20 



OBSERVATIONS AND RESULTS IN PHYSICAL OCEANOGRAPHY 



difference (T' - t) as large a value as is necessary to 

 cover the anticipated conditions. Except in restricted 

 environments (such as polar summers) this value of 

 (T' - t) will prot ibly be about 30' since water tempera- 

 tures as low as about 0° may be expected, and reading 

 temperatures as high as 30° are common. The process 

 is then repeated with T' assigned an even-degree value 

 near the other extreme of the range of the thermometer. 

 For most thermometers, the first two terms on the 

 right-hand side of the above equation determine the 

 value of (T' - t) with sufficient accuracy. 



The correction graph may now be constructed on 

 cross- section paper with the readings of the reversing 

 thermometer (T') as ordinates and the corrected read- 

 ings of the auxiliary thermometer (t) as abscissae. A 

 convenlont scale is 0.°! to the millimeter. The length of 

 the plotting' sheet should be somewhat longer than three 

 times the length of the finished graph which will occupy 

 approximately the middle third of the original plotting 

 sheet. On this graph the line of zero correction will be 

 a 45 "-line through all points of T' = t. This line is 

 drawn lightly througti those values of T' for which the 

 index correction is known. 



The values of (T' - t) computed as mentioned above, 

 are then laid off as points measured from the zero-cor- 

 rection line along the appropriate T' lines, one near the 

 upper edge and one near the lower edge of the graph. 

 These points are laid off in both directions from tlie zero- 

 correction line since the correction may have either 

 sign. Straight lines approximately parallel to the zero- 

 correction line, representing lines of equal temperature- 

 difference correction, are then drawn lightly through 

 those values of T' for which the index correction is 

 known. The graph would now be complete if there were 

 no index corrections, but the lines must be shifted either 

 to the right or to the left at all values of T' where the 

 index correction is not zero. Thus, if at 0" the index 

 correction is +0.°01, the zero-correction line as well as 

 all the other correction lines at T' = 0° are shifted one 

 line (or 0.°01 correction) to the right. When these shifts 

 have been made to accommodate all known index correc- 

 tions, the resulting graph consists of a number of zigzag 

 lines, all approximately parallel and having an approxi- 

 made 45 '-trend. The correction lines e.xterior to the 

 required range of T' and t may now be cut off and the 

 graph is ready for use. A specimen correction graph is 

 shown in figure 1. 



As described above, the lines of equal correction 

 for temperature difference between reversal and reading 

 are assumed to be straight. As this assumption is not 

 exactly true, an error is introduced. This error is 

 greater, the greater the interval between the two values 

 of T' for which the points are computed, and is greater, 

 the greater the numerical value of (T' - t). As an exam- 

 ple of the magnitude of this error, let us take a graph 

 for a thermometer whose range is 0' to +20° C and pre- 

 pared for a maximum value of t = 30° C. In. this case 

 the maximum error in the graph will occur in the neigh- 

 borhood of T' = 10° and t = 30° where the error will be 

 approximately 0.003° C. Such an error is not usually 

 significant, but if greater accuracy is desired the values 

 of (T' - t) can be computed for intervening values of T', 

 thus breaking the single straight lines into two or more 

 parts. Because of the increased labor required in this 

 procedure and the small magnitude of the error involved, 

 the refinement is not recommended. 



In the case of unprotected thermometers, whers C 

 is again the temperature-difference correction 



(Tw - t) = 



CK 



(T' + vo) 



As with the protected thermometers, the temperature 

 difference (Tw - t) is evaluated for a series of C which 

 is varied in steps of 0.°01 and the computations carried 

 through for tv/o extreme values of T'. Now, however, a 

 plot of (Tw - t) against T' is to be prepared but is car- 

 ried out in much the same manner as the previously 

 described plot of T' against t, the index correction shifts 

 being made as before. 



Having determined the corrected readings of a pro- 

 tected thermometer and its accompanying unprotected 

 thermometer, the depth at which they were reversed 

 can be computed from the formula 



D = 



(Tu - T) 

 QPm 



where D is the depth in meters, Tu is the corrected 

 reading of the unprotected thermometer, T is the true 

 temperature given by the corrected reading of the pro- 

 tected thermometer, Q is the pressure constant of the 

 unprotected thermometer or the change in number of 

 degrees in the corrected reading of the unprotected 

 thermometer produced by a change in pressure of one- 

 tenth kilogram per square centimeter, and pm is the 

 mean specific gravity of the water coliimn above the 

 thermometers when they were reversed. The constant 

 Q is of the order of magnitude of 0.01 and is given in the 

 thermometer certificate, usually in the form of the de- 

 grees change in reading per kilogram per square centi- 

 meter change in pressure. 



The approximate depth of the various water bottles 

 and thermometers will be known from the wire angle 

 and the readings of the meter wheel. From the correct- 

 ed temperatures and the salinity measurements, the 

 density (at) of the water samples can be determined 

 from Knudsen's "Hydrographical tables." Knowing 

 these values, the values of density in situ (cr^Q) are de- 

 termined by applying three corrections, each of which 

 is given in tabular form in Hesselberg and Sverdrup's 

 paper in Bergens Museums Aarbok, 1914-1915. The 

 most important of these corrections is a function of 

 depth, and since the exact depth of the samples is un- 

 known tlie resulting values of density in situ will be only 

 approximate. These values are then plotted against 

 their approximate depths, a curve drawn, and a value of 

 the mean density scaled from the curve at half the ap- 

 proximate depth. It is to be remembered that this density- 

 depth chart is constructed solely for the purpose of de- 

 termining a mean density which is to be used as a factor 

 in the reduction of thermometer depths. It is only nec- 

 essary to determine this mean density to the nearest 

 unit in the third decimal place; for example, to know 

 that the mean density is 1.034 rather than 1.033 or 

 1.035. In terms of crtD this would mean the nearest unit. 

 As the order of magnitude of depth variation of fftD is 

 about one unit per 200 meters, it is easily seen that the 

 density-depth curve need not be very accurate. Mter 

 the adjusted depths of the samples have been determined 

 in this manner, and the vertical distribution curves of 

 salinity and temperature have been drawn, these may be 



