REPORT ON THE TIDES. 1 
The equation to the fluid surface is therefore 
dQ da dQ 
dQ —q,/de'—wda Rae PRE AST quite wi dz=0. 
Bernoulli’s theory of the tides, or as it has been aptly termed 
by Mr. Whewell the equilibrium theory, rests upon the assump- 
tion that the equation to the fluid surface is 
dQ =0, or Q = constant, 
that is, it requires that the quantity 
a@ ts! dQ...) | ! dQ a iw! 
qait® +uldx+ doin! +udy+ dsl dz’+wdz. . (A) 
may be neglected. It seems desirable that some attempt should 
be made to investigate the nature of this quantity, in order to 
show @ priori that the quantity 
wde+tudy+w'dz 
may be disregarded. Having given the general equation to the 
surface of the fluid, to find when the distance from the centre of 
the earth is a maximum (or the time of high water) is not a diffi- 
cult geometrical problem. In Bernoulli’s theory, when the ex- 
pression for the height is differentiated, in order to solve this 
question in the usual way various quantities are treated as con- 
stants which are not so strictly ; and in order to obtain a rigorous 
solution, it would be necessary to substitute in the expression for 
the height before differentiation, expressions for the longitude, 
latitude, and distance of the luminary in terms of the time or 
mean longitude. 
The general equations of the motion of fluids referred to rec- 
tangular coordinates are given by M. Poisson, Zraité de Mé- 
canique, vol. ii. p. 669, and in other works. 
ee Se ee ae 
= da. dy dz . . . . . (B.) 
¢ 
i 
g 
1 
eS ee ee sw (CQ) 
g 
dg 
EEN a 6 by cals ban dey Me! 
