764 TRUEBLOOD. 



The results of the cahbration of a differential thermometer are 

 expressible in the form of a relation quadratic in the temperature or 

 in the resistance of one of the component thermometers. As far as 

 convenience in computation of temperature differences is concerned, 

 there is not much to choose between these two methods of repre- 

 sentation. As a check on the accuracy of the latter, three differential 

 thermometers, made up of thermometers 4, 6 and 7, were calibrated 

 at the ice, steam and napthalin points, and the differential ther- 

 mometer 67 was also calibrated at the boiling point of cumol. The 

 relation i?64 = Rei + Rn should hold for all temperatures. The ob- 

 served values of the three resistances satisfied this relation to within 

 0.00013 ohm (0°.0065 C.) at the steam and naphthalin points, and to 

 within 0.00006 ohm (0°.003 C.) at the ice point. These results may 

 be regarded as satisfactory, since the closing errors are to be divided 

 among the three thermometers. After forcing the closure at each 

 point, the following equations were obtained: 



^67 = 0.03071 + 0.000532 (/?7- 5.3003) -0.0003554 {R.-o.SOOSY 

 i?74 = 0.01823 + 0.027436 (/?7- 5.3003) -0.0000354 (i?7-5.3003)2 

 i?64 = 0.04894 + 0.028009 (i?6-5.3310) -0.000396 (i?6-5.3310)2 



From these one finds at the boiling point of cumol (165°.7, R^ = 8.748, 

 i?7 = 8.720) : 



i?67 = 0.02837, i?7-i = 0.11163, i?64 = 0.13992 



so that the closing error is 0.00008 ohm (0°.004). The observed value 

 of i?67 at cumol was 0.02842 ohm. Similarly one finds, for example, 

 at 130° C. (i?6 = 7.998, i?7 = 7.969) 



i?67 = 0.02960, 7?74 = 0.09120, i?64 = 0.12082 



from the above equations: here the closing error is only 0.00002 ohm. 

 It should, however, be stated that the satisfactory results set forth 

 in the preceding paragraph must be regarded as partly accidental — 

 or, at least, that more care was taken in the experimental work from 

 which they were derived than limitations of time ordinarily permit. 

 Thus three later calibrations of 67 give 0.00033, 0.00021 and 0.00013 

 ohm respectively for the difference between the observed normal 

 resistance in the vapor of boiling cumol and the value of this resistance 

 as calculated from an equation of the above form in which the con- 

 stants are determined from observations at the ice point and at the 

 boiling points of water and naphthalin. These discrepancies are 

 undoubtedly due in large measure to the difficulties of the calibration 



