3. — From equation (150): 



/3=i7O-0-7r/2 

 Or, when angles are expressed in' degrees: 



/3=i70-<^-90° (162 



The equation of the primary current is then: 



v=B sin (at+H'^-(t>-90°) (163) 



The values of B and <^ are determined as shown in paragraph 246; 

 and W, the initial phase of the head, is determined as shown in 

 paragraph 239. 



249. Exmnjjles. — The surface head between stations 180 + 30 and 

 225 in the Cape Cod Canal, at the tune t after a lunar transit, was 

 found in paragraph 240 to be: 



hs=0.58 cos (m2f+224°14') 



The length of the section is 4,470 feet, giving: ,5=0.58/4470 = 

 0.000,130. The hydraulic radius, at m.ean tide, at the time of the 

 observations, is given as 22.7 feet. As the bed is exceptionally rough, 

 an appropriate value of Kutter's "n" is 0.030. Taking the mean 

 slope as 0.0001, the corresponding value of Cis 90. From these data: 



P=1.0854CVr^=5.31, P/S=40,820. 



