10 U. S. COAST AND GEODETIC SURVEY. 



observations of the tide at any place and obtain a corrected formula 

 which will generally represent very satisfactorily the true height of 

 the tide at that place for any desired time. 



4. ASTRONOMICAL DATA. 



The reader of this volume is presumed to have a knowledge of 

 elementary astronomy, but it may be well to emphasize here some 

 of the important details which pertain especially to the tides. Be- 

 sides the earth the only celestial bodies with which we are directly 

 concerned in this discussion are the sun and the mocm. Because of 

 the greater distance or smaller size of all the other heavenly bodies 

 their direct effect upon the tides of the earth is negligible. The 

 principal motions to be considered are the rotation of the earth on its 

 axis, the revolution of the moon around the earth, and the revolution 

 of the earth around the sun (or the apparent revolution of the sun 

 around the earth) . 



The earth rotates on its axis once each day. There are however 

 several kinds of days — the sidereal day, the tropical day, the solar 

 day, the lunar day, and the component day; — depending upon the 

 object used as a reference for the rotation. Since the stars are the 

 most nearly fixed objects we have for comparison, the sidereal day, 

 which is the time between two successive passages of the same star 

 across any given meridian of the earth, is usually considered as the 

 true period of the earth's rotation. The tropical ^ day is the time 

 between two successive passages of the vernal equinox over a given 

 meridian, and the solar and lunar days are the time between two 

 successive transits of the sun and m,oon, respectively, over a given 

 meridian. A component day is the time between two successive 

 transits over a given meridian of a fictitious satellite which is assumed 

 to represent the cause of a component tide. Each diurnal component 

 will have its own component day. The solar and lunar days vary a 

 little in length because of the lack of uniform motion of the earth and 

 moon in their orbits, and for this reason the average or mean values 

 of each is taken as a standard unit of measure. The mean solar day 

 corresponds, of course, to the ordinary calendar day. Each day of 

 whatever kind may be divided into 24 equal parts, called hours, which 

 are qualified by the name of the day which was subdivided, as sidereal 

 hour, solar horn*, lunar hour, or component hour. 



The moon revolves around the earth in an elliptical orbit. Al- 

 though the average eccentricity of this orbit remains approximately 

 constant for long periods of time, there are a number of perturbations 

 in the moon's motion due, primarily, to the attractive force of the sun. 

 Besides the revolution of the line of apsides and the regression of the 

 nodes which take place more or less slowly, the principal inequalities 

 in the moon's motion which affect the tides are the evection and 

 variation. The evection depends upon the alternate increase and 

 decrease of the eccentricity of the moon's orbit, which is always a 

 maximum when the sun is passing the moon's line of apsides, and a 

 minimum when the sun is at right angles to it. The variation ine- 

 quality is due mainly to the tangential component of the disturbing 

 force. The period of the revolution of the moon around the earth 



2 Thetropical day is also generally called a sidereal day, since its length differs from the true sidereal 

 day witliin a hundredth part of a second. 



