CHAPTER 3 

 TEMPERATURE AND DEPTH CALCULATIONS 



3-1 GENERAL REMARKS,— The deter- 

 mination of true sea water temperatures and 

 the depths at which they are obtained by means 

 of Nansen bottles and deep-sea reversing ther- 

 mometers are relatively complex. This entire 

 chapter explains the methods and calculations 

 involved in computing these values. The for- 

 mulas given herein have been reduced to their 

 simplest forms to enable rapid processing of 

 data by observers in the field. For the person 

 desiring more detailed information as to the 

 derivation of these formulas, reference is made 

 to H. O. Pub. No. 614, Processing Oceano- 

 graphic Data, 



The calculations involved in determining 

 the temperatures and depths of Nansen bottle 

 samples are recorded on the A-sheet, which is 

 described in chapter 14, and on related graphs. 

 Although these calculations can be made with an 

 ordinary slide rule, the use of a special reversing 

 thermometer slide rule, or a calculator, makes 

 the process easier. The Hydrographic Office 

 uses a small, inexpensive, plastic slide rule 

 made for this purpose. 



3-2 Deep-Sea Reversing Thermometer Cal- 

 ibration Corrections. — Before each deep-sea 

 reversing thermometer can be used it must be 

 tested and precisely calibrated to determine 

 small errors in graduations of the scales of the 

 main and auxiliary thermometers; the volume 

 of mercury in the bulb of the main thermometer; 

 the glass constant; and for unprotected ther- 

 mometers, the pressure coefficients. Each ther- 

 mometer used by the Hydrographic Office is 

 tested and calibrated by the Bureau of Stand- 

 ards which issues a calibration sheet for it 

 before use at sea. 



When the thermometers are used at sea, 

 either a copy of the calibration sheet or a card 

 as shown in figure 3-1, giving the necessary 

 information, is provided for each thermometer. 

 Select the calibration sheet or card with the 

 thermometer manufacturer's serial number 

 corresponding to that of the reversing ther- 

 mometer being used, and obtain the volume of 

 mercury in the bulb of the main thermometer, 



H. O. 607 



called the Vq; the correction for the main 

 thermometer scale, called the index correction; 

 and the index correction for the auxiliary 

 thermometer. These walues are to be recorded 

 in the proper columns of the A-sheet. The glass 

 constant of each main thermometer, called K, 

 and the pressure coefficient of each unprotected 

 thermometer, called Q, are also given on this 

 sheet. 



3-3 THERMOMETER CORREC- 

 TIONS. — To determine the true temperatures 

 of the water samples, the protected thermom- 

 eter readings must be corrected to allow for 

 expansion of the glass and mercury after re- 

 versal and for the errors in the index scale. To 

 determine the true depths at which the samples 

 were actually taken, similar corrections must 

 be applied to the unprotected thermometers, 

 and also using the corrected temperatures of 

 the protected thermometers. Thus, slightly 

 different formulas are required to correct the 

 protected and unprotected thermometers. As 

 the formula to correct the unprotected ther- 

 mometers requires the use of the corrected 

 temperatures of the protected thermometers, 

 the calculations for the latter must be com- 

 pleted first. It is mainly for this reason that 

 when protected and unprotected thermometers 

 are paired on a Nansen bottle, the protected 

 thermometer is always placed in the left-hand 

 tube and the unprotected in the right-hand 

 tube of the thermometer frame. The data are 

 then recorded and the calculations carried out 

 on the A-sheet in the order in which they are 

 used. 



3-4 Correcting the PROTECTED Ther- 

 mometer. — The protected thermometer is cor- 

 rected to give the true temperature of the 

 water by the following formula : 



r„=The corrected value of the protected 

 reversing thermometer. This is the 

 true water temperature. 



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