110 SEVENTH REPORT—1837. 
In the Philosophical Transactions, 1837, Part I., we have 
transferred the London quantities to transit A by merely shifting 
them to the left half an hour, which suffices approximately. 
Upon comparing in this manner the diurnal inequality at Liver- 
pool and London, I find that it is extremely different ; for if we 
examine the high water caused hy the same tide at Liverpool 
and London, we find that if @ and / denote two successive 
‘heights of high water at Liverpool, and a’, b' successive heights 
at London, if a > b, then generally a! < 4’. I do not think 
that this circumstance was known previously, although Mr. 
Wiewell, in his examination of the Coast-guard observations, 
noticed an anomaly of which the origin is similar. : 
It is remarkable that while at Liverpool the diurnal inequality 
in the interval is almost inappreciable, at London it is well de- 
fined. 
The results seem to prove that semidiurnal inequalities in the 
height are proportional to the quantity #, as might be expected 
from theory. See Phil. Trans., 1836, p. 223. 
If X, ¥, Z denote the forces acting in the direction of the co- 
ordinate axes upon the fluid particle of which the rectangular 
coordinates are x, y, %, and if 
: 
] 
i 
¢ 
! 
| 
; 
; 
. 
. 
‘ 
| 
L 
_ de _ dy eis 
saath # OY aes dt’ 
_ du du y iu Fo 
Ca eae dae dig 
dv dv dy dv 
pee ee se dhind 
ibe ee CT Aaa Fe 
then the differential equation to the surface of the fluid is j 
(X —w)da+(Y—v) dy +(Z—w') dz=0. 4 
See Traité de Mécanique, by M. Poisson, vol. ii. p. 669. | 
If Q isa certain function of 2,y,2, the coordinates of the 
fluid molecule, and of 2’, y', z', the coordinates of the centre of 
the distant luminary, 
dQ dQ dQ dQ dQ dQ 
=e ee peti af pet eee Saas! fp eo tS ato 
Oe eet dg l! tay oY tae ee 
— , ~,_¢Q@,,,, dQ, dQ,,, 
=Xde«+Y¥dy+t ada geet aie tae 
