6S Prof. H. L. Callendar on the Thermodynamical 



of alcohol, shows a small positive difference of "001°. The 

 negative differences are undoubtedly due in part to the type 

 of empirical formula chosen. Chappuis himself considered 

 them to be impossible, because they imply that the mean 

 coefficient of expansion of nitrogen, after diminishing from 

 0° to 70° C, begins to increase again at this point, which 

 is highly improbable. For this reason, in the same paper in 

 which formula (44) is given, he calculated another formula, 

 with two terms instead of three, for deducing the mean 

 coefficient of expansion of nitrogen by reference to hydrogen. 

 He does not give the values of the scale-difference corre- 

 sponding to this formula, but I have calculated the values 

 given in the column headed " Corrected 1888 " from the 

 values which he tabulates of the mean coefficient of expansion 

 of nitrogen. It is at once evident that the formula of two 

 terms gives a more probable type of divergence between the 

 scales than the three-term formula (44) which is always 

 quoted. It agrees closely with that of Joule and Thomson at 

 the higher points, but gives rather larger differences at the 

 lower points, increasing to nearly double at — 20 c C. 



10. Graphic Method of Comparison, 



Since the thousandths of a degree in this table are uncertain 

 to the extent of at least *003 o , it is hardly necessary to say 

 that *the most that can be expected is a general agreement in 

 the order of magnitude of the correction. The value of the 

 experimental eAddence is most readily appreciated by the 

 graphic method. The actual observations are plotted in fig. 1, 

 in which the zero line represents the hydrogen scale, and the 

 ordinates of the curves the scale-differences. The continuous 

 curves represent the differences calculated from the obser- 

 vations of Joule and Thomson, the broken curves the differ- 

 ences calculated from the formulas of Chappuis. The black 

 dots about the zero line represent the deviations of the ob- 

 servations with the hydrogen thermometer from the smooth 

 formula chosen to represent them, and indicate the order of 

 accuracy of the comparison of the hydrogen and mercury 

 thermometers. The crosses (x) similarly indicate the diver- 

 gences of the observations with the nitrogen thermometer 

 from the smooth curve. The crosses inclosed in circles 

 represent the observations in the second series of comparisons 

 of the nitrogen thermometer, extending from — 24° to + 25° C. 

 In reducing these observations it was found that the curve 

 representing them did not pass through the zero point, as of 

 course it should. Chappuis assumed that this discrepancy 



