A. L. Day and J. K. Clement — Gas Thermometer. 441 



This interpolation formula is a simple equation of two 

 coefficients obtained by the method of least squares, giving 

 equal weight to all the observations. 



Inasmuch as no one of the differences between observed 

 and calculated values reaches 1 per cent in value, this form of 

 equation, which has been frequently employed for the pur- 

 pose, is perhaps as well adapted to represent the experimental 

 data as another. After it was discovered that the bar after 

 heating did not return to its initial length, but varied within 

 considerable limits from one heating to another, it became 

 apparent that if the contraction upon cooling was not uniform, 

 the expansion on reheating was probably also irregular to the 

 same degree, and that the room temperature observations 

 could not be expected to follow this or any other simple 

 equation very consistently. That such irregularities exist and 

 attain such magnitude as seriously to limit the power of any 

 simple formula to reproduce the expansions over the whole 

 range will be immediately apparent from an examination of 

 the columns of differences (Obs. — Cal.). It. is more directly 

 observable in the experimentally determined values of the 

 expansion between and 300° taken from the four series which 

 have just been given. 



Measured Expansion in Millimeters 

 between and 300°. 



Dec. 30, 1907 ._ 0-687 mm 



Feb. 25, 1908 ... 0*681 



Apr. 6, 1908 0'700 



Apr. 17, 1908 0'696 



By way of experiment we tried an equation of three coeffi- 

 cients on the last two series, both of which contain observations 

 at 50° intervals, omitting in each case the room temperature 

 observation in which the irregularity in the expansion itself 

 chiefly appears, and found it possible to reproduce the meas- 

 ured behavior of the bar in the region from 300° to 1000° with 

 differences less than one-fifth as large as those recorded in the 

 tables above. There is, therefore, abundant evidence that the 

 uncertain region is confined to the lower temperatures and that 

 the higher temperatures have so far offered no serious difficulty 

 or irregularity, either in measurement or convenient represen- 

 tation. The expansion measurements over the entire range 

 from 0° to 1000° are probably in error by about 0*5 per cent, 

 most of which is directly attributable to these irregularities in 

 the behavior of the metal at the lower temperatures. In the 

 gas thermometer this corresponds to about 0*25° at 1000°. 



This uncertainty in the expansion of the metal at low tem- 

 peratures appears in the gas thermometer data as a difference, 



