NOTE ON COMPUTATION OF DENSITY OF SEA WATER AND ON 

 CORRECTIONS FOR DEEP-SEA REVERSING THERMOMETERS 



In the reductions of the oceanographic observations 

 made on board the Carnegie during her seventh cruise, 

 it was fQund necessary to devise methods by which the 

 great amount of computational work involved might be 

 simplified and reduced. 



A considerable part of this work was the determi- 

 nation of the density of sea water from its values of sa- 

 linity and temperature, for which purpose special tables 

 were prepared in the Department of Terrestrial Mag- 

 netism. 



Table 1 is a table prepared for computing the den- 

 sity, t, being based on the formula 



o-t = Zt + (o-Q + 0.1324) [1 - At + Bt (o-q - 0.1324)] (1) 



together with the values of the involved constants as 

 given in Knudsen's "Hydrographical tables." 



Experience has proved the table more satisfactory 

 than graphs because of the more or less unwieldy graphs 

 resulting from the scale requirements imposed by the 

 requisite degree of refinement. 



Table 2 gives the corrections for depth and temper- 

 ature and for depth and salinity necessary to reduce the 

 values of density, Cf 'o those in situ, a^^J^. it is a 

 modification of the tables of Hesselberg and Sverdrup to 

 the extent that the separate corrections for depth and 

 for temperature of the latter tables have been combined, 

 thus reducing the number of entries from three to two. 



A similar modification was made of the Hesselberg 

 and Sverdrup correction tables for computing specific 

 volume and dynamic depth. 



The accompanying graph (fig. 1) was devised for 

 determining the corrections for unprotected deep-sea 

 reversing thermometers. It is based on the formula for 

 correction 



At = 



(Tw + Vo) (T' - t) 



(2) 



in which Tw is the recorded temperature of the unpro- 

 tected thermometer, T' the recorded temperature of 

 main thermometer, t is the recorded temperature (cor- 

 rected) of auxiliary thermometer, Vq is the volume of 

 broken-off column of mercury at 0°, and K the coeffi- 

 cient of expansion of the glass Qena 59"! for the ther- 

 mometers used on the Carnegie , for which K = 6100). 



Because of the large number of thermometers used 

 in the Carnegie observations, it was not deemed expedi- 

 ent to use graphs for obtaining the corrections for the 

 protected thermometers, since, because of the different 

 values of Vq, it would have been necessary to construct 

 a graph for each thermometer. 



Instead a table, of which table 3 is a specimen sheet, 

 was prepared which covered all the Carnegie values of 

 the tabular arguments and was based on the formula for 

 correction 



(T' + Vo)(T'-t) T'+Vo 



At = — + I + 



K 



(T' + Vo)(T'-t) 



K 



+ 1 (3) 



T' and t denoting, respectively, the recorded tempera- 

 tures of the main and auxiliary thermometers, I denoting 

 the index correction of the main thermometer, and Vq 

 and K having the same significance as in equation (2). 

 Making K = 6100, equation (3) reduces to 



At = 0.000164 (T' + Vo) (T' - t) [1 + 0.000164 (T' + Vq)] 

 + I + 0.000164 I (T' + Vo) (4) 



The first term of the right-hand member of (4) is repre- 

 sented by the tabular values in table 3, hence At = tabu- 

 lar value + I + 0.000164 I (T' + Vq). The term 0.000164 

 I (T' + Vo), may be considered negligible for well-made 

 thermometers for which I does not exceed 0.°10. 



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