694 Mr. A. H. Davis on 



Substituting in (1) we obtain 



h = (ke/ix<^Md/py. ( 3) 



Since " a?" is undetermined, we must write 



h = (kd/l) F{c 2 gl 3 a0/k 2 ) (4) 



Let us consider the assumption that expansion effects of 

 the fluid are negligible except in so far as they alter the 

 weight of unit volume and so set up gravity currents. With 

 large bodies this will be fairly true. But in an extreme 

 case of a hot thin wire, the mere volume changes of the 

 air near the wire may be far from negligible. Indeed 

 observation of smoke near a hot thin wire shows that the 

 effective diameter of the wire seems several times its true 

 diameter. In this case we shall not expect (4) to hold. 

 Convection data for wires, given by Langmuir *, show on 

 test that the relation (8) based on (4) does not hold ; and 

 in fact Langmuir, in his theory, supposes the wire sur- 

 rounded by a stationary film of fluid, of thickness several 

 times the actual diameter of the wire. For large bodies at 

 moderate temperatures our formula should be saiisfaclorv. 



For a viscous fluid w r e find, on introducing a term v* 

 (v being the kinematical viscosity coefficient with dimensions 

 L'T" 1 ), 



h=(k0/l)(c 2 9 Pa0/Py(cv/ky (5) 



For gases, by the kinetic theory, (cv/k) = const. Actually 

 it seems constant for a given kind of gas, and varies but 

 moderately from one kind to another. If, analogous to 

 Rayleigh's f treatment of convection in a stream of fluid, 

 (cv/k) be supposed constant for all fluids, the result reduces 

 to (3) as before. Viscosity, therefore, has less effect than 

 one might expect. 



On reflection this result may be made more or less clear. 

 The kinetic theory of gases shows how increasing the 

 viscosity (v) of a gas is equivalent to increasing its thermal 

 diff usivity (k\c) in the same ratio. Consequently, although 

 increase in viscosity may decrease the speed at which cold 

 gas sweeps over the heated body, still at the same time 

 the thermal diffusivity is increased, and the heat escapes 

 laterally by this means. 



* Lanomuir, Phys. Eev. vol. xxxiv. p. 416 (1912). 

 f Rayleigh, loc. cit. 



