820 Prof. 0. W. Richardson : 



1. Rectangular Coordinates. 



The axis of z is along the normal to the surface. 

 Xumber between z and z + d^ = nzF(z)d'z = 2nkm'ze~ mz dz 



,, ,, x and x-\- ax = nj (x) ax = ni — I e dx. 



y and ij + d'y = nf(y) dy = ni ■ — \ e kmy2 dy. 



where 3/4& is the mean kinetic energy and m is the mass 

 of the ions. 



2. Splierical Coordinates. 



Let yjr be the resultant velocity, let 6 be the angle it makes 

 with the normal to the surface, and </> the angle the plane 

 containing i/r and the normal makes with a fixed plane con- 

 taining the normal. Then the number emitted per unit area 

 per second which have ty between yjr and i/r-f<^r, 6 between 

 6 and 6 + dd, and </> between </> and <b-\-dcf) is 



mjr cos 6 ~F(^r cos d)f(ijr sin d cos <£)/(^ sin d sin $) yjr* dyjr sin d dd d<j> 

 = nf d F(yjr cos 6) Fi(^ sin <9) sin cos ^ dd d^ 



^ 3 6 -AW 2 sin Q cos 5> ^ ^ d Q u 



2Wm* 3 W ; 



3. Cylindrical coordinates. 



(a) The axis of z is along the normal to the surface, 

 |0=the radius perpendicular to the axis of z and 

 #=tbe angle p makes with a fixed plane passing 

 'through the z axis. 



The number between 



z and z + dz is nz¥(z) d'z = 2nkm'ze- hn ' 02 dz. 



whilst the number for which p is between p and p-i-dp and 

 simultaneously between 6 and d + dd is 



n f(p sin 6) /( p cos 0) dp pdd = n — £ *~^ 2 * <Z0. 



(/3) The axis of lies in the tangent plane to the surface. 

 cj) is the total component of velocity perpendicular 

 to z, i. e. the projection of the resultant velocity on 

 a plane perpendicular to the z axis. 6 is the angle 

 $ makes with the plane containing the axis of z 

 and the normal to the surface. 



