60 U. S. COAST AND GEODETIC SURVEY. 



The mean period of the compound tide 2MS is identical with that 

 of the equilibrium tide ^tj of (100) and the mean period of the com- 

 pound tide MSf is the same as that of the equilibrium tide MSf of 

 (100). The arguments, however, differ by small quantities which are 

 functions of the longitude of the moon's node and do not affect the 

 mean periods. In the analysis the compound and equilibrium tides 

 of equal period can not be separated from each other, and there is no 

 known theoretical relation in their magnitudes. For convenience in 

 reduction such tides are considered as arising from a single source. 

 Following the past practice of the Coast and Geodetic Survey, the 

 component n^ or 2MS will be treated as though it were entirely the 

 variational equilibrium tide represented by the term {A)^ of (100) 

 and the component MSf will be considered only as a compound tide. 

 According to the system of Sir George H. Darwin, both of these com- 

 ponents appear to be considered as compound tides. The differences 

 resulting from the two methods of treatment are negligible compared 

 with the probable errors in the final results. 



For the factor F for the reduction of the compound tides the 

 products of the corresponding factors for the elementary tides are 

 taken. 



Thus, 



Fof(MS), =FofM2 (252) 



/^of(MN), =(FofM2)x(Fof N2) = (/^of M^)^ (253) 



F of (MK)3 --= (F of M^) X {F of K,) (254) 



F q£ (2MK) 3 = (7^ of MJ X (F of K^) (255) 



i^of (2SM)2 =Fof M2 (256) 



F of MSf = F of M2 (257) 



The component /Xj or 2MS being treated as an equilibrium tide, the 

 factor F of this component is given by formula (165). 



20. METEOROLOGICAL TIDES. 



Meteorological conditions have a considerable influence upon the 

 tides, but, in general, the effects are very irregular and do not admit 

 of being represented by harmonic terms. There are, however, some 

 conditions that occur with a rough periodicity which may be so 

 represented. The land and sea breezes and the daily variation in 

 the atmospheric pressure may give rise to a tide whose period is a 

 solar day and the changes in the seasons to a tide with a period of a 

 tropical year. The former is designated as the Sj component and 

 has a speed just one-half that of the principal solar components Sj 

 [(B)i of (215)]. The latter is the Sa component, and, although it 

 may be accompanied by a number of overtides, the only one generally 

 sought in the analysis is the semiannual component Ssa, which is 

 also a component of the equilibrium tide [(5)51 of (215)]. Although 

 the determmation of meteorological tides from long series of observa- 

 tions is valuable for some purposes, their recurrence is not generally 

 certain enough to make them of much value in the tidal predictions. 



