38 



DYNAMIC METEOROLOGY AND HYDROGRAPHY. 



therefore identical with table 14 H, giving S arp , but with the difference that all 

 terms appear with the sign reversed.* 



30. Important Features of Specific Volume or Density of Sea-Water. 



Tables 9 h and 17 h show the regular decrease of the specific volume, or the 

 increase of density with increasing salinity. In the same way tables 8h and 

 16 h show the regular decrease of the specific volume, or increase of density with 

 increasing pressure. These tables do not show any marked peculiarities of the 

 sea-water. But very marked peculiarities are shown by the volume-tables 10 h, 

 11 h, and 12 h and the corresponding density-tables 18 h, 19 h, and 20 h. 



Table 10 h shows for sea-water of the salinity 35 /oo a regular decrease of 

 volume, and table 18 h the corresponding increase of density for decreasing tem- 

 perature. No maximum of density is found. Table 10 h used together with 11 h, 

 or 18 h used together with 19H, shows that we have a minimum of specific volume 

 or a maximum of density at 4 C. for fresh-water, at 2 for a salinity of about 

 9.5 "/a,,, at o for a salinity of about 19 /oo and at 2 for a salinity of 28 to 29 / 00 . 

 But for the normal oceanic salinity of about 35 / 00 , there exists no maximum of 

 density, and we shall, in the case of equilibrium, always have warmer water above 

 and colder below. This circumstance makes the equilibrium condition of the ocean 

 quite different from that of fresh-water lakes. 



*The first determinations of the compressibility of the sea-water were performed by P. G. Tait {Challenger 

 Report, Physics and Chemistry, vol. II, 1889). The first hjdrographical tables taking into account the compressi- 

 bility were calculated by Sandstrom and Helland-Hansen (Report on Norwegian Fishery and Marine Investigations, 

 vol. II, No. 4, Bergen, 1903). When our tables were first calculated, the only measurements performed upon sea- 

 water were still those of Tait, which had not by far the exactitude of Ekman's. Especially, no care had been taken 

 to determine the salinity of the samples of water experimented upon at the time when their compressibility was 

 measured. We therefore combined Tait's measurements for sea-water with those of Amagat for distilled water, 

 using Amagat's as absolute determinations and those of Tait only as relative comparisons of the compressibility 

 of sea-water and fresh-water of the same temperature. In the developments, section 27 (c), we therefore had to 

 subdivide every term where the pressure and the salinity entered into a main term depending upon the measure- 

 ments of Amagat upon fresh-water and a correction term depending upon the corresponding measurements of Tait 

 upon sea-water. Thanks to this method of calculation we had obtained tables which were in unexpectedly good 

 accordance with the new tables, which we have now calculated after the manuscript of the first tables had been sent 

 to press. The degree of accordance between the two 6ets of tables will be seen from the following data. 



The specific volume of normal sea-water (Amagat-Tait) was smaller than that registered in our new table Sh 

 for the pressures from zero to about 2200 d-bars, the maximal error being 0.00007 at 8 to 9 d-bars. Then the 

 volume was found greater from 2200 to 4400, the error varying between 0.00001 and 0.00002. For greater pressures 

 the specific volume was always found smaller, the error increasing gradually to 0.0001 at 5700 d-bars, to 0.001 at 

 S500 d-bars, and to 0.002 at 10,000 d-bars. Thus the error here runs up to 1/500 of the total volume. It should be 

 remarked, however, that these greater discrepancies only occur for the values which have been extrapolated, Tait's 

 experiments being extended to the pressure of 4629 and Ekman's to the pressure of 6000 d-bars. For depths in the 

 sea not exceeding 5000 meters the accordance is remarkably good, and hydrographic surroundings very seldom go 

 to a greater depth. The degree of accordance is very well illustrated by the following fact : The normal depth of 

 the isobaric surfaces calculated according to Tait never differs by so much as one decimeter from the corresponding 

 depths according to Ekman (table 7 h) for the first 5000 meters. For greater depths there are gradually increasing 

 discrepancies, the depth being found according to Tait 1 m. too small for the pressure of Sooo d-bars, 2m. too small 

 for the pressure of 9000 d-bars, and 3.6 m. too small for the pressure of 10,000 d-bars. But even these discrepancies 

 are of a secondary importance, for, as will be seen later, an error in the estimation of t the normal depth of the 

 isobaric surfaces will have practically no influence upon the discussion of the state of equilibrium or motion. Of 

 much greater importance are the much smaller corrections in tables 12 h and 13 H. The greater part of the numbers 

 in these tables have remained unaltered. But still there is a marked difference, the numbers being found numeric- 

 ally too small in both tables, the discrepancies in the most extreme cases mounting to 0.00004 m t ne values of 6 S p 

 and to 0.00007 > n the values of 6 TP . In spite of their smallness, these corrections are of real importance for the esti- 

 mation of the conditions of equilibrium and motion in the sea. 



The value of the quantity 6 srp was underestimated, so that no tabulation was found necessary. This may have 

 been an error due to the difficulties caused by the complicated method of calculation which had to be employed in 

 order to eliminate so much as possible the errors due to the inaccuracies of Tait's measurements. Thus table 1414 

 has been calculated only by Ekman's formula. 



The examples in Chapter VIII have been corrected according to the new tables, but the charts in Chapter IX 

 were already printed. However, the changes in these charts would in most cases be almost microscopical. 



