ATi.ANT. DEEP-SEA EXPKD. 1910. VOL i] PHYSICAL OCEANOGRAPHY AND METEOROLOOY 



105 



by the compass readings the way made by the ship when 

 swinging cannot be determined without knowing the di- 

 stance from tlie bow to the anchor, /. e. the position of 

 the anchor-wire in the water. A swing of the ship may 

 have but a comparatively Httle infkience upon tiie mea- 

 surements if the wire remains in a constant position. 



At Stat. 58, S. of the Azores, the ship had been 

 trawling when the trawl got stuck to the bottom in a 

 place where the bottom-depth was about 950 metres, in 

 this way the ship was well anchored, and we took ad- 

 vantage of the opportunity to make current measure- 

 ments. 



In a few cases observations with the current-meters 

 were made from the "Michael Sars" when it was drifting. 

 At Stat. 49 C a plankton-net of 3 metres diameter was 

 suspended by the trawl-wire at a depth of 1 000 metres. 

 The depth to the bottom was probably more than 5 000 

 metres. The big net and wire reduced the ship's mo- 

 vements. Many observations were made at 9 metres 

 below the surface, while at the same time measurements 

 were made at other levels down to 1 000 fathoms. At 

 Stats. 19 C and 47 a few measurements were made while 

 the ship was being slowly moved by the propeller at a 

 fairly constant speed. 



The observations at the three last stations were in- 

 tended to give some idea of the vertical differences of 

 velocity, not, of course, of the velocities themselves. 



The observations were made with Ekman's propeller 

 current-meter. 4 instruments were used. Their constants 

 are seen from the following equations: 



Instrument No. 7 : x' = 0-6 ^ 0-64 n 



„ 30: z; =r 0-5 + 0-39 n 



„ 31: z; ^ 0-7 + 0-37 n 



„ 41: z; = 0-5 -f- 0-38 //, 



where v means the velocity in centimetres per second and 

 n the number of revolutions per minute. Sometimes 

 two instruments were used simultaneously at the same 

 depth and showed a good agreement mutually. 



The results of the observations are recorded in Table 

 V where some particulars are also given of the circum- 

 stances in which the measurements were made. The 

 times recorded in the second and third column of this 

 table are the actual mean times of the observations. Be- 

 sides the observed velocity a reduced velocity is given, 

 the spreading of the shots being taken into account. The 

 reduced velocity refers to the average velocity in the 

 mean direction. 



The iron masses of the ship may appreciably affect 

 the compass of the current-meter at small depths. The 

 magnitude of the effect — the 'deviation' — naturally 

 depends on the magnetism of tiie ship and varies with 



the ship's heading. According to investigations made by 

 LoTTE M0LLER, A. SCHUMACHER and H. Thorade we may 

 infer that the magnetic influence of a ship like the "Michael 

 Sars" reaches down to about 30 metres below the surface. 

 At 9 metres where many measurements have been made 

 — the deviation in some cases amounts to 10° or more. 

 The error in the determination of the direction of current 

 at 5 metres is considerably greater, when the observ- 

 ations are made from the "Michael Sars" and not from 

 the rowing-boat. 1 have not tried to correct our observ- 

 ations for such errors. 



Even if the current-meters were rather heavily loaded 

 with lead weights the line was sometimes deflected to 

 an appreciable extent by the strength of the currents. 

 Such cases are noted in the tables. 



When the current measurements have been made 

 during a sufficient length of time to allow of harmonic 

 analysis, the N.- and E. -components have been com- 

 puted by interpolation for every complete lunar hour. 

 We have not sufficient observations from any of the sta- 

 tions to enable us to find the diurnal variations of the 

 currents; but at Stats. 18 and 58 measurements were made 

 during more than 12 hours, so the semi-diurnal variations 

 can be calculated. For the N-component we have the 

 following equation: 



v— V ^ P cos 30 t -\ Q sin 30 t 



and for the E. -component 



u — u + M cos 30 t Ar N sin 50 / 



where v and u mean the average values of the compo- 

 nents for 12 lunar hours, t is the time (in lunar hours) 

 reckoned from the first hour of observation. If, for in- 

 stance, the observations commence with 22 L. H., t is equal 

 to O for this hour, 1 for 23 L. H. etc. 



For determination of the major (2 a) and minor {2 b) 

 a.xis of the ellipse representing the tidal current we have 

 the following equations [Werenskiold, 1916]: 



2 a ^ \ (M + Q)2 + (N- P>2 _i_ |/^^ _ q;2 _!_ ^;v+ Pp 

 2b =] (M + Q)^-^(N^'P)^ - Y(M — Q)^ + (N-{-P)^ 



If b is negative the tidal-current turns cur?i sole, if 

 positive contra soleni. 



The angle, «, whicii the major a.xis forms with the 

 W. and E. direction (positive from E. towards N.) is found 

 tn' the equation : 



tg2u = 



2(M.P + N. Q) 



(M + Q)(M-Q) + (N -} P) (N - P) 



