HYDROGEN INTO ATOMS 175 



Comparing this with (22), we see that FW/) is equal to tlie partial 

 pressure of hydrogen atoms corresponding to equilihrium at the tempera- 

 ture of the filament. The degree of dissociation of the hydrogen in 

 equilibrium is therefore FW/)/P. 



At low temperatures we have already found expressions for the maxi- 

 mum value of W/) and the pressure at which this occurs. On the assumption 

 that C = E we may now find more general expressions applicable even 

 at high temperatures. Dififerentiating (42) and (43a) with respect to P, 

 placing dWp/dV = o and solving the resulting eciuation together with 

 (31), we obtain 



W„,„,. = i/(B + V4BE/K). , (44) 



P'= (E/B) + VEK/B. (45) 



CALCULATION OF RESULTS FROM EXPERIMENTAL DATA 



The equations that have been derived in the preceding section give us 

 means of calculating the coefficients B, C and E, and in this way of de- 

 termining the dissociation constant K. Thus from the experiments at low 

 pressures and at low temperatures it should be possible by (36) to find 

 the ratio \/K:E. Experiments at high pressures give by (37) VK:B, 

 while those at high temperatures and low pressures give C according 

 to (40). At high pressures and high temperatures we should then obtain 

 B by (41). By combining these results it would thus be possible to find the 

 actual values of B, C, E and K, separately. In practice, however, this 

 method gives difficulty, because the experiments do not cover a sufficiently 

 wide range of pressures or temperatures to allow these limiting equations 

 to hold accurately. Furthermore, the values of Wn obtained under the 

 extremes of temperature or pressure are often subject to unusually large 

 experimental error, and it is unwise to use such data exclusively for the 

 determination of the coefficients. A third difficulty is that Equations 36, 

 37, 40, and 41 all involve to some extent Tq, the temperature of the gas 

 around the wire, which is not accurately known. 



The method finally adopted to determine the coefficients B, C and F 

 has been chosen because of its relative freedom from these difficulties. 



I. The Value of C. — According to our theory, at very low pressures, 

 Wo does not increase indefinitely with rising temperature, but approaches 

 a limiting value equal to P/C (Equation 40). If we examine the ex- 

 perimental data of Table III we see, in fact, that W/, at the three lower 

 pressures, 0.015, 0.039 and 0.207 mm., becomes constant at temperatures 

 over 2700°. This is also readily seen from Fig. 2, in which log W/> has been, 

 plotted against i/T. The limiting value of W/> at high tem}>eratures for 



