112 SEVENTH REPORT—1837. 
Let « = r cos ¢ cosp y=rcos¢ sing z=rsin 9. 
In the problem of the tides ¢ may represent geographical la- * — 
titude, and y the sidereal time at the place. 
dr d¢ dp 
ize OF en te 
silat Yee Po ae 
Sear ** ieee tee 
"Sah ~ dy = see 
The general equations of motion referred to polar coordinates 
are 
dp _df dr rd? dp? 
edr dr dé dé — 700s" 6p 
dp 40 dd, drde_ ag dy 
pda, doe ery Tas dt r* sin > cos > dé 
dp. tt ie oleh d Grated d 6 
rg is r~ cos* > ; 27 COS” Pay diy ; 
—27 sin 4 cos o 5% SH, 
a5 
: 
Ifponit + 6, 
dp ay dé 
apy ath Ee th 93 
and if we neglect the quantities of the second order 
d¢dé d¢? 
ALAD ae &: 
dp dQ’ dr — 2 ns yea, yee dé 
edr dr az n-~r cos > 2 1 COBO a 
! dé 
ee a rT — n° * sin $ cos > — 2nr°sin cos > +5 
dé’ dr 
Ss SS peegsuie sora; Se 
= r cos’ > ae 2n 7 cos’ >a 
5 d¢ 
— 2n?* sin ¢ cos ange 
and the equation to the surface will be 
dQ dr 
dé 
een ee 24 —9D 22 2 a , 
1; ge ee od —2nr* cos* > ha 
