HARMONIC ANALYSIS AND PREDICTION OF TIDES. 



Part I.— DESCRIPTION. 



INTRODUCTION. 

 1. HISTORICAL STATEMENT. 



Sir William Thomson (Lord Kelvin) devised the method of 

 reduction of tides by harmonic analysis about the year 1867. The 

 principle upon which the system is based — which is that any peri- 

 odic motion or oscillation can always be resolved into the sum of a 

 series of simple harmonic motions — is said to have been discovered 

 by Eudoxas as early as 356 B. C.,when he explained the apparently 

 irregular motions of the planets by combinations of uniform circu- 

 lar motions.^ In the early part of the nineteenth century Laplace 

 recognized the existence of partial tides that might be expressed by 

 the cosine of an angle increasing uniformly with the time, and also 

 applied the essential principles of the harmonic analysis to the reduc- 

 tion of high and low waters. Dr. Thomas Young suggested the 

 iniportance of observing and analyzing the entire tidal curve rather 

 than the high and low waters only. Sir George B. Airy also had an 

 important part in laying the foundation for the harmonic analysis 

 of the tides. To Sir William Thomson, however, we may give the 

 •credit for having placed the analysis on a practical basis. 



In 1867 the British Association for the Advancement of Science 

 appointed a committee for the purpose of promoting the extension, 

 improvement, and harmonic analysis of tidal observations. The 

 report on the subject was prepared by Sir William Thomson and was 

 published in the Report ol the British Association for the Advance- 

 ment of Science in 1868. Supplementary reports were made from 

 time to time by the tidal committee and published in subsequent 

 reports of the British association. A few years later a committee, 

 consisting of Profs. G. H. Darwin and J. C. Adams, drew up a very 

 iull report on the subject, which was published in the Report of the 

 British Association for the Advancement of Science in 1883. 



Among the American mathematicians who have had an important 

 part in the development of this subject may be named Prof. William 

 JPerrel and Dr. Rollin A. Harris, both of whom were associated with 

 the U. S. Coast and Geodetic Survey, The Tidal Researches, by 

 Professor Ferrel, was published in 1874, and additional articles on 

 the harmonic analysis by the same author appeared from time to 

 time in the annual reports of the Superintendent of the Coast and 

 -Geodetic Survey. The best known work of Doctor Harris is his 

 Manual of Tides, which was published in several parts as appendices 

 to the annual reports of the Superintendent of the Coast and Geo- 

 detic Survey. The subject of the harmonic analysis was treated 

 principally in Part II of the Manual which appeared in 1897. 



1 Nautical Science, p. 279, by Charles Lane Poor. 



