On Thermionics. 



817 



surface yjr = and the tangent to the curve in which the sur- 

 faces w =<£ 3 , v = (f) 4 intersect, and it A Co is the angle between 

 the normals to the surfaces u = (f> 3 and v = (]) i . Thus 



sin 2 u A v = 



^3,?/i 3~i d^i§,yi/ \3^i 3^i 3#i 3^/ vS^ib.vi 3,yTQ-''i' 



3*1 3//l /b. 



cos (w r A ?iS) 



t'dfc'dfa _ 'd<t>s"d4>A^i r _ + /3 03 304 



\byi'd~i 3?i 3,yi /3fi \3~i 3^i 



3</> 3 30* __ 30s 30 4 V . / 30! °0i _ °0s B^i V 2 



LVBi/T 3*i 



3*i 3v t / \3-i 3#i 3. 



/a* 



\3.<'i 3yi 



53 094 V 



_ 30j30A3^ , /30r304 _ b</>3 0c/)4\b^ 

 cU'i b^i /3//i \B.**i 3yi 3.Vi 3#i /3*i 



/ o^>3 o</>4 _ dc/> 3 0^4 \ 2 i 5 r/^t V + I ^tY + / ^ V 2 ] § 



Vo^i byi o.y , b^-i 7 J LlW XdyJ \3% / J 



Hence* 



/30 3 30 4 _303 304\ cr^ + / 303 304 

 d d = \-d!,^ 3d 3,^7 3^, xOHb-n 



LVo^'i/ \bj/i/ 

 — 30 3 30A 3^ + /30 3 30. __ 30. ? 30A 3_^ 

 3fi 3~i j 3 vi \3-<'i 3//i 3,vi 3- ;, i / 3~i 



rfS. (8) 



If the probability of the ic component of the velocity lying 

 within the range ic and Wq + <Lwq is denoted by f z {ic )dw 

 the number of those reaching the surface \^ = with values 

 of iv within this range will be proportional to 



/30 3 3</>4 _3<fe30A3^ 



dS. 



