AND ON THE REMOTE HISTORY OF THE EARTH. 
455 
5 g 
T « 
(9) 
This is merely a symbolical way of writing down that every term in the tide¬ 
generating potential raises a lagging tide of its own type, but that tides of different 
speeds have different heights and lags. 
This same expression may also be written 
5 g 
t a 
• (9') 
Then if we put 
c —b= & t +X'" 
a—c= — X 6 
b — a= — 2 <b e 
c= |X £ 
d= -i*'. 
e — 
f= ~ < 
It is clear that 
^ ap—b^' 3 —cC'+ 2 d^^+ 2 e^+ 2 f'^. . . 
Whence 
2T(4 _ ^ =_S(0_bW_d(,,2_r)_ef,)+fff} ' 
l{4r 4)« = - Ha- C ){f- e (C- a - f vl -+ d #>)} • 
^-4)a-=-« b -‘)ft- f (f 3- T)- d ff + e vO __ 
Of which expressions use will be made shortly. 
( 10 ) 
( 11 ) 
( 12 ) 
§ 3. The couples about the axes A, B, C caused by the moon's attraction. 
The earth is supposed to be a homogeneous spheroid of mean radius a, and mass w 
per unit volume, so that its mass M=%niva 3 . When undisturbed by tidal distortion 
it is a spheroid of revolution about the axis C, and its greatest and least principal 
moments of inertia are C, A. Upon this mean spheroid of revolution is superposed 
the tide-wave cr. 
The attraction of the moon on the mean spheroid produces the ordinary precessional 
couples 2r(C—A)yz, —2 t(C — A)zx, 0 about the axes A, B, C respectively; besides 
MDCCCLXXIX. 3 N 
