66 



BJ0RN HELLAND-HANSEN 



[rep. of the "MICHAEL SARS" NORTH 



wards without producing a state of instability. Some 

 observations from the "Michael Sars" E.xpedition exhi- 

 bited an increase of temperature and decrease of ai down- 

 wards in the deep water of the North Atlantic and gave 

 rise to a renewed discussion of the adiabatic variations 

 in the sea and to the introduction of the notion of 

 potential temperatures in oceanography. It will therefore 

 be appropriate to deal more fully with these problems here. 

 The adiabatic change of temperature may be com- 

 puted by means of a formula by Lord Kelvin. When 

 using the metre-ton-second system of units we have: 



b 



-4 CT. e. g. 

 dr = 10 / ", 



dz 



Here 7 denotes the absolute temperature of the water 

 (273 + r), e the thermal coefficient of expansion, g the 

 acceleration of gravity, / the mechanical equivalent of 

 heat (0419), and Cp the specific heat at constant pressure. 

 The coefficient e varies considerably; it increases with 

 increasing values of any of the elements: temperature, 

 salinity or pressure. Cp is also variable. 



Professor Walfrid Ekman [1910, 1914] has published 

 tables which make it easy to calculate the adiabatic effect 

 in the case of sea-water. The following tables A — D 

 have been compiled in accordance with the data given 

 by Ekman. 



Tables A and B are calculated for .sea-water with a 

 value of Tg = 28-0, corresponding to 5 = 34-85 "/oo, 

 which is very nearly the salinity of the deep water in 

 the great oceans and in the Norwegian Sea. Such de- 

 viations from 5 ^ 34-85 "/o" ^s may occur in the deep 

 strata of the oceans, have so little effect upon the value 

 of the adiabatic variation that it amounts to less than 

 0-001° C. From Table A we may find the adiabatic cooling 

 when the water is raised from a depth m to the surface. 

 The argument im means the temperature /// 5//// at any 

 particular depth '). Table B shows the adiabatic heating 

 when the water is brought from the surface to the depth 

 m. The argument to means the temperature at the 

 surface. 



Table C is computed for salinities between 30-0 and 

 38-0 "/oo and temperatures between (f and 22° C. The 

 data are given for 1000 metres only, as such variations 



') Professor Schott published [1914] a table of tlie adiabatic 

 variations of temperature from different depths to the surface. Schott's 

 data differ somewhat from those given here because he does not take 

 into account that the temperature decreases all the time while the 

 water is being drawn upwards; he regards the argument of tempe- 

 rature as a constant for all depths. 



Within the interval of temperature between 0" and 4° C. the 

 difference is about 0055° for the drotli of 10000 metres. 



in salinity and temperature as are not covered by the 

 two former tables are only found in the upper strata of 

 the ocean (excluding areas like the Mediterranean and 

 the Red Sea). For depths down to 1000 metres it makes 

 practically no difference whether we use rm or To as the 

 argument ot temperature. The numbers printed in table 

 C are averages of the numbers found by starting from 

 1000 metres (cooling) and those found by starting from 

 the surface (heating). In any case the error only amounts 



to ooor C. 



Table D, calculated for the deep water of the Medi- 

 terranean, is based upon a ro-value of 31-0 iS = 38-57 "/o")- 

 The two halves of the table correspond to tables A and B. 



From Tables A — D the value of <) r at any value of 

 Tm or ro may be found with sufficient accuracy by linear 

 interpolation as far as the tabulated depths are concerned. 

 For other depths the graphical tables Fig. 24 and 25 

 may be useful in connection with Tables A and B. The 

 construction of the graphs is based upon a calculation of 

 the correction to be added to the number found in the 

 printed tables for the standard (some 1000 metres) level 

 next above the level of observation. Tiie diagrams are 

 divided in several parts applicable for intervals of 1000 

 metres: from 1000 to 2000 metres, 2000 to 3000 metres 

 and so on. Within each part, curves are drawn for every 

 50 metres; every second curve is numbered (from 1 to 

 9 dekametres). The scale of the initial temperature (rm 

 or To) is found along the abscissa, with sub-divisions for 

 every 0-2'. The correction for the adiabatic variation is 

 read along the ordinate, the numbers to the right and 

 left in the figures being expressed in 1 100° C. Horizon- 

 tal lines are drawn for every 0-001^. The use of the 

 tables may be demonstrated by the following example, 

 taken from observations in the Philippine Deep (cf. below): 



At a depth of 9788 metres the temperature /// silu 

 (rm) was found to be 2-60° C. By means of Table A 

 we find for 9000 metres and 2-60° by linear interpola- 

 tion di = — 1-133''. The graph in Fig. 24 gives for 

 the remaining 788 metres between 9000 and 10000 metres 

 and r = 2-60° an addition to dr of — 0-146°, so that 

 the final value of dr is — 1-279°. If, therefore, the 

 water is moved from 9788 metres to the surface the tem- 

 perature would decrease adiabatically to 2-60 — 1-279 

 = 1-321° C. 



On the other hand, when water of ro — 1-321° C. 

 is moved from the surface to 9788 metres we find in 

 Table B, 9000 metres: dr -= 1-124°, and in Fig. 25 an 

 additional number = 0-155°, or a total adiabatic varia- 

 tion of 1-279°, and hence a temperature at 9788 metres 

 of 1-321 -f- 1-279 = 2-60° C. 



To find the temperature which water at a depth of 

 a metres obtains adiabatically when moved to a depth 



