28 Rowland's Thermometers and the Paris Standard. 



according to Baud in 6166, as given by the present series of 

 comparisons (see Table VIII.). In order to get the ordinates 

 of the curve (T N — T RA ) T , which represents the difference 

 between the Paris nitrogen scale and Rowland's air-thermo- 

 meter scale according to Baudin 6166 and the Tonnelot 

 thermometers, the ordinates of the curves were added ; as 

 represented by the following equation : — 



(T H -T Ate )-(T RA -T Ata ) + (T N -T H ) = (T N -T EA ; 



T- 



In a similar manner the curve Tj— T RA is the smooth curve 

 which represents approximately the differences found by 

 Joule between his thermometer and Rowland's air-thermo- 

 meter, according to Baudin 6166. The curve Tj — T N , which 

 is a straight line, is taken to represent the difference between 

 Joule's thermometer and the Paris nitrogen thermometer, 

 according to the comparisons of Schuster. Schuster does not 

 give this curve, but merely its slope. If the points found by 

 his experiments are plotted on section-paper, the straight 

 line 



(Tj-T N ) = 0°0024 T N + 0°-009, 



which has the slope he gives, seems most nearly to represent 

 the average of the points. The final curve (T N — T RA )j is 

 found by subtracting ordinates as represented by the equation 



(T J -T EA )-(T J -T If ) = (T N -T EA ) J . 



As shown in fig. 5, this curve is not very unlike the curve 

 (T N — T RA ) T . The maxima are near 20° in both, and the 

 difference between the two is about o, 01, which is not very 

 great in view of the ignorance as to how Joule made his 

 comparisons, and the chances of a weak point in so long 

 a chain. 



10. Conclusion. 



These comparisons do not explain the discrepancy between 

 Rowland's value of the mechanical equivalent of heat and 

 the higher values found by recent experimenters using 

 electrical methods. They seem to show, however, that the 

 discrepancy is not one of thermometry. It is probable, 

 therefore, that it is due to some error in the measurement of 

 energy in Rowland's experiments, or to a similar error in the 

 electrical experiments. In Griffiths' measurement of electrical 

 energy expended in heat, the square of the electromotive 

 force enters as a factor in the value of J. This makes any 

 error in the measurement of this quantity have double the 



