3 58 PHENOMENA, ATOMS, AND MOLECULES 



X. GENERAL METHODS FOR CALCULATION OF v, e AND T 



Table I has been given to simplify calculations of v, 6 and T. In the 

 construction of this table the type of equation 



logioJ^ = A-B/r (24) 



was used, where for use in the equation with common logs 



A=^/2.303 and 3=5/2.303. (25) 



For example, Aa and Ba (for atom evaporation) refer to Eq. (i) as 

 previously given with natural logs, \n v ■= A —{B T). Aa and Ba have 

 been calculated from Eqs. (7), (8), (9) and (10), which give their de- 

 pendence on 6. In addition, the corresponding quantities have been cal- 

 culated for positive ion emission. For ion emission, 



yi p ^^^ Jx a in z, y 



5p = 5a+ll,606(Fc+F.-Fu,) 



= 5„- 86814- 11, 606 Fe, 



as given by Eq. (20). For electron emission the Boltzmann equation gives 

 In Ve = In v,^ -f Vcc/kT. 



In the range 6oo°-iooo° K. the electron emission from tungsten is very 

 closely given by 



Therefore 



or 



\nvy, = 6Z.U-A.16e/kT.* (26) 



In v« = 63.44-(fAr)(4.76- F.) 



^« = 63.44, 5, = 11,606(4.76- Fc). 



The contact potential (Fc) was calculated from atom evaporation data 

 for ^<o.5 and from emission data for ^>o.5. 



Here also the above values of A and B are for the equations with 

 natural logarithms of v, (In v). The A's and B's in Table I have been 

 converted (by Eq. (25)) for use in the equation with logarithm to the 

 base ten. 



As an example of the use of the table, in Fig. 22, v^, Vp, and Vg have 

 been calculated and plotted as functions of 6 at the constant temperature 

 1000° K. Fig. 19 is a similar example. Fig. 22 gives the relations between 



* See reference 2, Eqs. (7) and (98). 



