HYDROGEN INTO ATOMS 165 



absorbed, and some molecules from C travel to the wire, a certain fraction 

 of these absorbing heat from the wire. 



2. From C to D the heat is carried according to the ordinary laws of 

 heat conduction. 



3. From D to B the energy is transferred by a simple interchange of 

 molecules in a similar way to the transfer from A to C. 



Thus we consider a temperature discontinuity from A to C and from D 

 to B, but a continuous variation of temperature from C to D. 



Since we are dealing with small wires in relatively large cylinders, we 

 can readily see that the temperature drop from D to B will always be 

 negligible compared to that from A to D. We shall therefore leave it out 

 of consideration. 



Let us represent by T^ the temperature of the gas at C. We can now 

 calculate the temperature drop T2 — To.^" 



If we let w be the rate at which the gas comes into contact with the 

 wire (in grams per sq. cm. per second), then the heat carried from the wire 

 per second will be (per cm. of length) ^^ 



Wc = 4-19 T d (Cv/M) a (T2 — TJw. (9) 



Here Cv is the molecular heat at constant volume and the coefficient 

 4.19 converts calories to watt-seconds. The fraction a is the accommoda- 

 tion coefficient, and d is the diameter of the wire. 



In order to calculate T2 — To from Equation 9 we must now substitute 

 in it the value of m as given by Equation 5 of Part I, namely, 



m-^4^p. (5)- 



Here M is the molecular weight of the gas, T^ is the temperature of the 

 gas at a distance l. from the wire (at C in Fig. i). 



In the derivation of this formula Maxwell's distribution law was as- 

 sumed to hold. Where the temperature discontinuity at the surface is as 

 large as in the present experiments the distribution of velocities among the 



^° This is somewhat greater than the temperature drop defined by Smoluchowski, 

 for it includes the normal temperature difference between A and C. 



^^ Knudsen shows that this should be multiplied by 4/3, since the average velocity 

 of all the molecules striking any surface is greater than the average velocity of the 

 molecules in the body of the gas. This is due to the fact that the molecules of high 

 velocity have a much greater chance of striking a surface than those of low velocity. 

 On the other hand, for polyatomic gases the exchange of rotational energy is not com- 

 plete and, therefore, a quantity less than should be substituted in the above equation. 

 According to Smoluchowski, the combined effect of these two corrections would lead 

 to a coefficient of 16/15 in place of the 4/3 mentioned above. For the present purpose 

 this small correction may be neglected. 



