REPORT ON TIDE CALCULATIONS. 15 



north declination, and least when south. Is it possible to refer 

 this to anj'thing but the moon's difference of distance from the 

 two opposite surfaces of the ocean ? 



I next proceeded to discuss the observations of the times of 

 H.W. from my tide-gauge register, using the mean between two 

 equal altitudes, taken at :jth of the distance from H.W. to mean 

 water, instead of the actual or observed time of H.W. In the 

 first discussion of about twelve months' observations in this 

 way, made between Sept. 1837 and Jan. 1839, and laid down 

 on sheets 33 to 37, the anterior epoch of 44 hours was employed 

 as formerh\ A comparison of the lunar correction-curves from 

 the different epochs of 32^, 44^% and 56^\ seemed to indicate 

 that the epoch of 38'^, intermediate between those of 32^ and 

 44^, would probably afford correction- curves of parallax and 

 declination approximating more closely to each other, both in 

 form and in magnitude. At your request, I made the trial first 

 with about six months' observations, which, being treated in the 

 usual manner, yielded, after several approximations and a new 

 solar correction, cvirves of lunar declination and parallax of the 

 shape that had been anticipated, — the second loop in the decli- 

 nation-curves (at 8^ transit) diminishing, while that in the pa- 

 rallax-curves (at the same hour of transit) was increasing. An 

 improvement was also seen about the hours 1 and 2 of transit ; 

 the mean error was at the same time lessened. I next tried 

 (by your directions) the effect of this change of epoch on the 

 whole of the tide-gauge observations I possessed, equal to about 

 those of one year in all, and laid them down in a second series 

 of curves on the same sheets, Nos. 33 — 36. The solar and lunar 

 corrections were approximated several times, and those finally 

 obtained are given at the bottom of sheet No. 33. On trying 

 the mean error taken at every hour of transit throughout the 

 whole series of observations, it was found almost identical with 

 that before obtained from the same observations, with the old 

 epoch of 44 hours, viz. 2~ min. very nearly. You then requested 

 me to make a further trial, in order to determine, if possible, 

 whether the new epoch was better than the old one. To do 

 this properly, I found that it would be necessary to draw the 

 curves of observation afresh, and to interpolate the times of 

 transit for every 6 and 18 hours between those given in the Nau- 

 tical Almanac with greater nicety, namely, with second differ- 

 ences and decimals of minutes. I therefore made the necessary 

 corrections in the intervals, and laid them down anew. You know 

 we had proposed to use a larger number of observations in our 

 second trial of the comparative merits of the two epochs ; but 

 as it appeared, upon further consideration, that this would not 



