ON HARMONIC ANALYSIS OF TIDAL OBSERVATIONS. 339 



Karachi, San Diego and Fort Clinch. When its funds were exhausted Thomson tried 

 to obtain £150 from the Government but was unsuccessful. The amount was provided 

 by the Royal Society out of their Government Grant Fund, and with it records from 

 West Hartlepool, Port Leopold, Beechy Island, Brest and Toulon were analysed. 



For the 1876 British Association Meeting Thomson drew up a final report and 

 gave an investigation into the generating potential, tabulating speeds, arguments 

 and amplitudes. 



A record taken at Freemantle by the Admiralty provided the first case of 

 harmonic analysis for a station in the Southern Hemisphere. Under the influence 

 of Thomson the Hydrographic Office was searched for other Southern Hemisphere 

 records, but the only ones found were from Port Louis, Mauritius and Port Louis, 

 Berkely Sound. Harmonic constants from these as well as from records taken at 

 Toulon, Marseilles, and Malta, were published by Thomson and Capt. Evans, R.N. 



On Baird's return to India in 1877 the systematic observation and analysis of 

 tides was there begun, he training the original staff of observers and computers. 



Thomson next constructed the first mechanical harmonic analyser with the aid 

 of grams from the British Association and the Royal Society. It was designed to 

 determine the constituents 



M,, S„ K„ 0„ M, 

 but has never been used for this purpose. It is deposited in the Museum at South 

 Kensington. 



At the 1882 British Association Meeting Prof. Darwin (afterwards Sir George 

 Darwin) communicated a paper in which he pointed out that the methods of 

 analysis which had been used for the long-period constituents might be seriously 

 in error. A committee consisting of Profs. Darwin and Adams was appointed 

 to examine the whole subject of harmonic analysis. 



In 1883 and 1885 Darwin presented reports which have ever since formed the 

 standard manual on the subject. They contain an elaborate analysis of the 

 generating potential (several errors in the report of 1876 being indicated) and a 

 complete treatment of the methods of analysing hourly heights. These methods, 

 except for T.;, R2 and the long-period constituents, do not differ essentially from 

 those which had been used by Thomson's Committee ; they complete the evolution 

 of what we have called the B.A. methods. 



In 1885 Baird and Darwin published an up-to-date collection of results of 

 analysis ; the number of stations considered was 43. 



16. In 1885-6 the Canadian Expedition to Hudson Bay under Lieut. Gordon, R.N., 

 was made and short series of observations taken at five stations in Hudson Straits 

 were afterwards harmonically analysed by Gordon with the aid of Prof. Carpmael 

 of Toronto. 



In a final report (1886) of the British Association Committee Darwin gave his 

 methods of analysing short records. 



In 1886 Baird left the Tidal Department of the Survey of India and published 

 his ' Manual of Tidal Observations.' The methods of observation and analysis which 

 he had established have been continued without modification up to the present time ; 

 they consist precisely of the B.A. methods, Baird constructing auxiliary tables. 



In 1889 Darwin published a second up-to-date collection of results from all 

 sources, showing an increase of 27 stations since 1885. 



In 1890 Darwin gave his method of harmonically analysing observations of high 

 and low water, and in 1892 his new method for solar constituents and his short 

 method for long-period constituents. In the same year he published his design of 

 the * tidal abacus,' an apparatus for facilitating the computations in the analysis of 

 hourly heights. This apparatus has since been much used. 



In 1891 the Australasian Association appointed a committee to report on the 

 tides of South Australia. Two of the members of this committee. Prof. R. W. 

 Chapman and Capt. A. Inglis, afterwards analysed records from Port Adelaide and 

 Port Darwin. 



In 1894 the Survey of Tides and Currents in Canadian Waters was instituted by 

 the Canadian Government, and this organisation has worked continuously np to the 

 present time under the direction of Dr. W. Bell Dawson. The harmonic analj'ses 

 have been made for the Survey by Messrs. Roberts, a tirm of computers founded by 

 Mr. E. Roberts of Thomson's British Association Committee, bat only a few of the 

 results have been published. 



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