292 
THE REV. W. WHEWELL ON TIDE OBSERVATIONS 
freed from gross irregularity by this graphical correction, the mean interval was 
taken, making allowance for parallax and declination. 
6. This mean lunitidal interval, or corrected establishment of each place, differs 
from the vulgar establishment , or time of high water corresponding to new and full 
moon ; for the time of high water at syzygy is affected by the semimenstrual inequa- 
lity belonging to the moon’s position one or two days earlier, and is therefore later 
by about 30 m than the mean interval would give it. In my former paper on Cotidal 
Lines I used the statements of the vulgar establishment at each place ; in this, I shall 
employ the corrected establishment, as a more fixed element ; for it is as yet uncer- 
tain how far the semimenstrual inequality differs at different places. On this account 
the cotidal lines for 0 h 30 m , l h 30 m , 2 h 30 m , 3 h 30 m , &c., which I shall now obtain, re- 
present nearly the cotidal lines for l h , 2 h , 3 h , 4 h , &c. of my former charts. 
7- The mean lunitidal interval would be the mean of the greatest and least intervals, 
if the time of high water were not affected by the moon’s declination and parallax ; 
but in consequence of these circumstances a correction of the mean is requisite. 
In June 1835, if there had been no corrections for the moon’s parallax and declina- 
tion, the least interval at London would have been on the 16th, the greatest on the 
23rd, each 44 m from the mean. But, in fact, the least interval was on the 15th, and 
was 4 m greater than it would have been without the corrections ; and the greatest 
interval was on the 22nd, and was 9 m greater than it would have been without the 
corrections. Hence the mean of the observed intervals w r as 6^ m greater than it 
would be if declination and parallax did not affect it. If we use the Liverpool tables 
in the same way, we find the least interval, on the 14th, l m less than without the cor- 
rections ; the greatest interval, on the 21st, 15 m greater than without the corrections. 
Hence the mean of the observed greatest and least intervals is 7 m larger than the 
true mean. 
On this account I have found the mean lunitidal interval for each place by reading 
off the greatest and least ordinates of the curves of observation, graphically corrected 
as above, and by subtracting 7 m from the mean of these ordinates. The tables con- 
taining the result of this operation will be given in the sequel. In these tables the 
first and second columns contain the least and greatest lunitidal intervals : the third 
column is the difference of these two : the fourth column, the reduction is the half- 
difference minus 7 m ; and this added to the least interval gives the corrected establish- 
ments in the fifth column. 
8. In order to use the corrected establishments thus found for the purpose of draw- 
ing cotidal lines, they must be reduced to a common origin of time by adding the 
west longitude (expressed in time), or subtracting the east longitude. In the Tables 
of Lunitidal Intervals, the sixth column contains the longitude , and the seventh the 
Greenwich time of the corrected establishment. 
* When the semimenstrual inequality is unusually small, as in many places on the coast of America, I have 
used the half- difference minus 6 m for the reduction. 
