A. L. Day and J. K. Clement— Gas Thermometer. 433 



which a given measured length is then referred, is an integral 

 of a temperature range which varies all the way from that of 

 the room to some point considerably higher than that for which 

 the length measurement is recorded. This situation seems 

 to us to comport badly with the accuracy otherwise attainable 

 in measurements of this kind, if not to violate fundamental 

 definitions. Unless the expansion coefficient can be treated as 

 linear, such a determination is obviously only an approxima- 

 tion. Furthermore there is ample precedent for anticipating 

 inversions in an alloy of this character such that the expansion 

 coefficient of the material below the inversion temperature 

 would differ considerably from that above it. An integration, 

 therefore, in which the temperature range is large may well 

 overlap two physical states in such a way that the length 

 measurement loses all significance. We have not been able to 

 establish the fact that such an inversion exists in the 10 per 

 cent platin -iridium alloy within the temperature range over 

 which these measurements were made, although there is 

 an obvious break in the continuity of the expansion, of small 

 magnitude, which recurs with some persistence, as can be seen 

 from the tables which follow (pp. 437 et seq.). 



Supposing such an inversion to exist, it would of course fol- 

 low that the expansion would be a discontinuous function of 

 the temperature, a separate expansion coefficient would require 

 to be determined above and below this point, and the two 

 would not bear any necessary relation to each other. If such 

 a situation exists in the present bar, the difference is so small 

 as to be negligible for our present purpose, but the plain indi- 

 cation of an irregularity led us to appreciate the necessity of 

 maintaining the bar as nearly constant in temperature as pos- 

 sible during the length measurements in order to enable us to 

 interpret the measurements intelligently. 



The problem of accomplishing this result gave us consider- 

 able anxiety. As has been stated above, the scheme of making 

 optical measurements directly upon the bar without multiply- 

 ing device of any kind necessarily involves an opening in the 

 furnace coil opposite each end of the bar, and a consequent 

 cooling of that portion of the bar which is opposite the open- 

 ing. The amount of this cooling, which is greatest at the 

 highest temperatures, reached a value of about 4 per cent in 

 the first furnace coil which we wound. The temperature dis- 

 tribution along the bar is measurable with any accuracy desired 

 by moving the thermoelements about, or its effective average 

 can be determined by direct integration with a platinum resist- 

 ance thermometer of equal length, stretched parallel to the bar. 

 We chose the former method on the ground that it yielded 

 more information, and then sought in addition to diminish the 



