the late Dr. Joule's Thermometers. 497 



error was discovered in the pressure-coefficient of the Baudin 

 thermometer after all the above reductions had been made. 

 The corrected interval equation becomes 



t. = t B (l- -00084). 



The comparison between the Baudin and Tonnelot thermo- 

 meters made by Mr. Gannon and myself had given 



t T -t B = --00089^. 

 Hence, by combining the last two equations, 

 *. = * T (1 + -00005). 



This comparison would therefore show that the Joule and 

 Tonnelot thermometers read exactly alike. 



In all these measurements the Baudin and Joule were always 

 read like calorimeter thermometers, without regard to the 

 change of the freezing-point, while the Tonnelot was referred 

 in every case to its proper zero. The equality of the scale- 

 value of the two thermometers does not hold when they are 

 both read in the same way, but the same interval read on the 

 Tonnelot would be about one part in a thousand smaller than 

 if read on A. 



We may combine the results of the two series of com- 

 parisons by giving each weights inversely proportional to the 

 probable error of the quantity denoted by b. 



We therefore find as the most-probable value for fc, 

 t. = t T (l- -00027). 



Without attaching undue importance to this number, we 

 may say that it represents the relation between the Tonnelot 

 standard and Joule's thermometer as accurately as the divi- 

 sions and calibration of the latter will allow us to judge. The 

 number seems certainly not to be in error by more than one 

 part in a thousand, and probably by less. 



The transition to the nitrogen and hydrogen scale may now 

 be made. Using Chappuis' experimental investigation on the 

 French hard-glass thermometers, it is found that a temperature 

 of 16°' 5, to which Joule's last equivalent determination refers 

 the interval on the Tonnelot thermometer, is to be diminished 

 by -00268 or '00305 *, according as we want to obtain the 

 interval on the nitrogen or hydrogen scale. Thus writing 



^=^(±-•00268), 

 * H =* T (l--00305), 



we find t. =^(l + '0024), 



tj = # H (l + -0028 > >. 

 * See Schuster and Gannon, Proc. Boy. Soc. lvu. p. 28 



