201) M. K. Zoppritz cm some llydrodynamie Problems 

 or, after carrying out the integral, 



w = w < T z * — e \ * J v- sin -7— > . 



in it j ?i k ) 



Since 



-7r 2 = 0-1421. 



for a mean sea-depth of 4000 metres, to be expressed in cen- 

 tims., the exponent of e becomes 



0-1421 2 



400000 2 



extremely little as long as t is not enormously great, the series 

 consequently very feebly convergent. If £=10000 years, four 

 more terms must always be calculated in order to obtain an 

 approximation to within one thousandth of accuracy. If the 

 amount of the velocity w m in the half depth of the ocean, con- 

 sequently for ,«= ^, be required, all terms in the series vanish 



which contain exact multiples, while the remaining sines assume 

 the value ±1. We then get, for £=10,000 years, exactlv, 

 within 0-001, 



w. 



= W °{ *"" |( e ~°' 28 ° ~3 e ~ 2 " 52 ) } =0-037 *tf . 



Since after an infinite time the velocity 0'5iv must prevail 

 at this place, it is evident how inconsiderable a portion of the 

 definitive velocity has penetrated to such a depth only after 

 10,000 years. On the other hand, for £ = 100,000 years iv m 

 becomes 



= Wo j i __i,-2- 8 oJ_ 



•461 iv . 



Therefore the velocity has, after 100,000 years, already arrived 

 very near to the definitive value ; after 200,000 years it differs 

 from it only 0'002. 



From the foregoing theoretical considerations two results 

 especially are obtained, which more or less contradict views 

 hitherto accepted : — first, that the stationary motion proceed- 

 ing from an invariable surface-velocity makes itself perceptible 

 with linearly diminishing velocity right to the bottom in an 

 unlimited sheet of water, while the view has frequently been 

 expressed that the influence of such surface-currents (as, for 

 instance, the impulse generated in the equatorial regions of 

 the ocean by the trade-wind) extends downward to only very 

 limited depths. Secondly, we have found that all periodic or 



