PROCESSING OCEANOGRAPHIC DATA 



in presence of a suitable indicator. When cor- 

 responding depths, temperatures, and salinities 

 have been found for a cast, the relationship 

 between each pair of variables is plotted on 

 graph paper, and the three curves drawn. The 

 curves are cross-checked until mutually con- 

 sistent, and values of temperature and salinity 

 at standard depths are read from the curves. 



THERMOMETER CORRECTIONS 



Two types of correction to the readings of 

 protected and unprotected reversing thermom- 

 eters are necessary. One is an index correction 

 for errors in the thermometer scale. Such 

 errors are caused by variations in the cross 

 section of the capillary or by irregularities in 

 the scale etching. The correction at various 

 readings is determined by calibration, and is 

 listed on the calibration certificate for the indi- 

 vidual thermometer. 



Since the temperature at which the thermom- 

 eter is read may be quite different from that at 

 which it was reversed in the sea, a second cor- 

 rection for relative expansion of mercury and 

 glass subsequent to reversal is necessary. The 

 two formulae conmionly used for this correction 

 were developed by Schumacher (1923) (4) and 

 Sverdrup (1947) (5), respectively. Both start 

 from the expression 



C= 



K 



where the symbols in this and the following 

 formulae have the meanings listed below: 



7" = reading of the protected reversing thermometer. 

 ( = temperature at which protected reversing 

 thermometer is read, i. e., reading of the 

 auxiliary thermometer which accompanies 

 each protected reversing thermometer, cor- 

 rected for index errors. 

 7',„ = water temperature in situ, the corrected reading 

 of the protected reversing thermometer. 

 Tu,= T' + AT=T' + C+I. 

 7^^= reading of the unprotected reversing thermom- 

 eter. 

 <„ = temperature at which unprotected thermometer 

 is read, i. e., reading of the auxiliary ther- 

 mometer which accompanied each unprotected 

 reversing thermometer, corrected for index 

 errors. 

 7'„ = corrected reading of the unprotected reversing 

 thermometer, a function of both temperature 

 and pressure. T„= T^ +Ar= T^ + C-(-/. 

 C= correction for thermal expansion of the ther- 

 mometer system subsequent to reversal. 



/ = index correction for errors in the thermometer 

 scale. 



A 7"= total correction to be applied to the reading of 

 the reversing thermometer. AT=C+ 1. 



V'o= volume of mercury below the 0° C. mark, at 

 0° C. temperature, in the reversed thermom- 

 eter, expressed in degrees centigrade of scale. 

 This is a constant for each thermometer, and 

 is given on the calibration certificate, 

 it = reciprocal thermal coefficient of expansion of the 

 thermometer system. This is a constant 

 which depends upon the type of glass of which 

 the thermometer is made. For Jena 59'" 

 glass, A' = G100° C. For Jena 16'" glass and 

 for Corning Normal glass, A' = 6300° C. The 

 value of K is given on the thermometer cali- 

 bration certificate. 



Schumacher replaces the unknown Ty, with 

 T' to find a first approximation to the correc- 

 tion. Then, adding this correction to T' and 

 substituting again for T^, in the formula, he 

 finds a second approximation to the correc- 

 tion C. His complete expansion correction 

 formula is: 



^__ (T' + V o)(T'-t) n ^ {T'+Vo) + {T'-l) -\ 



+ 



{T'+Va )H T'-t)' 

 A'9 



Since the correction is usually desired to two 

 decimals, the last term, which never exceeds 

 0.00015, may be neglected. When the index 

 correction is added to this expansion correction 

 Schumacher's formula for the total correction 

 to protected thermometer readings is: 



^^_ {T'+Vo){T'-t) r ^ {T'+V.) + {T'-l) -\^ J 



Sverdrup has developed a slightly more 

 accurate formula by substituting T"-|-C'for T„. 

 Making this substitution in the exact expression 

 given above: 



C= 



{T'+Vo + C){T'-t-\-C) 

 K 



(T' + Vo){T'-t) , „r iT'+Vc) + {T'-t) -\ , C» 



The last term is never greater than 0.00015, 

 and may be neglected. Solving for C: 



„ { T'+Vo)(T'-t) r. {T'+V,)-\-{T'-t) -\ 

 ^- K L K J 



{T' + V,){T'-t) 

 ~K-iT' + Vo)-(T'-l) 



