ANALYSIS TO THE DYNA3IICAL THEORY OF THE TIDES. 
253 
observation^ it being noticeable at a glance at the Admiralty current charts that 
there is no tendency to cross the equator except in the immediate neighbourhood of 
the coasts. 
The rigorous treatment of the problem of ocean currents, as afPected by variations 
in the density of the water, appears to be hopelessly beyond the powers of mathe¬ 
matical analysis, and I will therefore leave the subject with the brief indications 
already given in this section, and will conclude the paper with an example illus¬ 
trating another means by which possibly ocean currents are in part maintained, and 
which is instructive in showing the very important part played by the rotation of 
the earth in rendering effective a cause which otherwise could give rise to no 
sensible currents. 
§. 15. On Currents due io Evaijoration and Precipitation. 
A cause which has been advocated ^ in explanation of ocean currents is the 
fact that in equatorial regions the amount of water evaporated into the atmosphere 
largely exceeds that precipitated in the form of rain in these regions. The excess of 
water in the atmosphere is carried away to be precipitated in temperate and polar 
regions, thereby giving rise to an excess of precipitation over evaporation in the 
latter regions. It has been urged with some reason that, as the actual amount 
of Avater in equatorial regions does not diminish nor that in polar regions increase 
from year to year, there must be a continual flow of water from the poles towards 
the equator. The fact that this flow of water is in the” opposite direction to 
that observed at the surface, which for the most part sets from the equator towards 
the poles, is explained by attributing the counterfloAv to undercurrents. If however 
we subject the question to the test of mathematical analysis, we shall find that 
though such a flow towards the equator must necessarily exist, it is so slow as to be 
completely masked by larger currents due to other causes. The flow in question 
will however give rise indirectly, in consequence of the rotation, to currents which 
in the absence of dissipative forces would tend to increase without limit. The 
explanation of this fact will be obvious after the discussions of § 11. 
The effects of evaporation and precipitation may be conveniently represented 
mathematically by an ajq^ropriate distribution of sources and sinks over the free 
surface. This will modify the surface-conditions at the free surface but will not 
interfere with the dynamical equations. Instead of equating W to 3^/3^ we must 
replace it by a certain function of the position on the surface, independent of 
the time, but depending on the rate of evaporation and precipitation at the place, 
* )See an Article by Proctok in ‘St. Paul’s Magazine,’ Sept., 1869, I’epriuted in ‘Light Science’ 
(1st series), p. 111. , . 
