ON THE ABSOLUTE EXPANSION OF MEKCURY. 7 



was taken as half the mean difference of temperature between the thermometers in a 

 horizontal direction. A correction for this difference of temperature was applied to 

 the columns of mercury in the gauge tubes below aa\ t fig. 2b, i.e., below the level of 

 the top of the cold column. This correction never amounted to more than 0'002 cm., 

 and is included in the recorded values of h given in the tables. The mean temperature 

 of the column representing the difference of level h was estimated from the vertical 

 and horizontal temperature gradients indicated by the thermometers, and is denoted 

 by t in the tables and equations. The accuracy required in the observation of the 

 gauge temperature was about fifty times less than in the temperatures of the hot and 

 cold columns. 



The platinum thermometers were annealed in place in the apparatus by heating the 

 whole to 350 C. shortly after its erection before filling with mercury. This annealing 

 reduced the resistance of each by 1 part in 3000. The apparatus was not heated 

 afterwards beyond 300 C., and the thermometers showed no signs of further change. 

 Owing to their great length the thermometers could not be tested satisfactorily, 

 except at and 100 C., and the value of the difference coefficient O'OOOISO was 

 assumed to be the same as that found for other thermometers constructed of the same 

 wire. The fundamental intervals of the thermometers were, for t\ t 4'6456, and for t a , 

 4 '6412 ohms. Headings were taken to O'l mm. on the bridge wire, corresponding to 

 0'002 C., giving an order of accuracy of 1 in 50,000 on the fundamental interval. 

 The values of ti and t a recorded in the tables were deduced from the observed 

 temperatures on the platinum scale pt i} pt a , by the formula, 



t-pt = 0'000150< (<-100), 

 which may possibly be in error by 0'03 C. (or 1 in 10,000) at 300 C. 



3. Theory and Notation. 



% 



The following notation is adopted : 



HI = 6/1 is the effective height of the cold column at a temperature t\. 



H 2 = 6/2 is the effective height of the hot column at a temperature t a . 



c/H = Hj HI is the effective height of the cross tubes at the air temperature t. 



h is the observed difference of level in the gauge tubes at the temperature t. 



h' = /i-0'OOOlS (h-dH.) (t-ti) is h corrected for dR and reduced to ti. 



The error of this reduction will not exceed 1 in 20,000 of h provided that the 

 temperature of the gauge t is known within 0'3 C., and that the temperature of the 

 cross tubes does not differ by more than 4 C. from the gauge. The approximate 

 value '000 180 of the coefficient of expansion suffices within the same limits of 

 accuracy provided that the difference of temperature t ti does not exceed 50 C. 

 The temperature of the gauge may be taken as known within 0'l C. The cross 



