TIDAL OBSERVATIONS. 127 



nents. Meteorological indications were also forwarded by J. Hartnup, Esq., 

 P.R.A.S., of the Observatory, Birkenhead, for the same period. 



57. Tables of the foregoing nine series of analyzed tide-components were 

 made, giving the heights due to each, and •were computed for every few 

 degrees of hour-angle. On account of the magnitude and quick variation of 

 its tide-components, the M series was computed for every degree of hour- 

 angle, which allowed the interpolation for the fraction of the degree of hour- 

 angle to be done with very little labour. All terms involving multiples of 

 the same hour-angle were included in each Table ; thus the M Table con- 

 tained the heights due to R,, K^, Eg, R^, R^, and R^, and the S Table those 

 due to Rj, R^, and R^. The K Table contained the heights due to Rj and R^. 

 The tide-components affected by the variation of the inclination of the moon's 

 orbit were corrected according to the equilibrium theory. The tide-com- 

 ponents so affected are the lunar semidiurnal (R^ of M series), the lunar 

 diurnal declinational (R, of series), and the lunar and solar diurnal and 

 semidiurnal (Rj and R^ of K series). The first was thus presumed to vary 

 as the square of the cosine of the inclination of the moon's orbit to the earth's 

 equator, and the other three as the square of the sine, assuming in the case 

 of the combined lunar and solar tides (K) that the ratio of the tide-generating 

 forces of the moon and sun were as 2 to 1. It was supposed that these as- 

 sumptions would represent these tides very fairly. The zero of reckoning of 

 the lunar diurnal (declinational) tide was also corrected for, on account of 

 the retrogression of the moon's node causing an oscUlation on the earth's 

 equator, of the intersection of this plane with the plane of the moon's orbit. 

 The zero of the K tides is similarly affected ; but as these are combined tides, 

 the zero was assumed to be nearer the intersection of the lunar orbit than 

 that of the solar in the ratio of the analyzed semidiurnal lunar and solar tides 

 (3 to 1). This inequality can be included in the regular analysis by intro- 

 ducing terms involving the period of the revolution of the moon's nodes, and 

 requiring a series of observations extending through a period (about eighteen 

 years) of their revolution for the evaluation of the tide-components, 



58. Tn order to eliminate signs in the Tables (which greatly facilitates the 

 summation of the different tide-values in the computation of the tide-height 

 at any moment), the amplitude of each tide has been added, throughout each 

 Table, to the calculated heights for the stated hour-angles. An example of 

 each kind of Table is here given, from which wUl be more readily understood 

 what has been done. The following represent the values of the height (h) 

 of the tide, being the smaller component (L) of the elliptic semidiurnal tide, 

 due to the revolution of the moon's perigee. The heights are computed for 

 every ten degrees of hour-angle (H.A.). The first Table gives the height as 

 computed from the formula 7i=R2 cos (2Mi—e2)=0-56ft.x cos (2n<—14S°-85). 

 In the second the value of R^ has been added to each value of h. The limits 

 of the first Table are H-R^ and — R^, and in the second 2R2 and 0. 



ni or H.A. h 



'T-^. s ft. 



o 180 —0-48 + 

 10 190 e'35 



20 ■ 200 — C)'i8 + 



30 210 +o'oi — 



40 220 0'20 



50 230 o'37 

 60 240 o"49 

 70 250 0-55 

 80 260 o'55 



90 270 +o'48 — 



nt or H.A. h 



, • s ft. 



90 270 i'04 



100 ■ 280 o'9i 



110 290 o'74 



120 300 o'55 



130 310 o'36 



140 320 o'i9 



150 330 0-07 



J 60 340 o*oi 



170 350 o-oi 



180 360 o"o8 



