210 On the Theory of Ocean Currents. 



The stationary state here also is independent of the friction- 

 coethVient. 



It follows, moreover, from these considerations, that, in a 

 liquid laver of constant depth, two currents parallel to the 

 same straight line, but flowing in opposite directions, can well 

 be adjacent without disturbing one another. Their dividing 

 surface is then a vertical plane parallel to their directions, in 

 which the velocity is 0, and which behaves exactly like a solid 

 bank. As long as the forces brought forth by each of the cur- 

 rents continue unchanged, the motions of both remain sta- 

 tionary, and neither current disturbs the other. 



The complete analogy shown by the distribution of velocity 

 in a mass of liquid possessing friction, with the heat-distribu- 

 tion in a solid body, gives a hint to pursue it also in another 

 direction. It has already been shown above, how extraordi- 

 narily slowly the velocity present at the surface is propagated 

 into the depths, provided here the velocity has previously 

 prevailed. From this it can be conversely inferred that the 

 after-effect of the initial state vanishes with the same slowness. 

 This is represented by the hitherto neglected first term of the 

 formulae (8), (11), and (13). If in them we put for /(f) a 

 constant or a linear function of f , the integral according to f 

 can be at once carried out, and the entire term dependent on 

 the initial state becomes in all three formulae a sum of the 

 same form as that which was obtained for the term dependent 

 on </>(X) when </>(X) was put = a constant. Since the expo- 

 nents of e are the same in both cases, the above calculated 

 numbers are valid for the vanishing of the initial state. 



If, for example, about 10,000 years ago (therefore at a 

 period of which we have no historic information), by any 

 cosmic event the equilibrium of the sea was so considerably 

 disturbed that strong currents resulted therefrom, the influence 

 of the then existing motions would certainly not yet have 

 totally disappeared from the present condition of the currents 

 — indeed it would at the present time predominantly deter- 

 mine the motion of the ocean in its greater depths — if the 

 earth were entirely covered with an ocean of the uniform depth 

 of 4000 metres. The interruption of the continuity of the 

 ocean by continents and island-masses of irregular shape will 

 contribute to soften down considerably that after-effect of pre- 

 vious states of motion, not so much by the increased friction 

 on the sea-bed as by the reflex and displacement currents 

 everywhere breaking in. Nevertheless, after the above nume- 

 rical proof of the slow spread of the influence of locally acting 

 changes of motion penetrating the mass, a caution is necessary 

 not to put aside the difficulty of more accurate calculation, as is 



