440 Br. P. Chappuis on Gas-Thermometry. 



and for the cubic dilatation, 



V,=Y (l + (8472-4i + 18-53i 2 )10- 9 ). 



On comparing this result with that obtained by Mr. Bedford, 

 it will be seen that the coefficient of the term in t 2 is here 

 about four times as great. It is also about twice as great as 

 that obtained formerly for Berlin porcelain (8*98 X 10 -9 ). 



If we recalculate the last experiments made by the Fizeau 

 apparatus, assuming the values of the coefficients as found by 

 Mr. Bedford, we obtain the following numbers, alongside 

 of which I have placed the values deduced from my ob- 

 servations: — 



T. 



Calculated 



from Bedford's 



Experiments. 



Fringes. 



Observed. 



Obs.-Calc. 



20° 



5-07 

 10-56 

 16-07 



21-58 



542 

 11-07 

 16-53 



21-82 



+0-35 

 +0-51 

 4-046 

 +0-24 



40° 



60° 



80° 



The divergences Obs. — Calc. are so large as to be quite in- 

 explicable by errors of observation, since in my experiments 

 the largest residual errors are very rarely as much as a tenth 

 of a fringe. It would appear, then, that there is an incom- 

 patibility between the two results, at least over the range of 

 temperature covered by both. But the measurements on the 

 Fizeau apparatus have revealed a fact, which 1 have mentioned 

 already and which, I think, is likely to be the principal 

 cause of the difference between us. On summarizing in 

 tabular form the displacements of the fringes, as measured 

 with regard to the different points of reference, it is evident 

 at once that the thick part of the tube expands less than the 

 thinner part. 



If the dilatation of the tube were uniform over its whole 

 cross-section, the differences between the readings obtained 

 for the different j)oints should be the same at all temperatures. 

 But if, in this case, we take for two widely differing tem- 

 peratures the differences from the mean for the six points 



