92 ■ TIDES AND BENCH MARKS 



The declination of the moon also makes a change in the lunitidal intervals 

 and heights of the tide, which is usually greatest when the declination becomes 

 a maximum, at which time the moon is not far from the tropics. Hence the 

 tides due to the moon's declination, when at their most pronounced type, are 

 called tropic tides. At the time of the tropic tides the two high or two low 

 waters of the same day are generally unequal, and the range from the higher 

 high water to the lower low water is called the great tropic range. 



The lunitidal intervals for the tropic higher high and lower high waters 

 and for the higher low and lower low waters may be obtained from the mean 

 intervals as follows : 



Tropic HffWI = HW'l - 2.07 X Table 44 (7) 



LHWI= HHI—2m X " 44 (8) 



HLWI^ LWI— 2.01! X " 44 (9) 



LLWI^ LWI— 2.07 X " 44. (10) 



The table referred to here is in Appendix 9, Coast and Geodetic Survey 

 Eeport for 1897, the argument being different for each phase of tide. The 

 tropic lunitidal intervals from (7), (8), (9), and (10), are: 



Tropic HHWI = 7" 27.7^'a Tropic HLWI= 1" 34.2"^ 



" LHWI= 7^ ILO"^ " LLWI = 0^ 4:C>.0'''a. 



A tropic lunitidal interval marked a indicates that if such an interval is 

 added to the time of an upper transit of the moon when in north declination, 

 or to a lower transit with south declination, it will give the time of the higher 

 high or lower low water, according to which interval is used. 



The tropic tides may be said to result from the combination of a semidiur- 

 nal with a diurnal wave. The tropic lunitidal interval of the diurnal wave, 

 putting Di for diurnal, may be found by the equation 



n.HWI - 0.0342 {Kl + 0',)a (1 1) 



which gives 



DyHWI = S"" 21.9'"a. 



The mean range of tide may be obtained from the harmonic constants by 

 the formula 



+ i/2 (cos V + cos w) + - J^ 2 J/4 (i' — lo) sin (23/° — M\) 



loU 



+ 2if6 COS {ZMl — Mt) — 2J/2 



