276 DEPARTMENT OF THE NAVAL SERVICE 



"With this formula, it is a very simple matter to calculate the influence of friction 

 upon the circulation, as also the acceleration of friction in a stationary current. As 

 an example, we may take the Gulf Stream. A closed curve along this will include 

 150,000 solenoids, and consequently, in the Gulf Stream the retarding influence of 

 the friction upon the circulation will amount to 



li = 150,000 



cm.^ 

 sec.2 



On dividing this figure by the length of the closed curve, 15 -10^ cm., we obtain the 

 mean value for retarding acceleration of friction for all water particles in the Gulf 

 Stream, 



/ = 0-0001 ^"^' 



sec.2 



As a second example, we may take a closed curve along the Gaspe current at the 

 surface, and at 60 metres depth, between Dr. Hjort's stations X 31 and XIII 38. On 

 calculating A for this, according to the scheme shown in table 3, we find that the 

 number of solenoids is 10880. For this, again, according to (12), 



K = 10880 - ''"'•^ 



sec.^ 



The length of the closed curve, via North, Cape Breton island, amounts to 2-10^, i.e., 



/ = 0.00005 -^, 

 sec.2 



It is surprising that the retarding effect of friction upon ocean currents should 

 be so great as this. If the solenoids ceased to operate, then the velocity of the Gulf 

 Stream would be diminished by 1 cm. per second per 3 hours, and the Gaspe current 

 by 1 cm. per second every 6 hours; in other words, save for the solenoids, currents of 

 this nature would soon come to a standstill. We realize, then, the fundamental im- 

 portance of the solenoids for propelling ocean currents. 



If the closed curve be drawn across a stationary current, then B disappears, and 

 (12) in consequence, gives place to 



2co ^ = A (14) 



a t 



by means of which formulae >we can calculate the movement of the water ifrom 

 the solenoids, see table 3 and plates XIV and XV. 



These two formulse (13) and (14) are, as hydrography now stands, the most im- 

 portant mathematical means for dynamic treatment of hydrographical observations. 



In applying these formulae, it is necessary to see that the conditions for which 

 they are intended to apply are fulfilled. One disturbing factor which has to be 

 reckoned with is the screwing movement of the water in a current. Owing to this, 

 the influence of the earth's rotation does not altogether disappear in the case of 

 closed curves lying in the longitudinal direction of a current. The part of such 

 curves which is situated at the surface, is, by this screwing movement, carried towards 

 the right, and we may easily find that the earth's rotation wiU therefore exert a 

 retarding influence upon the current. The retardation calculated by formula (13), 

 therefore, should not be ascribed exclusively to friction, as a part of it will be due 

 to the earth's rotation. The more stable the layers in a current are, however, the 



