Harmonic Analysis of Tidal Observations. 135 



and in brightness of the corona, as the sun slowly loses heat, and the 

 actions of the photosphere become less fervent. 



The candle of the sun is burning down, and so far as we can see, 

 must at last reach the socket. Then will begin a total eclipse which 

 will have no end : 



" Dies ilia 

 Solvet seclum in favilla." 



" Results of the Harmonic Analysis of Tidal Observations." 

 By A. W. Baird, Major R.E., and G. H. Darwin, F.R.S., 

 Fellow of Trinity College and Plumian Professor in the 

 University of Cambridge. Received March 19, 1885. 



The harmonic analysis of continuous tidal records, inaugurated by 

 a Committee of the British Association in 1868, has now been 

 carried out at a considerable number of ports. Some of the earlier 

 results were collected together in the Reports to the Association in 

 1872 and 1876, and in a paper by Sir W. Thomson and Captain Evans, 

 read before the Association in 1878, but the largest mass of data is 

 contained in the tide tables now being annually published for the 

 Indian ports under the authority of Her Majesty's Secretary of State 

 for India. 



The Report of the last Committee of the British Association, pub- 

 lished in the volume for the meeting at South port in 1883, is entirely 

 theoretical, and has been adopted in India as a manual of the method 

 of harmonic analysis. It is there shown how the results of the analysis 

 are to be presented in a form appropriate either for theoretical treat- 

 ment or for mechanical prediction by the instrument of the Indian 

 Government in London. It is also shown how the scattered results, 

 referred to above, may be reduced to the form which has been 

 adopted as a standard. Major Baird has collected the whole of the 

 Indian results, and those contained in the Reports of 1872 and 1876, 

 and, by the aid of his staff of computers at Poona, has reduced them 

 to this standard form. The greater part of the annexed tables is 

 the result of this work. 



We must refer to the Report to the British Association for 1883 for 

 an explanation of the method of harmonic analysis, but it will bd 

 well to give a few words of explanation. 



Each one of the tides, into which the oscillation of sea-level is re- 

 garded as analysed, is expressed in the form — 



fHcos(F+W— *).. 



V-\-u — k is the argument of the tide, and increases uniformly with 

 the time, so that this term represents a simple harmonic oscillation of 

 the sea-level with semi-range f H, 



