274 DEPARTMENT OF THE NAVAL SERVICE 



the other part relative to this, it will in this case give the actual velocity of the same. 

 Now, the movement of the water at great depths is inconsiderable, the greatest velo- 

 cities occurring in the upper water layers. We therefore select the closed curve in 

 such a manner that its one part is situated at the greatest possible depth, a'nd calcu- 

 late the velocity of the other, upper portion, relatively to this deeper part. 



The values in table 5 best suited to this calculation are those indicated as 2 A ^^^^. 

 This column gives A for closed curves having their vertical parts situated at a dis- 

 tance of 10 km. apart and with the one horizontal portion situated at the greatest 

 depth from which measurements are available. Taking this lower horizontal portion 

 as immobile, and the upper as moving at right angles to its own longitudinal direc- 

 tion with a velocity of u cm. per second, then obviously the increment of area in the 

 projection of the curve upon the level of the sea's surface amounts to 



d(j 



— = 10^ u 

 dt 



du 

 per second, 10 km. here representing 10^ cm. Inserting this value for — in (9), we 



dt 

 obtain : 



A 

 u = (10) 



145-8 sin <p 

 For the latitude "= 43° 19', which falls within our area of investigation, is 



145-8 sin ^ = 100 

 and in consequence: 



A 



u = — (11) 



100 



i.e., the 2 A lOkm- coluimis in table 5 give the velocity in hundredths of a cm. per 

 second. We need then only cut off two decimal points from the figures in this 

 column in order to obtain the velocity in cm. per second. 



In order to comprehend what is given in formula (11) we may consider a cur- 

 rent in the sea flowing over a substratum of still water. Owing to the rotation of 

 the earth, the current will veer off^to the right until it encounters a coast, which 

 it will then follow, still pressing towards the right, i.e., setting in towards the coast. 

 In consequence of this pressure, the current will become deeper near the coast than 

 farther out; i.e., the separating surface between the current and its substratum of 

 heavier water will lie obliquely. In this surface, then, there will be a number of 

 solenoids running in the longitudinal direction of the current. By taking a hydro- 

 graphical section across the current, and treating the observations according to the 

 scheme in table 3, we obtain the number of these solenoids. Formula (11) now 

 shows, that if 10 km. breadth of current contain 100 solenoids, then the current will 

 flow at a velocity of 1 cm. per second; if 1,000 solenoids, the velocity will be 10 cm. 

 per second, and with 10,000 solenoids, the velocity of the current will be one metre 

 per second. If the number of solenoids be 6,728, the velocity of the current will be 

 67-28 cm. per second. 



This simple relation is, of course, strictly speaking, valid only for latitude 43° 19'. 

 For other latitudes, we can obtain from table 6 the number of solenoids per 10 km. 

 breadth of current which will give a velocity of 1 cm. per second. By dividing the 

 values for number of solenoids obtained through the hydrogrnphic measurements by 

 the figure in table 6 corresponding to the latitude of the station, the due allowance for 



