269 , 



The value of c on any day of the year maj^ be computed from equa- 

 tion (2oA) by substituting- the value of h on that daj^ At the vernal 

 and autumnal equinoxes, March 22 and September 21, A=0 and 180° 

 respectively, and c has a minimum value of 0.668. At the summer 

 and winter solstices, June 22 and December 22, A=90° and 270°, 

 and c has a maximum value of 1.331. 



The correction to be added to the value of Ki for the month, to 

 give the value of K' , is then 



i^'-Ki=cKi-Ki=(c-l)Ki (26A) 



18. Expression for 1.02 Fi. — Substituting in equation (23x4) the ex- 

 pression for iv' given in equation (26 A) 



L>m' = aKi/(Ki) + (c-l)K:+O,/(O0] 

 and the reduction factor is: 



Z>m/Z)m/ = 1.02(7(Ki + Ox)/a((c-l+/(Ki))Ki + Oi/(Oi)] 

 = 1.02(l+Ki/O0/[((c-l+/(K0)Ki/O:+/(O0] 



The ratio K/d of the mean values of the equilibrium components is 

 taken as 1.4066. 



The reduction factor is written: 



1.02Fi 



in which: 



i^i=2.4066/[1.4066(c-l+y(K0)+/(Oi)] 



By substituting the values of c, /(Ki) and /(Oi) at the middle of 

 each month, the values of 1.02 Fi may be found as shown in table 

 VIII, paragraph 189. 



Approximate value of (Ki + OO/AL 



19. The statement was made in paragraph 175, that in the lack of 

 better information the ratio (Ki+OO/Mo for entering table VI is 

 taken as 2 (DHQ+DLQ)/Mn. It is not difficult to see that the 

 daily high water inequality, DHQ, closely approximates A cos a, 

 where Di is the length of the resultant of the diurnal components and 

 a is the angle between the position of its radius vector at high water 

 and the Y axis. At the next low water the radius vector of the re- 

 sultant of the semidiurnal components has moved through approxi- 

 mately 180°, and that of the diurnal components through approxi- 

 mately 90°. The daily low water inequality is therefore about equal 

 to Di sin a, and the sum of the two daily inequalities to 



Di (cos a + sin a) 



