A is ee RR cs 
Maj. Barnard on the Dynamic Theory of the Tides. 358 
Making the substitutions in — ®), and then substituting 
the value of 94 in equation (1), we 
(3) gu= ; Eat cos?o—1)(1-3 cos?0)+4 1s, ——sin 2 .sin 26 cos(nt-2-8). 
3S) 
+ fi cos 2a .sin 20. cos2 (nt+-w—s) +p”, 
If now, we suppose a particle of water running towards the 
south and’ call w the arc (in latitude) passed over at the end of 
the time ¢, oo will be the actual velocity of the particle, in this 
direction, and ste its acceleration. If 6 is the angular polar 
distance of the initial position of the particle, 00 will be the actual 
lineal polar distance, and Sas will be the differential coefficient 
of the pressure arising ion a i vice of 9, and by a slight by 
admissible extension of the fundamental equations of hydr 
hami Opel eigis 7 
¢s we should have dd b FIED 
But if the particle has, at the same time, a component of i het 
locity towards the east, represented by dsin9 > - ag being are in 
longitude moved over in the time 4) its aiid force is in- 
creas | 2h2 2 
oom b a (due to the earth’s rotation alone,) to 
+5)" b? sin 26, 
te ees 
bsin 
. the square of o since it is very small compared 
the difference between which is (omitting the 
Per 2nbsin 64 6 531 and the component of this increment, 2nbsin# 
42 
= ap Will press the particle towards the equator and is to be 
) Mided to the value of ta ye @ before obtained. Adding it and mul- 
: *nying by , we bere 
‘ ‘ og (4) 4 A_—— Tt 4-2nb2 sin 008 97, = 
4 idering now af iaaun of angular velocity to the east 
, 7 80ee the radius of the small circlé of latitude in which it 
| v wants, . XXVII, No, 81.—MAY, 1859. 
