16 NINTH REPORT — 1839. 



give a fair comparison, unless the same extension of the obser- 

 vations were also tried with the old epoch, which would have 

 greatly added to the labour, I determined to confine myself to 

 the same observations while using the epoch of 38 hours as had 

 been employed with the epoch of 44 hours j which was, in fact, 

 to go over the ground a second time with the shorter epoch, 

 endeavouring to avoid any small errors I might have incurred 

 before, such as that I have just explained. The corrections I 

 eventually obtained, and laid down on sheet No. 37, are, I be- 

 lieve, for the moon's effects a fourth approximation, and for the 

 sun's a third. On carefully measuring the mean residual error 

 after the two processes, I find a small improvement in that of the 

 38^ epoch, which is now 2-394 min., while that of the 44^ epoch 

 is 2*510 min. 



Whatever may be thought of this minute difference, which 

 accidental circumstances may have in some degree modified, I 

 think no one can hesitate to give to our new curves of lunar pa- 

 rallax and declination a preference before those numbered 1 and 

 1 on sheet 29, which were considered so good only twelve 

 months ago. A discussion of heights would probably afford 

 additional evidence in favour of our new epoch ; as there is lit- 

 tle doubt that the maximum height would fall much nearer than 

 formerly to the hour of 0^ transit ; though I believe it will now 

 be a little to the right hand of that hour line, as though the 

 epoch were rather too much shortened. If similarity of form 

 between the parallax and declination correction- curves be ad- 

 mitted as the proper test of the anterior epoch, it is pretty evi- 

 dent that 38^ is better than any other that we have yet tried. 



The observations of displacement of summit of the tide- 

 curves, or differences of equal altitude-times, and actual times 

 of H. W., are laid down on sheets Nos. 33 — 36, and the result- 

 ing corrections on No. 33. The observations are continued from 

 January to June, on sheets Nos. 42 and 43. I had transferred all 

 these observations to a separate sheet, and begun to discuss 

 them afresh : but seeing no reason for thinking I could throw 

 any further light on the subject just at present, I laid it aside 

 until more observations had been made, or until you had favoured 

 me with your opinion as to the best mode of proceeding. 



You will be pleased at hearing that Dr. Carpenter's exertions, 

 so ably seconded by your letter, have succeeded in procuring a 

 grant of 50/. from the Corporation, in addition to a previous 

 one of 20/. from the Society of Merchants, since increased to 

 25/., making together ^-^l-i which has been paid me in consi- 

 deration of my time and labour bestowed on attending to the 

 tide-gauge, and calculating a tide-table annually for the port. 



