THERMOMETRIC DETERMINATION OF DEPTH 



The thermometric method for determining depths in 

 the sea has recently been discussed by Dr. A. Schumacher 

 (1923) and part of this discussion will be repeated here 

 for the sake of completeness. An unprotected thermom- 

 eter which is subjected to a certain pressure will show 

 a fictitious temperature which can be regarded as con- 

 sisting of the actual temperature of the surroundings 

 plus the effect of the compressibility of the glass. On 

 account of this pressure effect the reading of the ther- 

 mometer will be higher than the reading corresponding 

 to the temperature of the surroundings and the increase 

 of the reading per unit increase of pressure can be de- 

 termined in laboratory. The difference between the in- 

 dications of two thermometers, one protected against 

 pressure and one unprotected, which both are subjected 

 to the same pressure in the same surroundings, can on 

 the other hand be used for determining the pressure, as- 

 suming the pressure coefficient of the unprotected ther- 

 mometer to be known. This method is used in oceano- 

 graphic work. Two thermometers, one protected and 

 one unprotected, are attached to the same water bottle 

 and the pressure at which the thermometers were re- 

 versed can be computed from the corrected readings. 

 Knowing the average density of the water from the sur- 

 face and down to the level where the thermometers were 

 reversed, the depth can be found. Since the pressure co- 

 efficient of the thermometers is given in degree centi- 

 grade per kg/cm2 of increase in pressure and since the 

 pressure of 10 meters of water of density 1 is equal to 

 1 kg/cm2, we get: ^ ^ ^^^ ^^^ 



q-Pm 



where D means the depth in meters, A the difference 

 between the corrected readings of the two thermometers, 

 q the pressure coefficient cf the unprotected thermome- 

 ter, and/jju the mean density from the surface to the 

 level at which the thermometers were reversed. 



The corrections which must be applied to the read- 

 ing of the protected reversing thermometer have already 

 been discussed. The correction to be applied to the 

 reading of the unprotected thermometer because it was 

 read off at a temperature which differs from the tem- 

 perature at which it was reversed, is found by means of 

 the same formula: 



6100 



where Tu means the "temperature" of the unprotected 

 thermometer Vq the volume of mercury at zero degrees 

 expressed in degrees, Tp the temperature at which the 

 thermometer was reversed, t the temperature at which 

 it was read off and where 6100 is a constant which de- 

 pends on the quality of the glass. The temperature at 

 which the thermometer was reversed is known exactly 

 from the indication of the protected thermometer, but 

 the indication of the unprotected thermometer at rever- 

 sal is not known. As a first approximation the reading 

 of the unprotected thermometer, Tu' is introduced in 

 equation (2) instead of Tu- This introduction leads inthe 

 case of the Carnegie observations to errors which never 

 exceed Of005 and may be regarded as negligible. The 

 correction on account of the thermometer being read at 

 a temperature which differs from the temperature at 



reversal has, therefore, been computed by means of the 

 formula: 



(Tu' + vo) (Tp - t) 



K 



(3) 



6100 



To the correction K the scale correction at the temper- 

 ature of reading has to be added. Practical methods of 

 determining this correction and of determining the depth 

 have been described by Ennis (1933) and Soule (1933). 



After these remarks about the corrections of the un- 

 protected thermometers, we can turn to a discussion of 

 the accuracy of the depth as determined by means of 

 pressure thermometers (equation 1). Following the pro- 

 cedure of Schumacher, we compute the inaccuracy in the 

 depth which would result from inaccuracy in the quanti- 

 ties At, q, and m^ 



l)dD = 



10 

 q Pm 



■dAt error inD arisingfromanerror dAtin At 



2)dD =i5ALdq error inD arising from an error dq in q 

 q^ Pm 



3)dD=- ^^^'•, d nj error inD arisingfrom an error dpnii"P 



qpm'' 



1. The pressure coefficient for the Carnegie thermome- 

 ter values was between 0.07 and 0.09. For the mean 



density we may introduce 1.035. The factor ^ ^^ lies, 



therefore, between the limits 138 and 107 and an error 

 in the temperature difference of 0.01 introduces, there- 

 fore, an error of 1.4 to 1.1 meter. The error of the dif- 

 ference depends on the accuracy of the two thermome- 

 ters. We have already discussed the accuracy of the 

 protected reversing thermometers and have arrived at 

 the conclusion that the error of one single temperature 

 determination is, as a rule, considerably smaller than 

 + 0.04 and never greater than +0.075. As to the errors 

 of the unprotected thermometers, we assume, since 

 these have a more narrow division of the scale, that the 

 errors may be twice as great--that means generally 

 smaller than +0.08 and never greater than +0.15. The 

 error in the difference between the corrected readings of 

 a protected and an unprotected thermometer will there- 

 fore as a rule be considerably smaller than +0.12 and 

 never greater than +0.225. The error in depth arising 

 from these errors will usually be considerably smaller 

 than +16 and never greater than +31 meters. 



2. The pressure factor q, was determined at the Physik- 

 kalische-Technische Reichsanstalt, Charlottenberg, and 

 entered on the certificate of the thermometer to the 

 fourth decimal place. Assuming the last decimal place 

 to be correct (which means the error in the factor q to 

 be smaller than 0.005), we find, taking /Sjn as a constant 

 and equal to 1.035: 



11 



