THEORY OF TIDES. 
stances : and if these periods were equal, the effect would be the 
same as if the whole resistance were attached to the slower 
vibration, which would obviously be such as is stated in the 
theorem. But for a more particular illustration, we may take 
n=%, and r =-±- : the distance of the virtual place will then 
become S-rd-sS-i-Pa? — — 1*103 9 *l63?-|-®a:: and by 
substituting in this formula a number ef different values for 
x, we find, when x =11 8°, — 252°, and — 623°, maxima 
amounting to 4.353, 4 367, and 4*342 respectively ; and, 
employing the other values of a and c, a maximum of 2*055 
when x=zl5 X 360° — 280°. Here it is obvious that the 
maximum for the virtual place is anterior to the true maximum, 
the excursion 4*367 being considerably greater than 4*353, 
which is nearest to the true maximum ; or, in other words, the 
true maximum happens a little after the perfect conjunction of 
the forces which occasion it, which if there were no resistance* 
would coincide with the maximum of the excursions. 
Theorem E. 
The disturbing force of a distant attractive body, urging a Disturbance* 
particle of a fluid in the direction of the surface of a sphere, fr° m gravity 
varies as the sine of twice the altitude of the body,— See 
Nicholson's Journal , XX. 20 9. 
Theorem F. 
The inclination of the surface of a spheroid, slightly ellipti- Equilibrium of 
cal, to that of the inscribed sphere, varies as the sine of twice spheroid^ 0 ” * 
the distance from the circle of contact 5 and a particle resting 
on any part of it without friction may be held in equilibrium 
by the attraction of a distant body. —See Nicholson's Journals 
XX. 209. 
Corrollary. Hence it may be calculated, neglecting the 
density of the sea, that the primitive 9olar side would be *807, 
and the lunar 2 0166 feet, supposing the lunar disturbing force 
to the solar as 5 to 2. 
Theorem G. 
The disturbing attraction of the thin shell, contained between Equilibrium ot 
1 r a spheroid, 
a spheroidical r 
