FLAMES OF ATOMIC HYDROGEN 119 



lected, must decrease the velocity below the value given by (i8). It is 

 interesting to note that this limiting velocity is the same for gases of differ- 

 ent densities. As an illustration let us take a case where h = ^ cm., T2 = 

 2000 deg., and Ti = 300 deg. We find that the velocities then cannot exceed 

 166 cm. per sec. The actual velocities set up by convection currents are 

 probably less than i/5th of this. 



Combining (18) and (15) and neglecting Ti compared to T2 in the 

 factor T2 — Ti, we find as an upper limit to the heat that can be carried by 

 convection currents 



For hydrogen at atmospheric pressure this reduces to 



W =\'2ycA \-h To / 7\ watts. 



Thus with /i =5, T2 = 2000 deg. and Ti = 300 deg. we find W =60 A, 

 which means that the maximum heat that can be carried by a convection 

 current (at 2000 deg.) is only 60 watts per sq. cm. It is evident that con- 

 vection currents of molecular hydrogen are entirely inadequate as a means 

 of carrying away the 1500 watts per cm. of length that were observed in 

 the hydrogen arc. 



HEAT CARRIED BY DIFFUSION OF HYDROGEN ATOMS 



Let us now consider whether the observed energy loss can be explained 

 as due to the diffusion of hydrogen atoms. Assuming that the hydrogen 

 in the arc is completely dissociated, we place in equation (13) : x = 1, 

 P = I atmosphere, and Wd = 1 500 /, and thus find 



5\/fr=280 / 

 and from (14) 



log (a/r) = 0.0224 \/T^ 



The temperature T2 enters this equation only because the diflfusion co- 

 efficient and the density of the atomic hydrogen vary with the temperature. 

 It is thus reasonable to put for T2 the temperature at which the hydrogen 

 is about half dissociated even if the temperature in the arc itself is much 

 greater than this. Thus putting T2 = 3800 deg. we find a/r — 4. 



From the derivation of the equations we see that the radii a and r 

 correspond to places where x = o and x =1, respectively. The diameter 

 of the arc was observed to be 0.5 mm. Suppose the temperature at the 

 surface of the arc is 10,000 deg. Then between this surface and the surface 

 at which the temperature is 5000 deg. the heat cannot be carried by diffusion 

 of hydrogen atoms, for even at the lower of these temperatures the dis- 



