238 Harmonic Analysis and the Theory of the Tides. 



ocean currents, and it is therefore of interest to examine the nature 

 of the free steady motions which could exist on a rotating globe. Tt 

 is shown that so long as the depth is uniform the only steady motions 

 possible are those in which the particles of water move along paral- 

 lels of latitude, while, if the depth be variable, the stream lines of 

 the possible steady motions coincide with the lines 



Jijfi — const., 



where h denotes the depth, and /u the sine of the latitude. 



5. These currents differ materially from the actual currents of the 

 ocean, and the difference is probably to be explained from the fact 

 that the density of the water has been treated as uniform, whereas 

 the density of the ocean varies from point to point in consequence 

 of differences of temperature, salinity, &c. These variations of den- 

 sity have been claimed by some authorities as the sole cause by which 

 ocean currents are maintained, but as free currents could exist, and 

 would almost certainly be excited by such causes as the winds, even 

 if there were no variations in the density, it is improbable that such 

 is the case, though there can be no doubt that the density- variations 

 play an important role in modifying the possible forms of the free 

 steady motions, and thus determining the course which the currents 

 pursue. 



6. Though these currents have been described as " free," they 

 could not exist in nature without some disturbing force in con- 

 sequence of the action of viscosity. If, however, the coefficient of 

 viscosity of the water be sufficiently small, a very small amount of 

 disturbing force will be sufficient to excite and maintain them. As 

 an example of the manner in which they could be maintained by a small 

 disturbance, an attempt is made to estimate the effects of the unequal 

 distribution of rainfall and evaporation over the surface of the earth. 

 It is shewn that this cause will give rise to a slow current from the 

 poles towards the equator of quite insensible amount, and not changing 

 from time to time ; but, in addition to this flow, there will be set up 

 currents along the free stream lines which, in the absence of friction, 

 would increase uniformly with the time. When the water is viscous, 

 the latter currents will, however, eventually attain a magnitude equal 

 to that which they would acquire in a period equal to the modulus of 

 decay of the type of motion set up, after which they will remain 

 steady. Such currents might attain a magnitude comparable with 

 the actual currents of the ocean if the modulus of decay of any of the 

 types of current motion be as long as twenty years, and as this value 

 for the modulus of decay is not improbable, it is concluded that such 

 causes as the unequal distribution of rainfall are sufficient to give 

 rise to currents quite comparable with those which exist on the 

 earth. 



