133 REPORT— 1870. 



1 height of mean level. 



4 coefficients for lunar diurnal tides. 



2 „ „ solar diurnal tides, corresponding to the time of year 

 when the observations were made. 



2 coefficients for lunar semidiurnal tides, 

 2 „ „ solar semidiurnal tides. 



11 



48. The labour of solving these equations by directly calculating the de- 

 terminants would be very great ; and the obvious method of successive ap- 

 proximations which renders the solution of the equations of § 28 very easy 

 is not obviously applicable in this case, because iu this case the equations 

 have not the characteristic property* exhibited in the equations of § 28, that 

 the coefficient of one of the unknown quantities is comparatively large, and 

 the coefficients of all the others small in each equation, so that each of the 

 unknown quantities is approximately determined by one alone of the equa- 

 tions. It is probable that some algebraic artifice wiU be found to reduce 

 within moderate compass the labour of solving the Fiji and other similar 

 sets of equations, and so give a useful practical character to the harmonic 

 analysis for short series of tidal observations, continued through broken 

 periods. But the most for the N atiu-al History of the Pacific tides that could 

 be expected from the results of so limited a series of observations as that 

 which we have from the Fiji islands is much less than can be had with ease 

 by the method already worked out for Eamsgato, Liverpool, and Bombay, 

 when observations made continuously through long periods are available. 

 Accordingly, on learning from volumes of the United States' Coast Survey, 

 which I received last November, that self-registering tide-gauges had been 

 established by the Government of the United States at various stations both 

 on their East and on their West coasts, I immediately applied, on the part 

 of the Committee, by letter, of date Nov. 19, 1868, to Professor Pierce, 

 Superintendent of the Survey, for a series of trustworthy observations of Pa- 

 cific Tides. Through his kind compliance with my request a year's tide- 

 heights, taken from the diagrams, executed by a tide-gauge at Fort Point, 

 California, reached mo last April, and were immediately put into Mr. lioberts's 

 hands to be reduced on the same plan as that which we have followed for the 

 other stations. 



49. Besides the work on these observations, we have had on hand the 

 calculation of additional terms from the Ramsgate 1864, the Bombay, and 

 the Liverpool 1857-58 observations, and the complete harmonic reduction 

 ah initio of Liverpool observations for the two foUowiug years — all of which 

 is now nearly finished. The ability, industry, and intelligence A\ath which 

 Mr. Eoberts has performed the work, and directed assistants, when practi- 

 cable, have been highly satisfactory ; and I trust that the large amount of 

 results obtained in consequence will justify amply the expenditure of labour 

 which it has cost. As some of the most important results have only reached 

 me from Mr. Roberts within the last few days, I have not found it prac- 

 ticable to attempt to put them into a form in which the details could be fully 

 explained to this Meeting. The resultsf themselves are given complete in 

 the file of letters and tables which accompanies this Report. 



_ * Depending on the condition that the time through which the obserrations are con- 

 tinued either is approximately one complete period or an integral number of complete 

 periods, or is very great in comparison with the period of each constituent tide, 

 t They are comprehended jji tho " statement" by Mr. Eoberts which forms part (§§ 54- 



