in reference to the Theory of Ocean Currents. 203 



Now,, if (f>(t) is constantly =iv , it is at once evident that v 

 becomes the same for pairs of values m, t and x r , t', for which 

 the lower limit of the integral is the same ; therefore 



77 = 7^ < 15 > 



j. e. the same velocity occurs at different depths which are to 

 one another as the square roots of the times. 



The formula that is valid for a constant superficial velocity 

 tv , namely 



X 



zScTt 



can be made use of to calculate, with the help of the Tables 

 that exist for the value of Kramp's integral, the time that 

 elapses before a point in a given depth reaches a certain velo- 

 city. The velocity w of the surface first reaches a point after 

 an infinite time. If we take a point at the depth #=100 

 metres, and inquire after what time it will possess the half- 

 velocity of the surface (v = ^io ), we have to solve the trans- 

 cendental equation 



kt 



" ^Jo' 



in which, for a, its value (see p. 195) is put. Herein #=100 

 metres, and instead of h and fi their values for the liquid in 

 question, are to be inserted. Since, according to Encke's 

 Tables in the Berliner astronomischen Jahrbucli for 1834, the 

 integral value 0*5027 corresponds to the upper limit 0*48, the 

 time sought, t, is very approximately determined by the equa- 

 tion 



-4--,v/£ =0-48. 



2s/tV k 



The coefficient of friction for water and very dilute salt- 

 solutions is, at ordinary temperature, according to O. E. Meyer*, 

 about 0-01 3-0-015. Taking 0-0144 and still putting ^=1, 

 from which the density of sea-water differs only in the third 

 place of decimals, we can put for application to the ocean 



Vi- 



0-12' 

 * Pogg. Ann. vol, cxiii. p. 400. 



