104 U. S. COAST AND GEODETIC SURVEY 



The moon's change in decHnation is taken account of by two components 

 denoted by the symbols Ki and Oi. The speeds of these are'determined by the 

 following considerations: The average period from one maximum declination to 

 another is a half tropic month, or 13.66 days. The speeds of these two compo- 

 nents should, therefore, be such that when the moon is at its maximum declina- 

 tion they shall both be at a maximum, and when the moon is on the Equator they 

 shall neutralize each other; that is, in a period of 13.66 days Ki shall gain on Oi 



360° 

 one full revolution. The difference in their hourly speeds, therefore, is ^. ^„ „„ 



= 1°.098. The mean of the speeds of these two components must be that of 



the apparent diurnal movement of the moon about the earth, or x . ^^ . =14°.49. 



The speeds are therefore derived from the equations ^-^--=14°. 49 and Ki — Oj 



= 1°.09S, from which K, = 15°.04 and Oi = 13°.94. 



It is customary to designate the amplitude of any component by the symbol of 

 the component and the epoch by the symbol with a degree mark added. Thus 

 M2 stands for the amplitude of the M2 tide and M2° for the epoch of this tide. 

 The five components enumerated above are the principal ones. Between 20 and 

 30 components permit the prediction of the time and height of the tide at any- 

 given place with considerable precision. 



From the harmonic constants the characteristics of the tide at any place can 

 be very readily determined. 1 The five principal constants alone permit the ap- 

 proximate determination of the tidal characteristics very easily. Thus, approxi- 

 mately, the mean range is 2M2, spring range 2(M2 + S2), neap range 2(M2 — S2), 

 perigean range 2(M2 + N2), apogean range 2(M2 — N2), diurnal inequality at time 



TV /r o 



of tropic tides 2(Ki + 0i), high-water lunitidal interval 90 qo- The various ages 



of the tide can likewise be readilv determined. Approximately, the ages in hours 

 are: Phase age, 82° — Mz"; parallax age, 2(M2° — N2°); diurnal age, Ki° — Oi°. 

 The type of tide, too, may be determined from the harmonic constants through 



the ratio ■.} , g' - Where this ratio is less than 0.25, the tide is of the semi- 



M2+b2 



diurnal type; where the ratio is between 0.25 and 1.25, the tide is of the mixed 

 type; and where the ratio is over 1.25, the tide is of the diurnal type. 



The periods of the various component tides, like the periods of the tide-produc- 

 ing forces, group themselves into three classes. The tides in the first class have 

 periods of approximately half a day and are known as semidiurnal tides; the 

 periods of the tides in the second class are approximately one day, and these 

 tides are known as diurnal tides; the tides in the third class have periods of 

 half a month or more and are known as long-period tides. In shallow waters, 

 due to the effects of decreased depth, the tides are modified and another class 

 of simple tides is introduced having periods of less than half a day, and these 

 are known as shallow-water tides. 



The class to which any component tide belongs is generally indicated by the 

 subscript used in the notation for the component tides, the subscript giving the 

 number of periods in a day. With long-period tides generally no subscript is 

 used; with semidiurnal tides the subscript is 2; with diurnal tides the subscript 

 is 1, and with shallow-water tides the subscript is 3, 4, or more. Thus Sa repre- 

 sents a solar annual component. Pi a solar diurnal component, M2 a lunar semi- 

 diurnal component, S4 a solar shallow-water component with a period of one- 

 quarter of a day, and Mg a lunar shallow-water component with a period of 

 one-sixth of a dav. 



TIDAL DATUM PLANES 



Tidal planes of reference form the basis of all rational datum planes used 

 in practical or scientific work. The advantage of the datum plane based on tidal 

 determination lies not only in simplicity of definition, but also in the fact that 

 it may be recovered at any time, even though all bench-mark connections be 

 lost. 



The principal tidal plane is that of mean sea level, which miy be defined as 

 the plane about which the tide oscillates, or as the surface the sea would assume 

 when undisturbed by the rise and fall of the tide. At any given place this 

 plane may be determined by deriving the mean height of the tide. This is 



1 See R. A. Harris, Manual of Tides, Pt. Ill (U. S. Coast and Geodetic Survey Report for 1894, 

 Appendix 7). 



