TIDAL OBSERVATIONS. 121 



work has been performed by Mr. E. Eoberts and assistant calculators in the 

 Nautical Almanac Office, ■vrorking under his immediate direction, according 

 to the plans described in the Eeport presented by the Committee of 1867-68 

 to the Association at Norwich a year ago, with modifications suggested by 

 experience, and extensions to include parts of the investigation not reached 

 ia the first year's work. The results obtained up to January 1869 are de- 

 scribed in a supplement to that.'report, which has been printed, and is pub- 

 lished in the yearly volume of the Association. 



43. The long-period tides, shown in §§ 28, 29 of this supplement, that 

 is to say, the lunar monthly (elliptic), the lunar fortnightly (declinational), 

 the solar annual, and the solar semiannual, were calculated in consequence 

 of the astronomical anticipation of the existence of such tides indicated in 

 the general schedule of § 2 of the first Keport. There is a mistake in the 

 argument printed for the lunar monthly, which has been pointed out to me 

 by Mr. Eoberts. It ought to be (ff— or) t, instead of a t. The error produces 

 scarcely a sensible influence on the calculations which have been made, and 

 it is easily allowed for. 



44. The " luni-solar fortnightly shaUow-water (synodic) tide " is a tide 

 the existence of which was suggested by Helmholtz's theory |of compound 

 sounds (§§ 24, 25 of first Report). The harmonic analysis consequently 

 applied to discover it has proved it to be very sensible both at Eamsgate 

 and Liverpool ; and has shown that in each station it gives highest average 

 level at the times of neap-tides, and lowest average at the times of spring- 

 tides. Its amount for Eamsgate (§ 28) is a tenth of a foot above and below 

 the mean level. Its amount at Liverpool is rather less, being only seven- 

 hundi'edths of a foot above and below mean level, as will be seen later. 



45. It will be seen that the lunar declinational fortnightly and the solar 

 (declinational or meteorological) semiannual present no agreement with 

 astronomical theory. The solar is of more than twice the amount of the 

 lunar. The lunar is so small that it may be merely a result of errors of the 

 tide-gauge. The solar semiannual (seven-hundredths of a foot above and 

 below mean level) giving highest average level Feb. 14 and Aug. 15, seems 

 too large to be not genuine ; but it cannot be astronomical, or there would 

 be a corresponding lunar tide. 



46. The solar annual (referred to in § 10), as shown by the calculations, 

 (Eamsgate, year 1864, being '13 of a foot above and below mean), is cer- 

 tainly much too large to be attributable to the eccentricity of the earth's 

 orbit, and the time of its maximum (Sept. 21) does not at all siiit the astro- 

 nomical theory. Its origin (as well as that of the semiannual?) is in all 

 probability meteorological. The Liverpool observations for 1857-58 show a 

 greater difference (-36 of a foot above and below mean level) ; and time of 

 maximum average height, Oct. 20. 



Progress after date of Mr. Roberts's Svjjplementary Report. 



47. The deduction of the hinar and solar semidiurnal and diurnal tides 

 from the Fiji observations (§§ 26, 38), which is no doubt practicable, is a 

 mathematical problem of considerable interest. A good deal of work towards 



. it has been performed by Mr. Eoberts since the date of the conclusion of his 

 Supplementary Eeport. The plan followed has been simply a direct applica- 

 tion of the method of least squares, as in § 28, and it has been carried out 

 so far as the formation of eleven simple equations for the determination of 

 eleven unknown quantities, viz. : — 



