Astronomical and Nautical Collections. 299 
regularity in the operation of the causes concerned. Since the 
subject has hitherto been considered as extremely intricate, and has 
not indeed yet been freed from all its embarrassments, we shall 
here endeavour to explain the principles on which the investigation 
has been conducted. 
** The attempts that were made by Newton, to compute the 
effects of the solar and lunar attraction on the sea, went no further 
than to the determination of the magnitude of the elevation which 
would at any given time afford a temporary equilibrium: and even 
Maclaurin was satisfied with having ascertained the precise nature 
of the form which the waters must assume in such a case. But it 
is obvious that these determinations are by no means sufficient for 
ascertaining the motions which arise from the change of relative 
situation induced by the earth’s rotation, since the form, thus ascer- 
tained, only affords us a measure of the force by which the waters 
are urged, when they do not accord with it, and by no means ena- 
bles us to say, without further calculation, how nearly they will at 
any time approach to it. In fact, the change of the conditions of 
equilibrium determines only the magnitude of this force, such as it 
would be if the sea remained at rest, while it is in reality materially 
modified, at any given time, by the effect of the motions which have 
previously taken place: and supposing its true magnitude to be 
ascertained, its immediate operation will at all times be complicated 
with the conditions, under which an impulse of any kind is capable 
of being communicated to the neighbouring parts of the sea, which 
depend on the depth of the sea, as well as on the form of the earth. 
“‘ Mr. Laplace has undertaken the investigation of the theory of 
the tides, with all these additional complications ; and he considers 
it as constituting, without exception, the most difficult depart- 
ment of the whole science of astronomy; and yet this consummate 
mathematician has omitted to include in his calculation the effects 
to be attributed to resistances of various kinds, and to the irregu- 
larities of the form of the sea, which appear to us to constitute by 
far the more material difficulties in the inquiry. The general 
problem, relating to the oscillation of a fluid completely covering a 
sphere, and moving with little or no resistance, which Mr. Laplace 
