162 PHENOMENA, ATOMS, AND MOLECULES 



The force producing convection currents is proportional to the dififer- 

 ence in the densities of the ascending and descending currents of the gas. 

 Since the density of a gas is equal to pM/RT it is readily seen that the 

 force producing convection is thus proportional to 





This force is directly proportional to the density of the gas and to the 

 fraction (To — Ti)/T2. As To hecomes large this fraction approaches 

 unity as a limit, so that, at very high temperatures, there is little tendency 

 for convection to increase, and even this is largely counteracted by the 

 increasing viscosity of the gas at high temperatures. 



The experimental results themselves, however, furnish us with data by 

 which we can estimate the effect of convection currents. * 



At temperatures below that at which perceptible dissociation of hy- 

 drogen occurs, we have seen that the heat losses from the filament are 

 given fairly accurately by the equation (see Table III, Part I). 



Wc = S(cpo-(pi). (2) 



The shape factor S for concentric cylinders is equal to (Phys. Rev., 34, 

 407 (1912)) 



^=h^ ^^^^ 



where h is the diameter of the film of gas around the wire through which 

 conduction takes place and d is the diameter of the wire. 



Let us now substitute the experimentally determined values of S from 

 Table III in this equation, together with the known value of rf (= 0.00706 

 cm.) and solve the equation for h. We thus find 



At atmospheric pressure the effective diameter of the film of conducting 

 gas around the tungsten wire is about one centimeter, but at 200 mm. 

 pressure the diameter is already 9 cm., which is larger than the diameter 

 of the bulb (7 cm.). This means that the heat loss from the filament is 

 actually less than if there were no convection currents and the ordinary 

 laws of heat conduction could be applied. At lower pressures the heat 

 loss becomes still less, although we know that the true heat conductivity 

 of gases is independent of the pressure. 



