2 ME. T. Gr. BUNT’S DISCUSSION OF TIDE OBSEEVATIONS AT BEISTOL. 
regular progression, but are alternately higher and lower than such a progression would 
require. The intervals also between the times of high water and the preceding lunar 
transit to which they are referred, are found to be alternately longer and shorter, so as 
to present a similar irregularity. 
The Diurnal Inequality of Height in the Tides of Bristol, though of no great magni- 
tude, averaging only 2^ inches up and down, is at once apparent on the most cursory 
examination; the inequality of time is not quite so easily detected. It was indeed 
stated by Sir John Lubbock: so lately as in 1839, in his ‘Elementary Treatise on the 
Tides,’ p. 39, that “the diurnal inequality in the interval is inappreciable on our 
coasts and again, at p. 40, “ the diurnal inequality in the time of high water on our 
coasts is too minute to be detached from the inevitable errors of observation.” 
There will, I apprehend, be little difficulty in showing that this remark of Sir John 
Lubbock’s is not applicable to the port of Bristol. For although the diurnal inequality 
in the times of high water is not large, its average magnitude, on comparing two succes- 
sive intervals, being little more than four minutes between both, or two minutes for the 
single inequality in each, yet it is almost always perceptible in the Tide-Gauge Obser- 
vations in tolerably calm weather. In the. accompanying Plates of six months’ observa- 
tions in 1865, the diurnal inequality of both times and heights is everywhere apparent. 
At Dr. "Whe well’s request, I bestowed much time and labour from the first, in 
endeavouring to trace out the laws of both these inequalities, and especially that of the 
times, but for several years with but little success, chiefly for want of a greater number 
of observations. After several modes of arrangement which Dr. Whewell suggested 
had been tried, he at length arrived at the conclusion that, in order to succeed, we must 
divide our observations, first into twenty-four groups for the twenty-four half months, 
and then each of these into twenty-four smaller groups for the twenty-four hours of 
lunar transit. It thus became evident that little progress could be made in this investi- 
gation, until a large mass of observations had been accumulated. 
These being now obtained, I have again taken the subject in hand, and embodied the 
results in the accompanying Plates. For the Inequality of the Times I have taken 
nearly the whole of the observations. The anterior epoch employed throughout is that 
of the third preceding lunar transit, averaging an interval of about forty-four hours. 
The time of every high water had been already calculated (for my annual tide table) by 
adding to the time of moon’s transit the corresponding semimenstrual interval, with the 
corrections for lunar and solar parallax and declination. From this computed time, the 
observed time of high water had been subtracted, and the residue, or error, with its 
proper sign, recorded ; being supposed to consist mainly of the uncorrected diurnal 
inequality. The amount of the inequality was taken thus. Let a be the error of a 
time of high water computed from a south transit of the moon, and l, V the preceding 
and following error, then (a— b') will be =4 times the inequality of the high 
' water which has the error a. The quadruple inequality of every south transit observa- 
tion was thus taken, and inserted in its proper group. The (24x24=)576 groups thus 
