53 



if S' be the salinity corresponding to the conductivity C, whence 



S=S'[1-(M-M0/MBS'] (7) 



Now let impedances M and M ' be considered to be composed of a 

 fixed impedance R, plus dail-con trolled impedances m and m', re- 

 spectively. From the work of E. Ruppin^ and A. L. Thuras^ mean 

 values for the constants A and B give the relation that 



C=C35(0.10925 + 0.02545S) 



If S' = 35.00 %o and 7^i' = 50.15 ohms and B = 0.02545, then BS' = 

 0.89075 and 



35(m- 50.15) .. 



•^"0.89075(35- S) ^ ^^' 



The value of R was designed to be about 200 ohms, but in order to 

 determine its effective value the 14 experimentally determined points 

 on the calibration curve were separated into four groups, and for each 

 group a centrally located point having a value of m and S was selected. 

 Each of these four groups was used to determine a value of R by 

 substituting in equation (8). The mean value was 204.267 ohms, 

 though of course not significant to this number of figures, the non- 

 significant figures being retained only for computation. 



Substituting this value of R in equation (8) and rearranging, we get 



8=9996.74/(204.267 + w)-4.293 (9) 



as the expression for the calibration curve of the new salinity bridge. 



In the above development of the equation for the calibration curve 

 it was assumed that the impedance of the arm containing the first 

 cell was made up entirely of the impedance of the solution in the cell. 

 A part of the impedance of this arm is embodied in the cell terminals 

 and leads, but this part is negligibly small. A generous estimate 

 of this fixed impedance would be about 0.2 ohm, or about 0.05 percent 

 of the impedance of the arm. 



A tentative calibration curve was then constructed by computation, 

 using equation (9). This calibration curve was used to reduce the 

 bridge measurements to salinities subject to future revision if subse- 

 quent simultaneous bridge and titration measurements indicated 

 such revision to be necessary. Accordingly, the salinities of all the 

 samples collected on the May oceanographic cruise were measured in 

 the bridge and 15 samples of well-distributed salinities were saved, 

 and after the General Greene returned to St. Johns were measured 

 by both bridge and titration methods within a few hours. These 



• O. Knimmel, Handbuch der Ozeanographie, Band I, p. 291; Stuttgart, 1907. 

 » A. L. Thuras, J. Acad. Sci., Washington, D. C, 8, p. 685; 1918. 



