HYDROGEN INTO ATOMS 181 



change of slope, we may, however, estimate the vahie of C and in this 

 way find Ta- 



By substituting the value of K from (43) in the modified form of van't 

 HoflF's Equation 50 and carrying out the indicated operations, we obtain 

 (considering F as constant and Tg = To) 



2J_lnW_p F^WpMi/T) _g ^^^^ 



■dii/T) P — FWp R' 



If we let - — U be the slope of the curve obtained by plotting log W/> 

 against i/T, then the first term of this equation becomes equal to — 2 X 

 2.30 U and in the second term we find rfW/>/c?(i/T) = — 2.30 U Wd. 

 Substituting these values in the equation and solving for U we find (since 

 R = 1.98) 



4.57V2P - FWz)/ 



At lower temperatures FW/j becomes negligibly small compared to P, 

 so that U approches a definite limit Uo which is equal to 0.109 q. From 

 this relation we can eliminate q from (56) and then solve for F, with the 

 result : 



^"wL-Uo-V2U- ^57) 



From the curve of Fig. 2 we find the slope of the curve at 2700° 

 (i/T = 0.000370) to be 3760. We have already calculated that q is ap- 

 proximately 85000 and from this we obtain Uo =^ 0.109^ = 9300. Sub- 

 stituting these in (57), together with Wo (at 2700°) = 5.7 and P= i.i, we 

 obtain 



F = 0.145. 



According to (42) F = BP -f E. The term BP is very small compared 

 to E. We shall see that B = 0.23/ VT^ and have already found E = 0.0048 

 VTo. Substituting these values of B, E and F in (42) and solving for T„, 

 we find Ta = 810. From this we may now calculate T^ at all other filament 

 temperatures, as we did at the lower pressures. Thus, taking S = 1.2 

 from Table X, we calculate qp^ — cp^ from the corresponding values of 

 W in Table II. If we use these values of cpa — cpi we obtain temperatures 

 for Ta that are much too high. However, by empirically taking 0.26 

 ((pa — <Pi) we find, at filament temperature of 2700°, the value Ta = 810 

 in agreement with the calculation above. The values of Ta for other filament 

 temperatures are obtained from the corresponding values of 0.26 {^)a — ^>^)■ 

 The results are recorded in Table XI. 



Having thus determined T^, it is easy to find F at other temperatures 



