The Representation of Oceanic Movements and Kinematics 357 



De Bilt, 1935-6). From this atlas the part contained in Fig. 149 was taken; for an 

 explanation of this picture see the legend underneath. 



A picture of current conditions easier to interpret can be obtained if only a selection 

 of the particularly typical vectors are given as, for example, in the Deutsche Seewarte 

 Atlas containing twelve monthly charts; however, in these the subjective viewpoint of 

 the investigator has a large effect. A different type of representation has been used in 

 the British Admiralty charts. The ship reckoning displacement is not shown by a 

 straight arrow, but by a wave-like arrow with the mean velocity in nautical miles per 

 day indicated by a number underneath. Where there is no displacement the chart is 

 left blank but along the usual shipping routes they accumulate. In practice this method 

 has the advantage that it shows the variations and the uncertainty in the occurrence 

 of the ocean currents and the greater or lesser prevalence of current free regions or only 

 of weak currents. 



(b) Representation of Average Current Conditions by Means of Stream Lines 



Instead of giving statistics of individual ship displacements in form of compass cards, 

 these statistics can also be used to give the mean value of the currents in the degree 

 squares. This has been done by the Netherlands Meteorological Institute (1908, 1915, 

 1919). A vectorial mean for one or two degree squares is taken of ship displacements, 

 and calculations are also made of the scalar means and the stability. The results have 

 been published in tables and charts. This observational material has then formed the 

 basis for a whole series of investigations on ocean currents. Attempts to derive a 

 comprehensive picture of the currents from these mean current vectors are of two types 

 (Schumacher, 1922); one of these represents the current by stream lines broken up 

 into arrows with the feathering or the thickness of the arrows indicating the velocity. 

 The other gives the direction of the current by continuous stream lines and the velocity 

 by isolines (isotachs). To the first group belong the investigations of Michaelis 

 (1923) and Willimzik (1927) on the Indian Ocean, of Meyer (1923) on the Atlantic, a 

 study by Merz (1929) on the Pacific Ocean, and by Willimzik (1929) on the Antarctic 

 surface current and others. The second method was first used in oceanography by 

 Bjerknes and co-workers (1913) for the currents in the Gulf of Mexico. During a 

 renewal of the monthly current charts for the North Atlantic Schumacher (1940) 

 later used another method of representation. The arrows here were drawn to represent 

 not the mean direction and velocity but the most frequent, which is more valuable both 

 for the practical user and in most cases also for scientific purposes. All the available 

 data on observed ship displacement were evaluated on this most frequent value (mode) 

 principle. The quadrant containing the largest number of observations was found for 

 each point; the enormous amount of work required was handled by a punched-card 

 system (Hollerith). The direction separating this quadrant into two halves was then 

 taken as the prevailing direction of the current. The velocity was taken as that usually 

 found in the prevailing direction, that is, the scalar mean of the ship displacements 

 falling within the selected quadrant. 



Also, the stabiHty was determined as before and was characterized by the probability 

 of a displacement in the selected quadrant, i.e. by the numerical ratio of the number 

 of observations falling within the quadrant to the total number of observations. Four 

 different grades of stability were distinguished. If at least one-third of all observations 



