410 MISCELLANEOUS STUDIES 



where dA is an element of the vertical surface enclosing the column, 

 and the integral is taken over the whole vertical surface. Similarly 

 because of the invariability of the amount of salts in the volume 



r 2 W 1 8 a +fvSdA = 0. (203) 



Let 



S = S + *S (204) 



where S is the constant mean salinity for the whole volume and AS 

 is a variable increment. Then equation (203) becomes 



(205) 



and substituting the value of J Vd A from equation (202) we have 

 r a W 1 8 a '8(r. t W l E) +JV(Afl)<Li=() (206) 



or solving for W 1 



HE Cv(8)dA 



W,= - J- - = - (207) 



r 2 (8 2 S) 



An estimate of I V(&S)dA can be made as follows: Let the 



volume be so turned that two of its parallel faces are parallel to the 

 coast line and therefore perpendicular to the horizontal velocity T 

 directed away from the coast and given by equation (p. 401 ) 



(208) 



Then neglecting the variation of the salinity in a direction parallel to 

 the coast, the integral 



y (209) 



Cv(*8)dA= Cv i (*S) 1 dy + Cv 

 J J J , 



where V l and (A$)j correspond to the face next to the coast and V 2 

 and (AS) 2 to the face farthest from the coast. From a study of our 

 salinity observations (McEwen, 1916, especially plates 20, 21, 22. and 

 24) made from five to fifteen miles offshore, it appears that the hori- 

 zontal gradient parallel to the coast is negligible as compared to that 

 perpendicular to the coast, thus justifying equation (209). The 

 numerical values of the horizontal salinity gradient per meter esti- 

 mated from our observations are given for a series of depths in table 17. 



