76 Mr. A. Stansfiekl on some Improvements in 



T 



the E.M.F. at the cold junction, and </>(T) is f \a-a')dT 3 



is i (o— < 



the difference between the Thomson effects in the two wires. 



No theoretical investigations have as yet determined the 

 form of <f)(T), so that it is impossible to obtain, from purely 

 theoretical considerations, an equation connecting the tem- 

 perature and the electromotive force of the couple. 



Equation (A) does, however, enable us to calculate the values 

 of the Peltier and the Thomson E.M.F.'s from a series of data 

 connecting the observed E.M.F. and the temperature of the 

 thermo-junction, and the results of such a calculation for the 

 thermo-couple No. 11 are given in fig. 6. 



The contact or Peltier E.M.F. of the thermo-junction is 



represented in the equation by T-^, and may be deduced 



«1 ?T^ 



from the thermo-electric power or -r^ curve by multiplv- 



dE " 



ing each value of —^ by the corresponding absolute tem- 

 perature T. cil 



dE 

 The T-^n curve, embodying the results of these calculations, 



has been plotted in the figure, the ordinates are measured 

 from a datum-line placed at a distance below the temperature- 

 scale equal to the E.M.F. across the cold junction; so that its 

 ordinates from the temperature- scale give the difference 

 between the E.M.F/s at the hot and cold junctions. The 

 difference between this curve and the E.M.F. curve E repre- 

 sents the resultant of the Thomson effects in the two wires. 

 The curve marked " Thomson E.M.F."" obtained in this way 

 has been plotted for convenience above the temperature-scale 

 line, but it must be remembered that this E.M.F. is opposed 

 in direction to the resultant of the contact E.M.F.'s. 



It will be noticed that the curve representing the contact 



dE 

 E.M.F., or T-77p is practically a straight line. In fact, the 



divergences at 1000° only correspond to an uncertainty of 

 about 2° in the assumed temperatures. 

 If, then, we assume that 



r/E 



we obtain by integration E == aT + b log T -f c. 



This equation requires three relations between E and T to 

 determine the values of the three constants a, b, and c, and 

 these can be accurately obtained for the temperatures 0°, 100°, 

 and the boiling-point of sulphur (444°*53). 



