190 
SECOND REPORT — 1882 . 
turbed by a periodic force expressed by a series of cosines of 
variable angles, the height of the tide is represented by a simi¬ 
lar series of which the arguments are the same, but the epochs 
and the coefficients different. The adoption, however, of the 
preceding principle must be considered rather as an evasion of 
the difficulties by an indirect method, than an accurate and 
complete solution of the problem. 
Lately, the Academy of Sciences of Petersburg has pro¬ 
posed the problem of the Tides for a prize question. The 
programme may be seen in the Number of the Annales tie 
Chimie for February of the present year (1832). 
Since the publication of the researches of Laplace, the theory 
of the integration of partial differential equations has been 
very materially improved by Fourier, and by MM. Poisson and 
Cauchy. The small undulations of an incompressible fluid, acted 
upon by gravity, which were not previously understood, were 
completely made out by the latter mathematicians, about the 
same time, in 1815. This case however, in which the force 
acting upon the fluid is constant, and in parallel lines, is the 
simplest which can be proposed; while the problem of the Tides 
in which the motions of the fluid are due to the action of a force 
of which the intensity and direction are continually changing, 
presents more serious difficulties, which are further increased 
by the circumstance that the bed of the ocean is far too irre¬ 
gular to be represented even approximately by any algebraic 
curve surface, and by the effect of the resistance and friction 
of the water against the shores, which cannot be considered as 
insensible. 
The attention of Laplace does not appear to have been direct¬ 
ed to the construction of Tide Tables for predicting the time 
and height of high water at any port; and indeed up to the pre¬ 
sent time the Table for this purpose published in the Annuaire 
du Bureau ties Longitudes, is deduced, by a very slight altera¬ 
tion of form, from that given by Bernoulli in his prize essay. 
Nor does the subject appear, until very lately, to have met with 
any attention in this country, no attempt having been made 
previously to ascertain how far the theories of Bernoulli or 
Laplace can be reconciled with the results of observation on 
our coasts. 
Formerly, the time of high w r ater at London Bridge w T as ob¬ 
tained by adding a constant quantity, three hours, to the time 
of the moon’s southing. As the mean interval is now very little 
more than tw r o hours, w r e may infer that the time of high w T ater 
in our river has been considerably accelerated; and this circum¬ 
stance shows the importance of continual observations, and the 
