“4a 
REPORT ON THE TIDES. 113 
pan. odd ge hog state a 
rete se n? 7? sin $ cos > aur sin $ CoS 6-75 d¢ 
. fd 2, af! peae 
+45, — Moos a7 —2m7 cos oa 
— 2nr%sing cos So bdu=0, 
which is in accordance with Laplace’s equation, Méc. Cél., vol. i. 
p.98. The remaining equations are to be deduced from the 
_ invariability of the mass of the element dm. 
ioe te fac oe Cae 
The elementary parallelopiped 
rcosodrdddp 
is bounded by the sides 
MA = dr, MB=rd4, MC =>7r cos ¢$ dp, 
the coordinates of the point M being 7, 4, p#, 
— A — rt+dr, 9, pK, 
—_—_ — B — 7r¢+44, & 
C — 7, $,¢+ dp. 
By reasoning similar to that employed in the Zraité de Mé- 
canique, vol. ii. p. 671, the following equation may be obtained, 
which is equivalent to a transformation of equation (D) : 
dg d.er d.og dion 2err _. sing 9) _ 
dt’ dr ie d¢ ij dy A Se cos > ec 
or 
dr. dq, dp 2r' snd JQ _ 
= rr en date 
For incompressible fiuids, when the effect of changes of 
_ temperature is neglected, ge! = 0 separately, and 
dv’ dq dp! 2” sing 
dr'do ‘dp r_ cose 
which equation agrees with that given by Laplace, Méc. Cél., 
vol. i. p. 101. 
PH If r denote the temperature, Fourier has shown that 
(dr d.ur. d.vr -d.wr K far 
* da * dy ak <, =C1 
and if e denote the temperature which corresponds to a given 
Cr <dis 
dat ay?t ed (E.) 
nperature , 
| VOL. vi. 1837. I 
e) 
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