276 REPORT— 1870. 



of the Council of the Royal Society, some further results obtained by aid of 

 grants of =£100 and .£50 made by it to Sir "W. Thomson out of the Govern- 

 ment-Grant Fund for scientific investigation. The work has been all done, as 

 heretofore, for the Committee, under the suiierinteudence of Sir W. Thomson, 

 by Mr.Eoberts and assistant calculators working under his immediate direction, 

 according to the plans described in the Reports for 1868 and 1869 and sum- 

 marized in the Report for 1 872. The work done for the Committee consists 

 of the full harmonic reduction of: — 



(1) Ten years' observations taken by the self-registering tide-gauge at 

 Helbre Island, at the junction of the Mersey and the Dee. 



(2) Two years of Kurrachee, in addition to the three years previously 

 analyzed and published. 



(3) Two years' tidal observations by self-registering tide-gauge at San Diego 

 (lat. 32° 42' N., long. 117° 13' W.) on the coast of Cahfornia, and one year's 

 observations at Fort Clinch, Fernandina (30° 43' N., long. 81° 27'W.), Florida. 

 The work of the Royal Society consists of full harmonic reductions for three 

 years' observations by self-registering tide-gauge of West Hartlepool ; nine 

 months of Port Leopold; 119 days of Beechey Island; one year of Brest; 

 and (a first attack on Mediterranean tides) one year of Toulon. 



Helhre Island, 1858 to 1867 inchisive. — The results for Helbre Island have 

 been found from nearly ten years' consecutive observations taken by a self- 

 registering tide-gauge at Great Helbre, about eight miles direct or sixteen miles 

 by water-channels from the tide-gauge at Liverpool, on the St.George's landing- 

 stage. Both these tide-gauges are under the charge of Captain Graham H. 

 Hills, R.N., Marine Surveyor to the Board of the Mersey-Dock Estate ; and 

 the Committee is indebted to him for the loan of the tide-diagrams from which 

 the present results are obtained. The float of the Helbre Island tide-gauge 

 works in a well, into which the tidal water is admitted by a pipe below 

 low-water level. This connecting pipe is kept free hy about once every month 

 closing its mouth, and allowing the water to rush out at low water. The 

 tide-gauge clock is kept accurately to Greenwich mean time by time-signal 

 from Bidstonc Observatory. In the years 1860, 1863, and 1864, on account 

 of accidental interruptions, the observations only began on March 1, March 29, 

 and June 3 respectively ; in each of the other seven years the observations 

 began on Jan. 1. The results of the harmonic analysis are given in the Tables 

 below. The datum_-level from which the mean heights A^, are calculated is 

 the same as that used for Liverpool, being 12 feet below the level of the " old 

 dock sill." 



The results shown in the Tables for the separate years agree fairly well to- 

 gether. For example, the extreme difference for the value between the ampli- 

 tudes of the solar semidiurnal (E^ of S) is -0879 of a foot, or scarcely more 

 than an inch, and the epochs of the same tide 2°-l of the circle, or 4-2 minutes of 

 time. The amplitude of the mean lunar semidiurnal tide (R, of M) varies from 

 year to yeai', on account of the varying inclination of the moon's orbit to the 

 earth's equatoi-, very nearly in accordance with the equilibrium theory as 

 set forth in Tables II. and II'. (pp. 305 & 307). 



The variations which the Tables show in the values of the lunar declina- 

 tional diurnal tides (E, of 0) and the lunisolar declinational diui'nal and 

 lunisolar declinational semidiurnal (R^, R, of K) are likewise perfectly 

 accouuted for. 



The following comparison between the evaluated results of the mean solar 

 and mean lunar semidiurnal tides and their overtides, and of the compound 

 Helmholtz lunisolar quarter-diurnal tide of Liverpool and Helbre Island, is 



I 



