ANALYSIS TO THE DYNAMICAL THEORY OF THE TIDES. 
205 
resistances in the course of a few clays.* If this assumption be correct it will of 
course be necessary to invoke some more constant cause than the fickle winds in 
explanation of ocean currents, but unfortunately the causes put forward by the chief 
opponents of the wind theory, namely, the differences of density arising from 
differences of temperature, salinity, &c., though no doubt satisfying the criterion of 
being more constant in their action, seem to be equally ineffective in maintaining the 
currents against such large resistances as would be required to destroy the currents 
due to the winds in a few days. If, on the other hand, the period of subsidence of 
the free current-motions is to be reckoned rather by years, these motions could not 
fail to be excited and maintained by such causes as the winds even against the 
action of friction. 
In § 14 I have dealt with the dynamics of ocean currents on the supposition that 
they are of the nature of free steady motions (probably maintained by a variety of 
causes), and that the influences of viscosity are extremely small. A remarkable 
result is the extremely restricted character of the po.sslble forms of steady motion as 
contrasted with the case where the ocean covers a non-rotating globe, in which latter 
case the possible forms of steady motion are to a large extent arbitrary. It is found 
that if the density of the water is uniform, the only forms of steady motion possible 
when the depth depends on the latitude alone are those in which the water always 
moves along parallels of latitude, while in general the paths of the fluid particles 
coincide with certain lines depending only on the distribution of land and water and 
on the configuration of the ocean bed. The equation by which these lines are defined 
is of an extremely sinq^le character, and from it we could at once trace out the forms 
of the stream-lines on a chart if we had a sufiicient knowledge of the configuration 
of the ocean bed. The equator will always be one of these stream-lines, and herein 
we seem to have the explanation of the fact that the ocean-currents always tend to 
set along the equator, but in other respects it is shewn that the effects of variations 
of density will seriously interfere with the sinqfie laws which must hold so long as 
the density is uniform. 
The importance of the earth’s rotation in influencing ocean-currents has long been 
recognised by physicists, but I am not aware that any previous attempt has been 
made to investigate this influence mathematically. The numerical results obtained 
in § 15 are interesting, as showing how a cause, which on a non-rotating globe could 
not give rise to any appreciable currents, may be rendered highly effective in main¬ 
taining currents as a consequence of the rotation of the earth. 
In attempting to account for ocean currents, the real question at issue is : How 
far are the suggested causes capable of maintaining currents against the action of 
friction ? To answer this Cjuestion an investigation, either mathematical or experi¬ 
mental, as to the effects of friction is essential. Such an investigation I have endeavoured 
* Mauey, ‘ Physical Geography of the Sea,’ § 9.3. 
