MANUAL OF HARMONIC ANALYSIS 
AND PREDICTION OF TIDES 
INTRODUCTION 
HISTORICAL STATEMENT 
1. 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 
importance 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. 
2. 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 of 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 committe, 
consisting of Profs. G. H. Darwin and J. C. Adams, drew up a very 
full report on the subject, which was published in the Report of the 
British Association for the Advancement of Science in 1883. 
3. Among the American mathematicians who have had an important 
part in the development of this subject may be named Prof. William 
Ferrel 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. 
