470 Prof. Silas W. Holman on 



expression is the equation to a straight line if we regard 

 log 2o e and log t as the variables. If, therefore, a series of 

 values of 2 e and t are known for a given couple, points 

 obtained by plotting log t as abscissas and log 2 e as ordinates 

 should lie along a straight line. Thus a couple may be com- 

 pletely " calibrated " for all temperatures by measuring 2 e 

 and t for any two values of t (suitably disposed) . The con- 

 stants m and n may be computed, or a plot of log 2 e and log t 

 may be made, and a straight line be drawn through them. 

 Graphical interpolation on this line will then of course yield 

 the values of log t and hence of t corresponding to observed 

 values of 2 e, and vice versa, and, if desired, the constants 

 m and n. The expression for t as a function of 2 e is of 

 course t x 



t=m<t%eT\ or «=(^)«- 



This formula is well adapted to pyrometric work not of the 

 very highest grade of accuracy, and has been advantageously 

 employed in connexion with the Le Chatelier thermo-electric 

 pyrometer in a method to be described in a later article. 



Test of Formula?. 



This will be made by applying the several formulae to the 

 experimental data of Barus, Holborn and Wien, Chassagny 

 and Abraham, and Noll. These investigators employed 

 modern methods of thermometry and of electrical measure- 

 ment. Temperatures are either made in or reduced to the 

 scale of the hydrogen (C. & A.), or of the air thermometer 

 (B., H. & W., N.). Constants for the formulae will be 

 deduced, and the residuals or deviations of the data from the 

 equations (i.e. 8 = data — equation) will be computed for the 

 observed points. For discussion these deviations will be 



expressed in percentages, viz. 100 -, rather than in micro- 

 volts or degrees. This is preferable because the process of 

 measurement of the E.M.F., and to some extent at least of 

 the temperature, is such as to yield results of a nearly constant 

 fractional or percentage precision at all temperatures rather 

 than of a constant number of microvolts or degrees. Thus by 

 comparing percentages we eliminate a complication arising 

 otherwise from the increasing value of 8 as t increases. 

 Incidentally there are also other well recognized advantages 

 frequently attending the comparison of percentages rather 

 than of absolute quantities. 



The Barus Data, — Taking the data in the order of priority, 



