ANALYSIS TO THL DYNAMICAL THEORY OF THE TIDES. 
249 
the equator. The water however coming from higher latitudes into lower will reach 
these lower latitudes with an amount of rotation less than that which is appropriate 
for these latitudes if the whole were in a state of steady motion as a rigid body. 
There are no forces acting which tend to modify the angular momentum about the 
polar axis of an elementary ring of water, which coincides with a parallel of latitude, 
and consequently currents will be started, in virtue of which each particle of fluid 
will move along a parallel of latitude from east to west. The effect of the disturbing 
force is therefore to modify the state of steady motion about which the free oscilla¬ 
tions take place from a uniform rotation of the whole system as a rigid body to a state 
in which there exist horizontal westerly currents. If, as is usual in dealing with 
forced oscillations, we suppose the free oscillations to be annulled, we see that the 
“forced oscillation " arising from such a constant disturbance as we have been con¬ 
sidering will be of the nature of a steady motion relatively to the rotating earth, 
consisting of a westerly flow of the whole ocean, the velocity however varying with 
the latitude. 
In the case of a periodic disturbance of very long period, the motion set up at any 
instant will be of like character, provided that the viscosity of the fluid is not 
sufficient to sensibly affect the currents in question in the course of a single period. 
An equilibrium-theory will only be applicable when the rate of dissipation of such 
motions is so rapid that they practically disappear in a time which is short compared 
with the period of the disturbing force. Now in an ocean whose depth is equal 
to the mean depth of the actual ocean, it seems highly improbable that such 
curreiits would be appreciably affected by viscosity in the course of a few months. 
Hence it appears that the present theory in which the effects of viscosity are totally 
disregarded will almost certainly give a far bettei’ representation of the lunar long- 
period tides than the equilibrium theory, and most probably also ofdh^ long-period 
solar tides. ■ . • 
§14. Free Steady Motions. 
In the last section we have called attention to the fact that free oscillations of 
infinite period are possible, or that the system with which we are concerned is 
capable of free steady motions. We proceed in the present section to examine the 
nature of these steady motions. 
Referring back to §§ 2-4, we see that the general equations of motion of the ocean 
when free from external disturbing influence, and at the same time supposed steady, 
so that \ = 0, can be expressed in the form 
2 K 
MDCCCXCVII.—A. 
