6 
THE REV. W. WHEWELL ON THE EMPIRICAL LAWS 
in the following- way. Let it be supposed that the ocean-spheroid assumes a form 
agreeing with the equilibrium-spheroid at the moment, and that the pole of this 
spheroid follows the position of the pole of the equilibrium-spheroid at a certain 
mean interval, say 90°. Let it be supposed that at a certain time a tide is sent off 
from this ocean-spheroid along a channel in which it is no longer affected by the 
moon or sun, and thus reaches Liverpool, producing the tide there. The following 
assumptions will then represent the facts. 
When the horizontal parallax is 54', the tide is sent off along the channel in lon- 
gitude 48^° east of Liverpool, at 45 h 6 m before the time of Liverpool high water, and 
the pole of the ocean-spheroid follows the position of equilibrium at a distance 90° 24'. 
When the horizontal parallax is 57', the tide is sent off along the Liverpool channel 
in longitude 94^° east, at 48 h 36 m before the Liverpool high water, and the actual 
spheroid is 90° behind the position of equilibrium. 
When the horizontal parallax is 61', the tide is sent off along the channel in lon- 
gitude 159^° east, at 53 b 0 m before the occurrence of high water, and the actual 
spheroid is 89° 16' behind the position of equilibrium. 
This hypothesis thus modified represents the circumstances of the Liverpool tide as 
affected by lunar parallax. The effect of lunar declination might be represented in a 
similar manner. 
It is not to be imagined that this hypothetical representation is near to the true 
state of the case. The changes in the lagging, in the length of the channel of 
transmission, and in the velocity of transmission, are not such as the forces can be 
supposed likely to produce. Nor is it likely that the original tide is exactly what it 
would be if the condition of equilibrium were fully attained. The tide-spheroid not 
only lags behind the position of equilibrium, but deviates from the form of equi- 
librium ; and other differences, besides the retroposition in longitude and in time, are 
introduced by the waters being in motion instead of at rest. This is seen in our 
results ; for the tidal force of the moon, which, in the equilibrium-spheroid, varies as 
the cube of the parallax, appears in the observations to vary more nearly as the 
square of the parallax : and though this difference may be referred to the inaccuracy 
of the observations, it may, I think with more probability, be considered as resulting 
from the condition of the waters being a condition of motion, not of equilibrium. 
The temporary variations of the force do not affect the form of the waters in the same 
proportion as the mean force, which is constantly dragging the waters after it, round 
the earth. 
11. In what has been hitherto stated with regard to the hypothetical representation 
of the tides, we have had a reference solely to Liverpool. It cannot, however, be 
doubted that the general laws of the tides at other places would resemble those of 
that port, and therefore might be represented in a similar manner. It has already 
been shown in my former memoir, though less satisfactorily and precisely than in 
this, that the tides of London follow the same rules as those now described. 
'flic numbers, however, which enter into these formulae will not necessarily be the 
