deter ruined by Hydrogen and Helium Gas Thermometers. 47 



H + /i, pressure at temperature T, after all corrections have been 

 made. 



On putting /3 = as already explained, equation (1), by algebraic 

 transformation and without any approximation, was altered into the 

 form 



T - T » S + i!g -;^)-TA (2), 



where Tl = Jr., ' % (3) ' 



v 



in which P and P replace H and H + h, and x = Tr — . 



V (l + at) 



.The gases used as thermometric substances were hydrogen, oxygen, 

 helium, and carbonic acid. The values of oc adopted in equation (3) 

 were taken from Chappuis' memoir, and were 0*00366254 for the first 

 three, and 0*00371634 for carbonic acid. The reciprocals of these 

 coefficients are 273*035 and 269*083. The number "273 " which 

 appears in is so nearly equal to the reciprocal of the former value 

 for a that it was allowed to remain for the first three gases ; but in 

 dealing with carbonic acid it was replaced by 269*083. 



In these experiments Ti is always negative, and numerically less than 

 273, so that the value of 6 is always greater than unity j nevertheless 

 it differs from it but slightly, its value being unity when Ti = - 273° C, 

 and rising to 1*02 when Ti = 0° C. in the case of thermometer No. I, 

 where x = 1 /50. It may be noted that when 8 is neglected Ti is the 

 usual value given by Boyle's law ; there is a convenience, therefore, in 

 this form of Chappuis' formula for approximation, because Ti can 

 quickly be calculated, and the correcting factor can be applied later 

 if desired. 



In the first experiment (No. 1 of subjoined Table I) thermometer 

 No. I was filled with electrolytic hydrogen. The initial pressure (the 

 pressure at 0° C.) was almost three-eighths of an atmosphere, and was 

 taken low in order to obviate any complication from condensation on 

 the walls of the reservoir. Two other possible causes might abnormally 

 reduce the pressure at very low temperatures ; these were polymerisa- 

 tion and the presence as impurity of small quantities of gases liquefying 

 above the boiling point of hydrogen. The measurement of the density 

 of the gas at its boiling point showed that there was no polymerisation, 

 and further proof of this was evident in the constancy of the value of 

 the boiling point when different initial pressures were taken. To guard 

 against the presence of gases with a higher boiling point than hydrogen, 

 the electrolytic hydrogen was allowed to pass continuously for eighteen 

 hours through the thermometric bulb before it was sealed off'. It was 

 further calculated that an impurity of oxygen necessary to reduce the 

 boiling point of hydrogen by a degree would amount to 3 per cent,, a 



