6 



minutes), from the Greenwich intervals, increased if necessary by 

 12.42 hom-s. 



Thus, the mean interval from the tabulated Greenwich transits to 

 standard times of observed high water at Seattle, Wash., in January 

 1928 was found to be 4.98 hours. As the standard time meridian at 

 the locality is 120° west of Greenwich, the Greenwich interval is 

 found by adding 120/15 = 8 hours. As the sum, 12.98 hours, exceeds 

 the interval between lunar transits, the average Greenwich interval 

 at the station during the month is recorded as 12.98 — 12.42 = 0.56 

 hours. The longitude of the station is 122°20'' W. The correction 

 to be subtracted from the Greenwich interval to give the local lunitidal 

 interval is (122)0X0.069 = 8.44 hours. The average local high-w^ater 

 interval for the month is then 12.98 — 8.44=4.54 hours. 



Wliile lunitidal intervals are conventionally given as local intervals, 

 the Greenwich intervals are more convenient for most purposes, 

 since the difference between the times of high (or low) water at any 

 two stations is given directly by the differences in their Greenwich 

 intervals, without correction for the different longitudes of the 

 stations. 



13. Establishment of the port. — The high-water interval at the full 

 and change of the moon is called, in England, the "establishment of 

 the port," and the high-water interval at spring tides the "corrected 

 establishment." These terms are not current in the United States. 



While the time of full moon is commonly thought of as a day, it is 

 in fact an instant, duly set forth in the Nautical Almanac. The 

 m^oon's transit nearest the moment of full or change evidently is 

 nearly but not quite at noon or midnight, and the mean solar time of 

 high water is close to the high-water interval. The establishment of 

 the port is also defined therefore as the local time of high water at the 

 full and change of the moon. The term is not further used in the 

 treatment of the tides herein followed. 



THE TIDE-PRODUCING FORCES 



14. It is an elementary principle of physics that the gravitational 

 attraction between two bodies varies inversely as the square of the 

 distance separating them; and an elementary theorem that the 

 attraction between two spheres, such as the moon and the earth, is 

 the same as though their respective masses were concentrated at their 

 centers. But the attraction between the moon and any individual 

 unit of mass in the earth depends upon the distance of this unit from 

 the center of the moon, which is not, in general, the same as the dis- 

 tance from the earth's center to the center of the moon. The conse- 

 quent varying differential in the force of attraction over the earth's 

 surface as compared with the average attraction per unit of mass of 



