NOTE ON THE PRACTICAL CORRECTION OF DEEP-SEA REVERSING 



THERMOMETERS AND THE DETERMINATION OF THE DEPTH OF 

 REVERSAL FROM PROTECTED AND UNPROTECTED THERMOMETERS 



Because of its simplicity and its elementary char- 

 acter, little has been published regarding the actual 

 steps involved in the practical reduction of the readings 

 of the deep-sea reversing thermometers, protected and 

 unprotected, to obtain temperatures and depths. Yet, 

 judging from the number of requests for such informa- 

 tion, there seems to be a need for its publication. The 

 aim of this article is to supply that need and no claim 

 of originality is made for the following. 



In a reversing thermometer there are two correc- 

 tions which must be applied. One is the index or scale 

 correction, I, which arises from irregularities in the 

 cross section of the capillary tube, and the other is a 

 temperature-difference correction arising from the fact 

 that the temperature at which the thermometer is read 

 is usually different from the temperature at which it 

 was reversed. The index correction is determined by 

 calibration and is dependent only on the reading of the 

 thermometer. As the temperature-difference correc- 

 tion is a correction for expansion, however, it depends 

 on both the reading of the thermometer and the temper- 

 ature at which it is read. Since the exact temperature- 

 difference correction involves the temperature of rever- 

 sal which is unknown, the practical formula used is an 

 approximation which may take various forms. In the 

 Russian Oceanographical Tables, 1931, compiled by 

 N. N. Subow, S. W. Boujewicz, and Was. W. Shoulejkin, 

 the correction for protected thermometers has the form 



AT = [ 



( T- - t) (T' -h Vq) 

 K J 



[1 ^ '^^^V I 



where AT is the total correction, T' is the reading of 

 the main thermometer, t is the reading of the auxiliary 

 thermometer (the temperature at which the reversing 

 thermometer is read), vq is the volume of mercury in 

 the thermometer after reversal at 0° C expressed as 

 degrees, K is a constant depending on the relative ther- 

 mal coefficient of expansion of mercury and the glass of 

 which the thermometer is made, and I is the index cor- 

 rection. 



In the Memoirs of the Imperial Marine Observatory 

 (1932), Koji Hidaka gives the correction for protected 

 thermometers as 



AT 



(T' - t) (T' + vo) 



K[l 



(T' + Vq -J) 



K 



+ I 



where the symbols all have the significance described 

 above. 



The correction given by Schumacher (1923) is, 

 using the same symbols 



AT 



(T^ - t) (T' + Vq) 



K ^ 



[1 



(T' - t) + (T' + Vq) 



K ^ 



+ I 



As an unprotected thermometer is used in conjunction 

 with a protected thermometer, the temperature of re- 

 versal is known from the protected thermometer. The 



temperature-difference correction, in the case of an 

 unprotected thermometer, is therefore more simple, 

 and the total correction is 



AT = 



(Tw - t) (T' + Vq) 



K 



+ I 



where Tw is the temperature of reversal as determined 

 by the protected thermometer and where the other sym- 

 bols have the same significance as before. 



The constant K is determined by the quality of the 

 glass, and is 6100 for Jena 59iii and 6300 for Jena ISi". 

 As most deep-sea reversing thermometers are made 

 from either one or the other of these kinds of glass, it 

 is possible to prepare a table, based on one or the other 

 of these values of K, giving the value of the temperature- 

 difference correction for different values of (T' - t) and 

 (T' + Vq). If two tables are prepared, one for K = 6100 

 and one for K = 6300, it is then possible by their use to 

 correct any protected thermometer whose index correc- 

 tion has been determined. Similar tables may also be 

 prepared for unprotected thermometers, but such tables 

 should give the correction for different values of (Tw - 1) 

 and (T' + Vq). Such tables may be converted into graphi- 

 cal form. 



The time required at sea for reducing observations, 

 however, is greatly lessened by the preparation ashore 

 of complete correction graphs for individual thermome- 

 ters. Such graphs may be constructed as follows: If C 

 represents the temperature-difference correction, we 

 have from Schumacher's formula for protected ther- 

 mometers given above 



(T'-t)(T' + Vo) 

 K 



or, rearrangmg 



(T'-t)(T'-h Vo)2+ (T' 

 k2 



t)2(T'+Vo) 



(T>.t)2(-I^MT'-t) r-'-°)';/'^'--°^ ]-C.O 



whence 



,T' f\ (T' ^ vo ^ K) -./ (T' ^ Vq ^ K)2 k2 



Now if the radical of the right-hand member of the above 

 equation is expanded by the binomial theorem, we have 



(T' 



(T' -t) = 

 Vo + K)3(r' 



k2 



(T' + vo + K) (T' + Vo) 



,c2+ 2K6 ^3 



'■"^ ^(T'^Vo+K)!'(T' + Vo)3'' •■•■ 



Vo) 



Now T' is assigned a selected value near one ex- 

 treme of the range of the thermometer and (T' - t) is 

 evaluated as C isassigneddifferent values in steps of 0.01 

 from 0.00 to such a figure as will give the temperature 



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