46 U. S. COAST AND GEODETIC SURVEY 
The node factors for the middle of each year 1850 to 1999 are included 
in table 14. Logarithms of the reciprocal reduction factors for each 
tenth of a degree of J are given in table 12. 
135. The semidiurnal terms Ay and By may be combined in a 
similar manner. Letting A represent the lunar coefficient 0.5023 
sin?/ and B the solar coefficient 0.0365, we have 
Ay=A cos (2T+2h—2p) 
=A cos 2v cos (27+2h)+A sin 2 sin (27+ 2h) (228) 
By=B cos (2T+2h) (229) 
K,=(A cos 27+ B) cos (27+2h)+A sin 2p sin (27+ 2h) 
A sin 2p 
nee 2 2) 4 BSS =I 
=(A’+2AB cos 2v+B’)? cos | 27 +-2h tan Aviary eB 
=(C, cos (2T-+2h—2v’’) (230) 
in which 
C,= (A?+2AB cos 2v+ B?)t 
= (0.2523 sin* J+ 0.0367 sin? J cos 2v+0.0013): (231) 
Bi Manes A sin 2» ee sin *J sin 2y 
te Anos 27358 + 8 sin ecost27 BOT (232) 
Values for 2v’’ for each degree of N are included in table 6. 
136. The obliquity factor for K, will be taken to include the entire 
coefficient (A?+2AB cos 2v+ 5?) and its mean value will be taken 
as the mean of the product (A?+2AB cos 2v+B?)* cos 2y’’, 
From (232) 
cos 2v”=(A cos 2v+ B)/(A?+2AB cos 2v+ B?)i (233) 
Then for the mean value of coefficient of K, 
[(A?+2AB cos 2v+ B’)? cos 2v”|>=[A cos 27+ B]) 
= [0.5023 sin? J cos 2v-+0.0365])>=0.1151 (234) 
the numerical mean for sin? J cos 2v being obtained from formula 
(71). For the node factor of Ky divide the coefficient of (230) by its 
mean value and obtain 
f (Ky) = (0.2523 sin* [+0.0367 sin? J cos 2v+0.0013)? /0°1151 
= (19.0444 sin* J+-2.7702 sin? J cos 2v+-0.0981): (235) 
See table 14 for node factors and table 12 for reciprocal reduction 
factors. 
METEOROLOGICAL AND SHALLOW-WATER TIDES 
137. In addition to the elementary constituents obtained from the 
development of the tide-producing forces of the moon and the sun, 
there are a number of harmonic terms that have their origin in 
meteorological changes or in shallow-water conditions. Variations 
in temperature, barometric pressure, and in the direction and force 
of the wind may be expected to cause fluctuations in the water level. 
Although in general such fluctuations are very irregular, there are 
some seasonal and daily variations which occur with a rough periodic- 
ity that admit of being expressed by harmonic terms. The meteoro- 
logical constituents usually taken into account in the tidal analysis are 
