The Representation of Oceanic Movements and Kinematics 343 



recovery of the bottle ; an approximate mean value for the velocity of the current can 

 be calculated from the path which the bottle is presumed to have taken and the inter- 

 val between the two times. Large errors may occur in both these numerical values. 

 These circumstances have brought the method into disrepute, but as shown by the 

 results of Carruthers and Tait (1930) with the use of care and frequent repetition 

 it may still give a good idea about the system of currents over small areas of the sea. See 

 Thorade (1933fl) for further details. 



More accurate knowledge of the course of the currents can be obtained by following 

 the course of the drifting body directly by means of continuous triangular measure- 

 ment from three fixed points. Kruger (1911) and Schulz (1925) have used this 

 method for the investigation of the currents in the Jade near Wangeroog and off the 

 Flemish coast and have obtained valuable results. 



{b) Calculated Displacement 



The method of determining the course of the currents at the surface of the ocean 

 most used in practice depends on the comparison of an astronomical position with a 

 position given "by dead reckoning". The first gives the true position of the ship found 

 by astronomical observations and the latter gives the position of the ship as calculated 

 from the course steered by the ship and its speed, taking the wind-drift of the vessel 

 into account, and the distance covered according to the log (the position by dead 

 reckoning). Usually this does not coincide with the astronomical position of the ship, 

 since it has been calculated from the apparent speed of the ship in the water. The 

 difference between the two positions is called the ship's displacement and is considered 

 to be due to currents in the time interval between successive positions (usually de- 

 termined at noon). For example, a ship with a noon position 52° 25' N., 42° 16' W. 

 (Fig. 139, point A) has travelled 225 nautical miles in the water in the direction 

 S. 35° W. by the following noon. The triangle AA^C gives the difference in latitude 

 between A and the position by dead reckoning A^, = AC = 184 nautical miles = 

 184 minutes of latitude. The difference in longitude A^C is 129 nautical miles. Division 

 by the cosine of the mean latitude gives the difference in longitude in arc minutes as 

 3° 24', while the difference in latitude is 3° 4'. The position by dead reckoning at 

 point Ao is thus: 49°2rN., 45°40'W. Astronomical observation, however, gave 

 49°44'N., 46°22' W. Thus 



</,j = 49° 44', 9^2 = 49° 21', Acf, = 23', A^B = 23 nautical miles; 



Ai = 46°22', A2 = 45°40', ZlA = 42', A5 = 42' cos 49° 32' = 27 nautical miles. 



From these values the drift A^A^ is 35-6 nautical miles and y = 49° 47'; it is thus 

 N. 50° W., 36 nautical miles. The calculation can be considerably shortened by the 

 use of numerical or graphical tables. 



Usually the ship displacement is regarded as the effect of an ocean current, so that 

 displacement = current. This is not entirely correct, since the drift includes all the 

 errors which have been made during the calculation of the position by dead reckoning 

 and during the astronomical determination of the position (see Meyer, 1923). It 

 can fairly safely be assumed that all the errors in both determinations are due mainly 

 to chance; thus the mean of a sufficiently large number of displacement values at 



