MADE ON THE COACTS OF EUROPE AND AMERICA IN JUNE 1835. 293 
9. But there is also another correction necessary in order that the series of esta- 
blishments thus obtained may rightly express the continued motion of the tide-wave. 
It is to a certain extent optional whether we will take the lunitidal interval resulting 
from the moon’s transit next preceding, or next but one preceding ; but when we pass 
from one transit to another in going through a series of places, we disconnect the 
establishments as representing the motion of the same tide-wave. 
Thus, let there be two places on the same meridian, and on the afternoon of a cer- 
tain day let it be high water at these places at two and at three o’clock ; then the 
tide-wave is one hour in passing from one place to the other. But let the times of 
the moon’s transit on this day, in the morning and afternoon, be 2 h 24 m and 2 h 48 m 
respectively ; the tide at 3 h is referred to the p.m. transit immediately preceding at 
2 b 48 m , and the lunitidal interval is 0 h 12 m ; but the tide at 2 h is necessarily referred 
to the a.m. transit, because the p.m transit happens after the tide : hence the lunitidal 
interval here is 14 h — 2 h 24 m , or ll b 36 m . But if the cotidal lines were drawn accord- 
ing to these intervals, ll h 36 m and 12 h 12 m , they would give a difference of 36 m only, 
instead of 60 m . 
Such discrepancies will be removed, and the lunitidal intervals reduced to a con- 
nected series, so as to give a consistent series of cotidal lines, if we diminish each 
lunitidal interval in the ratio of 12 h 24 m (the interval of two lunar transits) to 12 h , 
that is, if we subtract l m for every half hour. Thus, in the above case, the lunitidal 
interval ll h 36 m will become ll h 13 m , which, compared with 0 h 12 m , or 12 h 12 m , gives 
59 m for the time employed in the passage of the tide-wave from the one place to the 
other. The corrected establishment thus further corrected (and reduced to Green- 
wich time) I call the cotidal hour in the tables of intervals. 
The observations being estimated, grouped, and reduced by the above methods, I 
proceeded to combine them, so as to obtain from them systems of cotidal lines, and 
other information. 
Sect. II. On the form of the Cotidal Lines. 
10. The above reductions gave me the cotidal hour, or mean interval of time at 
which the tides follow the moon’s transit, along the whole coast of America, from 
Florida to Nova Scotia, and along the oceanic coast of Europe from Gibraltar to the 
North Cape of Norway. The cotidal hours being laid down along the coasts, and 
lines drawn through the places where the same hour occurs, in such a manner as to 
be consistent with a possible motion of the tide-wave, we have the cotidal lines. 
I have already, in the memoir already referred to % endeavoured to discover the 
general form of such lines, both for the ocean at large and for the coasts of the 
British Isles in particular ; and I have now to consider how far my new materials 
enable me to correct my first attempt. For this purpose the observations notv before 
me are highly valuable, and their inaccuracy is scarcely of any moment. That they 
* Essay towards a First Approximation to a Map of Cotidal Lines. 
