1]4 SEVENTH REPORT—1837. 
e=e{l+h(r—b)} . .. . . (FB) 
K, C, and ’ being constants. Mémoires de l’ Institut, vol. xiii. 
p-519. When the temperature varies, the two last equations 
supply the place of the equation p! = 0. 
The left hand side of the equation (E.) is of the same form as 
equation (D.), p. 25; hence by the help of a known transform- 
ation it is easy to transform equation (E.) to polar coordinates, 
and we obtain 
dr d.r7r d.rq@  d.cp! rr sind |, 
dit dr de ag eee 
ap Spans en 2 
~ Crs dr r? cos? > \ dp? 
d.rr 
1 (dey is) (E.) 
To costa d¢ 
« The general equations of the motion of fluids have not yet 
been successfully applied to problems even of less difficulty than 
*uat of the tides, which is complicated by the irregular shape of 
the channel in which the tide-wave travels, and by the resist- 
ance which it meets with in its passage. An improvement, how- 
ever, of theory as regards single observations, or for the purpose 
of prediction, is scarcely wanted, except as regards the fluc- 
tuations of the establishment, on account partly of the inevitable 
difficulty attendant upon observations of the time and height of 
high water, and partly on account of the derangement produced 
by causes which are at present far beyond the reach of analysis, 
such as winds and the varying atmospheric pressure. But when 
the averages of numerous observations are employed, it is evi- 
dent that in the instance which I have adduced p. 20, and per- — 
haps also in some others, the equilibrium theory appears at 
least to be insufficient, Its general agreement with the pheno- — 
mena, to which I have adyerted on former occasions, is extremely 
remarkable, and the merit of Bernoulli’s investigation does not 
seem to have been sufficiently appreciated. But whether or not 
Bernoulli’s theory may soon receive improvement, at all events 
the approximation is generally so close that I have thought it 
desirable constantly to compare the results afforded by the ob- 
servations with those deduced from his expressions. More-— 
over, the results given in the tables have been laid down in dia- 
grams, by which means their relation to each other and to theo 
is better perceived. The advantages of this method, of which 
