THEORY OF TIDES. 
223 
local causes which have been described, as likely to influence 
this proportion : in fact it is not improbable that the irregula- 
ties of the form of the seas are so great as to set at defiance all 
calculation, even if they were ascertained. 
Corollary 6. The time of high water is also subjected to Effect of re- 
.. . , sistance on 
various modifications, according to the resistances concerned, the time of 
It is easy to see, that a resistance of any kind will produce a ^. Hter . 
J 1 and or spring 
retardation of the direct, and an acceleration of the inverted tides. 
tides, (Cor. 3) ; but the law of a resistance varying as the 
square of the velocity produces two remarkable consequences 
with respect to the time of high water : first, that the spring 
tides will be retarded or accelerated more than the neap tides $ 
and secondly, that the highest tides will not be precisely at the 
syzygies, but may be before or after them, according to circum- 
stances. The first of these consequences has not been suffi- 
ciently established by observation, although it has been re- 
marked in general, that high tides happen earlier than lower 
ones, other things being equal. But in many of the harbours 
in which the most accurate observations have been made, the 
time of high water may perhaps be somewhat modified by the 
different resistances opposed to tides of different magnitudes in 
their passage from the seas in which they originate. The se- 
cond circumstance is observed in a greater degree than can be 
well explained from the present state of the calculation. It is 
not easy to suppose the conditions more favourable to the retar- 
dation of the spring tides, than they have been assumed in the 
case stated in theorem D ; and the maximum is here scarcely 
at the distance of a single tide from the conjunction, the second 
excursion being somewhat smaller than the excursion immedi- 
ately preceding the conjunction, nor is it probable, that the im- 
perfection of the mode of calculation is so great, as to afford a 
result very materially different from the truth. It must, there- 
fore, remain, for the present, as a difficulty to be solved by fu- 
ture investigations, that in many ports not far remote from the 
open sea, to which the tides can by no means be, as Laplace 
seems to suppose, a day and a half in travelling, the third tide 
after the syzygy is, in general, the highest j if, indeed, this fact 
should 
