100 A. L. Day and B. B. Sosman — 



(4) The Manometer. — The bulb communicated, by a capil- 

 lary tube leading out through the furnace jacket, with the 

 manometer, which consisted of two glass tubes communicat- 

 ing through a steel reservoir. At the top of the shorter arm, 

 where the capillary joined it, was a fixed reference point to 

 which the mercury was brought for each measurement of the 

 pressure. A detailed description of the manometer will be 

 found in the previous paper.* 



3. Details, Errors and Corrections. 



The gas thermometer for high temperatures has now reached 

 a stage of development where it becomes necessary to examine 

 many small sources of error. These will be discussed in the 

 succeeding paragraphs without attempting to classify separately 

 the variable errors of observation, and the systematic errors 

 which may arise from conditions of the measurements or from 

 constant corrections. 



To bring out the plan of investigation of these errors, it 

 will be well to recall the derivation of the gas thermometer 

 formula. The gas scale, as is well known, is defined by the 

 relation 



-J^ = K (1) 



1 + at V ' 



in which K and a are constants and t is a function of p and v y 

 the pressure and volume of a fixed mass of the gas. K and a 

 are determined by two further conventions : 

 When^>=£> and v — v Q (at melting point of ice), £=0 (2) 



When p=p ioo and v = v 100 (at boiling point of water), £=100 (3) 



It is then evident that 



P 100 V z-—Po 



100 p 



which defines a as the mean pressure coefficient of the gas 

 between 0° and 100° (when v i00 and v are nearly equal) ; and 



K==p v . 



The temperature, t, is therefore defined by the formula : 



the scale depending upon the gas chosen, the value of p , and 



v 

 the ratio — . In the theoretical constant-volume thermometer, 



i\. 



* Loc. cit., p. 415, and this article, p, 107. 



