354 Maj. Barnard on the Dynamic Theory of the Tidas, 
moves is bsin 4, the actual lineal component of velocity would 
be dsin 4 while the differential coefficient of the pressure (in 
and considering this motion alone, we 
space) will be fie Odes’ 
d2y 
should have = - Z Fg = 2 8ind Th | 
But the particle of water has at the same time a southerly 
component of velocity b- =, 
It is evident that, as it is passing to a lower and larger cirele 
of latitude, to maintain its position in longitude, the moment of 
its quantity of motion, with reference to the axis of the earth's 
rotation, will be increase 
The principle that the moment of the accelerating foree is 
equal to — & (the moment of the quantity of motion) (which can 
be hy naam from the equations of rotation around a fixed 
axis—see Bartlett ope te greet: par. 229,) will enable ws 
to determine the value of @ — — corresponding to this cause. The 
accelerating force in this case a bes the pressure generated by this 
vv 
motion of the particle) i is 2 , and its moment with reference 
bsinéda 
> c dp’ 
to the earth’s axis is ge tap 
icle of water 
_. The moment of the quantity of motion of the parti 
(per unit of mass) due to the earth’s rotation, is nb 
which the 3 is 2nb? sin 6 cos 6 at But as the change in the polit 
distance ie hs particle is due to the component of velocity 
will be ies by the same, and hence, from hsm 
a gin 96, of 
dt? dt 
we should have =— 2nb? sin 4 cos a 4 =, (The negative of 
is used since the ‘breading of the ‘liakeees is in —— ‘ 
tion to that of a a oo 
Adding this value to that previously obtained, we het . 
dp’”" du d?v 
(5) e — 2nb? sin9 cos — 6? sin? OF 
Another equation my be obtained from the condition 4 
dietary in the fluid = 
