54 BEPORT— 1886. 



instrument shows that on each of the days, 7th and 8th February, 1885, 

 there was only one high and low water, whereas our table, of course, 

 gives a double tide as usual. Again, on the 9th February there is an error 

 of 68 minutes in a high water. These discrepancies are to be expected, 

 since the approximate method is here pushed beyond its due limits ; and 

 for such a port as Aden special methods of numerical approximation 

 would have to be devised. 



In a table computed for Amherst the agreement is not quite so good 

 as was to be hoped; the error in heights amounts in two cases in fifteen 

 days to nearly a foot, and in two other cases to three-quarters of an hour 

 in time. It may be remarked, however, that the tides are large at 

 Amherst, having a spring range of 20 ft. and a neap range of 6 ft., that 

 the diurnal tide is considerable, and that the sum of the semi-ranges of 

 the over-tides M4, S4 (which we neglect entirely) amounts to 6 inches. 

 It appears also that the tidal constants are somewhat abnormal, for 

 ■ H"=,4H, instead of H"=,.;j7H,, and further Hp=.^H' instead of Hp=^H'. 



Under these circumstances it is perhaps not surprising that the dis- 

 crepancies are as great as they are. 



Tables were also computed for Liverpool and West Hartlepool, but no 

 correction was here applied for the diurnal tides. The results were 

 compared with the Admiralty tide-tables for Liverpool and Sunderland. 

 In the case of Liverpool there were four tides in a fortnight in which there 

 was a discrepancy in the times amounting to 12 minutes, and four other 

 tides in which there was a discrepancy of a foot, and one with a dis- 

 crepancy of l.ft. 2 ins. It was obvious, however, that the agreement 

 would have been better if the correction for the diarnal tides had been 

 applied. The spring rise of tide at Liverpool is 26 ft. 



In the case of Sunderland there were in a fortnight two discrepancies 

 of 15 m., two of 14 m., two of 13 m., two of 12 m., &c. in the times, and 

 in the heights one discrepancy of 3 ins., and four of 2 ins., &c. The spring 

 rise at West Hartlepool is 14 ft. 



These two tables are quite as satisfactory as could be expected con- 

 sidering the approximate nature of the methods employed. 



Finally, in order to test the methods both of reduction and of predic- 

 tion, Mr. Allnutt took the hai-monic constants derived from our analysis 

 of a fortnight of hourly observation at Port Blair, from April 19 to May 2, 

 1880, and computed therefrom a tide-table for that same fortnight. He 

 then, by interpolation in the observed hourly heights, determined the 

 actual high waters and low waters during that period. 



The results of the comparison are exhibited in the table on next page. 



If our method had been perfect, of course, the errors should be every- 

 where zero. 



It must be admitted that the agreement ivS less perfect than might 

 have been hoped. If, however, the calculated and observed tide curves 

 are plotted down graphically side by side, it will be seen that the errors 

 are inconsiderable fractions of the whole intervals of time and heights 

 under consideration. 



When we consider the extreme complication of tidal phenomena, 

 together with meteorological perturbation, it is, perhaps, not reasonable 

 to expect any better results from an admittedly approximate method, 

 adapted for all ports, and making use of a very limited number of tidal 

 constants. In devising these rules for reduction and prediction I could 

 find no model to work from, and it seems probable that advantageous 



