178 PHENOMENA, ATOMS, AND MOLECULES 



3. Calculation of 02 and Lozver Limit for E. — Substituting (51) in 

 (47), we obtain 



a2 = 0.68. (52) 



This means that 68% of all the hydrogen molecules which strike the 

 filament at high temperatures are absorbed by the filament. 

 If we substitute (51) in (34), we obtain 



E = 0.0046 VTa/ai. (53 ) 



Since Oi cannot exceed unity, E must be greater than 0.0046 \/Ta. 



The coefficient ai gives the fraction of the hydrogen atoms striking the 

 filament which dissolve in it or are absorbed by it. There is a strong 

 probability that this fraction should be very close to unity, for there i.' 

 every reason to think that hydrogen atoms would be absorbed by a meta' 

 surface much more readily than the molecules, and we have just seen thai 

 68% of the latter are absorbed. We shall see, however, that there is anothei 

 way of estimating the value of ai. 



4. Upper Limit for B. — According to (41), the limit which W^ ap 

 proaches at high temperatures does not increase indefinitely with th( 

 pressure, but ultimately becomes equal to i/B. By examining the result,' 

 given in Table III for the higher pressures we see that Wd does not become 

 constant even at the highest temperatures. This merely indicates that i/P 

 must be considerably greater than 117, the highest value of W/> observed 

 Or in other words, B must be less and probably much less than 1/117 

 or 0.008. 



5. Estimation of Ratio E: B. — According to (39) at low filament tem 

 peratures the fraction E/B should be equal to the pressure at which thf 

 maximum values of W/j occur. By referring to Table III we see that th' 

 highest values of W7) are observed at 50 mm. pressure. At the lower tem 

 peratures there is evidence that the maximum* should lie at a pressure rathe- 

 lower than 50 mm., although above 25 mm. The lack of experimental dat?'. 

 at intermediate pressures makes it impossible to determine this pressur- 

 with much accuracy, but, making allowance for the heating of the gase . 

 in the bulb, it is probable that the true pressure at which the maximum W;, 

 would occur is approximately 50 mm. From this we may conclude ths: 

 E/B = 50. 



6. Most Probable Values of E and ai. — Since B must be considerably 

 less than 0.008 and E/B is equal to 50, we may conclude that E must be 

 considerably smaller than 50 X 0.008 or o 40. We have already seen that 

 E must be greater than 0.0046 VT„. If we take T^ = 2500, E would 

 have to be greater than 0.23. Therefore, E must lie between the com • 

 paratively narrow limits 0.23 and 0.40. There is, however, no reason fo ■ 



