102 , A. L. Day and E. B. Sosman — 



the mass of the gas within the bulb is proportional to — — - . 



1 -\-at 



If we now suppose the unheated space raised to the uniform 

 temperature t without change of volume, the pressure being 



thereby raised to p, the total mass is proportional to — - i - \ 



1 +at 



Therefore, 



whence 



p'v, p'Y _ p(Y + t\) 



l+at 1 1+at ~ 1+at 



, , / . V t at —at\ \ 



This correction is easily calculated and tabulated ; or, better, 

 the factor in parenthesis (in the second member of the equa- 

 tion) is plotted against temperature. In practice, the volume 

 v 1 is divided into three portions at temperatures £/, t/% and t{" 

 as explained on p. 109, and the corrections obtained from the 

 curve for each of these portions are simply added together to 

 obtain the total correction^?— p' . With these corrected pres- 

 sures, p and p, the temperature t is calculated by formula (5) 

 on page 101. 



The discussion of errors and corrections will now be taken 

 up under the general outline sketched on page 96. 



A. Temperature of the Gas in the Bulb, (a) Uni- 

 formity. — Above the temperatures where a liquid or vapor 

 bath can be used to secure uniformity, the differences of tem- 

 perature between different parts of a furnace has always been 

 a serious limitation to the accuracy of the gas thermometer. 

 This variation, even in a furnace containing well-conducting 

 materials, is much larger than has usually been assumed, and the 

 three equalizing factors of conductivity, radiation, and convec- 

 tion by air-currents, are all credited with much greater influence 

 in bringing about uniformity than they really possess. It 

 sometimes happens that our faith in these factors is inversely 

 proportional to our quantitative information. 



To remove this source of uncertainty, Day and Clement 

 introduced two auxiliary heating coils in the furnace, one at 

 each end, and by varying the three independent currents, 

 brought the temperature at the middle and at both ends, on 

 the outside of the bulb, to equality. 



In our first measurements with the new bulb, the end ele- 

 ments were placed on the axis of the bulb, in positions 1 and 

 9 (fig. 1), instead of on the outside surface. It became evi- 

 dent at once that the supporting tube in the bottom of the 

 furnace, used in the work of Day and Clement, had a consid- 



