6 UNITED STATES COAST AND GEODETIC SURVEY. 



speed in an elliptical orbit inclined to the equator about 23^°, a 

 ficticious or theoretical sun moving with uniform speed in a circular 

 orbit in the plane of the equator, and likewise, for the real moon, 

 which moves with varying speed in an elliptical orbit inclined about 

 5° to the ecliptic, a theoretical moon with uniform speed in a circular 

 orbit also in the equatorial plane is assumed. It further provides 

 for additional imaginary bodies or components, each with its own 

 uniform speed and period of revolution, so designed that the whole, 

 when combined in proper relation to each other, will represent accu- 

 rately the very complex motions of the real sun and moon. 



All the important theoretical bodies or components were care- 

 fully determined by Sir William Thomson and published in a table, 

 later extended and improved by Sir George H, Darwin, in which 

 their speeds are expressed in degrees and fractions to the seventh 

 decimal place per mean solar hour. Each component is known by a 

 symbol which is part of a system of notation adopted for the sake of 

 convenience. This table has since been used the world over by all 

 who have to deal with tidal computations. 



As these components, properly applied to the theoretical mean sun 

 and moon, practically correct their regular but incorrect motions to the 

 irregular actual motions of the real sun and moon, they also act as 

 correctives to the forces represented by them, and it is permissible to 

 regard each of them as an independent tide-producing body. 



Knowing the time element and consequently the period of revolu- 

 tion of each component, the complicated curve traced and marked 

 into mean solar hour spaces by the tide gauge can be decomposed into 

 its harmonic elements; provided, of course, that it extend over a 

 sufficient length of time, preferably not less than one year, so that 

 the effects of windstorms, freshets, etc., may be eliminated. 



For convenience, the periods of revolution of the components are 

 regarded as component days, and the twenty-fourth part of each 

 period as a component hour. The length of the component day, 

 expressed in meaii solar hours, is equal to 360° divided by the hourly 

 speed of the component, taken from Thomson's table above mentioned. 

 A twenty-fourth part is, of course, the length in mean solar time of 

 the component hour. 



By starting from any convenient point at the beginning of the tide 

 curve and measuring the heights of the tide throughout its length for 

 a year or more at intervals of a component hour we obtain all the 

 heights at the first, second, third, and so on to the twenty-fourth 

 hour. These readings reduced to 24 means, expressed in feet and 

 fractions, represent quite accurately the effect upon the sea due to the 

 particular component at the station where the curve was made. 

 In a general sense, these 24 hourly means may be regarded as repre- 

 senting a component tide curve. The semirange of this curve, or the 



