plots above the line (.000) in Figure 1 which indicates the density of 

 freezing. In the case of the first point (^ ; Id- ^ ) shown in the 



figure, it is evident that the column of water(o h )can be given a 

 uniform density ( o" ^ )by temperature chf iges alone and that no freezing 

 results. However, for the column of water (o h 2 ) with coordinates 

 ( °"h2 j So h 2 ) temperature changes alone can take it only to the 



line of the density of freezing. In order_to obtain the uniform density 

 ( a h z )i a c h an ge in the mean salinity (A S h ) ^ s needed. 



From the geometry it is clear that 



AS 0j h = ( "h-°'f) tan «,. (5) 



but 



therefore, 



°f = S o,h cotcc < + b < i ( 6) 



A S ,h =( <r h-b l ) tan a,- S h ( 7 ) 



A mean salinity change of ASoh nas (Defant, 1949) an ice equivalent 

 of hAS 



lj (h) = 



oA 



< tPj \5« h 



P w 



9z-r°- 



where P\/Pw (the ratio of the density of ice to that of sea water) is 

 taken to be 0.9, and where k is the proportional part of the salt re- 

 leased from the sea water that is frozen (k averages about 0„85)» 

 Eolation 8 becomes 



'' (h » = h ( -H-Hir 1 M ,oncc '-i 1 



L L b o, h J J 



or in numerical units 



ij(h) = h (|) [ 137 '*u b L-m.m] , 



s o, h 



where lj is expressed in centimeters, h in meters, Sq h ^ °/oo, anc * °"h 

 in density units {P — 1) x 10 3 . 



*See Appendix III 



(9) 



(10) 



