ATLANT. DEEP-SEA EXPED. 1910. VOL. l] PHYSICAL OCEANOGRAPHY AND METEOROLOGY 



99 



sonal variations in the upper water-strata have no iniiuence 

 upon the charts for other strata, and variations in the 

 times when the different stations have been worl\ed hardly 

 affect depths below 200 metres. Thus topographical 

 charts when rightly constructed may serve as current charts. 

 It was mentioned above (p. 79) that Professor Walfrid 

 Ekman has discovered a general law according to which 

 the direction of a gradient current depends upon varia- 

 tions in the depth to the sea-bottom, hi order to see 

 whether this law finds expression in charts of dynamic 

 topography Professor Ekman and the author in 1922 

 studied some such charts from the North Atlantic. We 

 were immediately struck by the almost complete agreement 

 between the series of dynamic isobaths drawn for different 

 isobaric surfaces. There is nothing remarkable in the 

 fact that a current connected with a soienoidal field runs 

 at ail levels appro.ximateiy in one main direction. This 

 is only what one would expect as a normal state of things. 

 But the agreement was in this case so close that the 

 question naturally arose as to whether it depended upon 

 some universal mechanical law. We believed that this 

 question could be answered in the affirmative as far as 

 stationary hydrographic conditions were concerned. Our 

 reasons were as follows: Stationary hydrographic con- 

 ditions imply that the isohaline and isothermal surfaces, 

 and therefore the isosteric surfaces as well, /. e. surfaces 

 combining all points with constant value of specific volume, 

 retain their positions unaltered. Consequently any motion 

 of the water across these surfaces is excluded, if allow- 

 ance is made for the quite insignificant alterations of 

 salinity and temperature which an individual bulk of 

 water may undergo owing to diffusion and conduction 

 of heat. Let us suppose that the isosteric surfaces slope 

 — which they must in the case of gradient currents — 

 and that the current itself is horizontal. Then the motion 

 of the water, if it is not to crocs the stationary isosteric sur- 

 faces, must necessarily follow the horizontal tangents of 

 the latter. On the other hand, according to a well-known 

 dynamical law and leaving viscosity out of account, the 

 relative velocity of a water-layer immediately below is 

 directed along the same horizontal tangent, /. e. in the 

 same direction or in an exactly contrary direction. From 

 this it follows that the gradient current at all levels runs 

 in one direction or in two exactly opposite directions only. 

 From another point of view the same thing may be ex- 

 pressed by saying that all isosteric surface elements (and 

 all isothermal and isohaline surface elements) along one 

 vertical line must slope in the same, or in two exactly 

 opposite directions.') 



') A more detailed proof of tliis tlieorcm is found in a publica- 

 tion by V. W. Ekman 11923). 



The reader will have observed already that the va- 

 lidity of this "theorem of the parallel fields of solenoids" 

 depends upon several assumptions besides the obviously 

 necessary assumption of a stationary hydrographical con- 

 dition. One of these assumptions is implied in the use 

 of the ordinary dynamical connection between pressure 

 gradient and velocity, for this is only possible, as Ek.man 

 has shown [1923), when the horizontal dimensions of the 

 region considered are not very small and when the stream- 

 lines of the current are not very sharply bent as they 

 would be, for instance, off a promontory. Other impor- 

 tant assumptions are the disregard of viscosity and of 

 any inclination of the stream-lines in comparison with 

 the inclination of the isosteric surfaces. The necessity 

 of all these assumptions involves us in some uncertainty 

 as to the validity of the theorem. Nevertheless the un- 

 doubted theoretical reasons in its favour, in connection 

 with the remarkable way in which it is applicable to the 

 Great Atlantic Current and other cases, are a sufficient 

 motive for retaining it as a working hypothesis and for 

 trying to have it tested by observations. 



43. Numerical Calculations. 



The first object of the dynamical calculations is to 

 find the pressure at different level surfaces or the dynamic 

 depth from the sea surface to different isobaric surfaces. 

 The basic observations of temperature and salinity at the 

 stations are made at different depths in ordinary metres. 

 A depth of 1000 ordinary metres corresponds to about 

 980 dynamic metres and a pressure of about 1010 decibars. 

 For dynamic depths it is convenient to use standard num- 

 bers in dynamic metres and for pressures standard numbers 

 in decibars similar to those used for the ordinary depths 

 for which the records of temperature and salinity are given 

 (standard depths, cf. section 16). The values of tempera- 

 ture and salinity at, for instance, 1000 dynamic metres are 

 a little different from the values observed at 1000 common 

 metres. The real values at the standard dynamic depths 

 and the standard pressures could, of course, be found from 

 the observations by interpolation, but the differences are 

 so small that such an interpolation is unnecessary for 

 practical purposes, and an observation from a certain 

 standard depth, measured in ordinary metres, may be 

 used without alteration as applicable to a depth of just 

 as many dynamic metres or decibars. 



In Table 111 the argument a means either ordinary 

 metres, or dynamic metres, or decibars. The values of 

 temperature, salinity and density without compression (col- 

 umns 2 — 4) are given for the standard depths in ordinary 

 metres, but they are also used directly, without any cor- 



