PROF. HUGH L. CALLENDAR AND MR. HERBERT MOSS 



nee 



RKGNAULT 0'00018153. 



WULLNER 0-00018253. 



BROCH 0-00018216. 



The discrepancy amounts to 1 in 180 even at this temperature, and would be 

 equivalent to an uncertainty of about 4 per cent, in the expansion of a glass bulb 

 determined with mercury by the weight thermometer method. The uncertainty of 

 the mean coefficient is naturally greater at higher temperatures. If, in place 

 mean coefficient, we take the actual coefficient at any temperature, the various 

 reductions of RENAULT'S work are still more discordant, and the rate of variation oi 

 the coefficient with temperature, which is nearly as important as the value of 

 mean coefficient itself in certain physical problems, becomes so uncertain that the 

 discrepancies often exceed the value of the correction sought. It is only fair to 

 RBGNAULT to say that these discrepancies arise to some extent from the various 

 assumptions made in reducing his results, and are not altogether inherent in the 

 observations themselves. 



The method of the weight thermometer permits an order of accuracy of about 

 1 in 20,000 in the determination of the weight of mercury expelled corresponding to 

 the fundamental interval, but it necessarily leaves the absolute value of the 

 fundamental coefficient uncertain, because it is obviously unfair to assume that the 

 expansion of the containing bulb, however carefully annealed, is the same in all 

 directions. 



The recent determinations of the expansion of mercury by CHAPPUIS (' Travaux et 

 Me'moires du Bureau International, 1907) by the weight thermometer method, 

 employing a cylindrical bulb of verre dur of which the linear coefficient of expansion 

 had been previously determined, gave results agreeing very closely between C. 

 and 100 C. with WULLNER'S reduction of REGNAULT'S observations. But as all the 

 observations, with the exception of those at 100 C., were confined to the limits C. 

 and 44* C., the resulting equation for the expansion of mercury could not be applied 

 with any confidence at temperatures above 100 C., especially as the values deduced 

 from it differ by nearly 2'5 per cent, from REGNAULT'S at 300 C. The agreement 

 with WULLNER'S reduction is possibly fortuitous, and the discrepancy from BROCH'S 

 value of the fundamental coefficient might easily be explained by supposing that the 

 expansion of the bulb employed by CHAPPUIS was about 2 per cent, less in the 

 direction of its diameter than in the direction of its length, a supposition which is 

 well within the limits of probability. It will be evident from the above summary 

 that, in order to obtain trustworthy results for the cubical expansion of a bulb 

 between 0" and 300 C., there was no alternative but to repeat REGNAULT'S method 

 on a larger scale with modern appliances, the whole apparatus being designed, as far 



