IMPARTED TD A VACUUM RY HOT CONDUCTDPS. 
508 
where 1 refers to the metal and 2 to the iieig'hhourmg space, p being the pressure 
and V the volume occupied Ijy a corpuscle at any point. Substituting for p its value 
Rd/y from the gas equation, Ave get 
log Vg — log = <iyild ; 
whence, if he the numl)er of corpuscles ]jer unit Amhnne outside and ??, the number 
per unit volume inside the metal, Ave havm 
Noav the numl;er ol corpuscles shot oli from the surface per second is not equal to the 
number per unit volume of the space, Imt is equal to this multiplied by the a-A^erage 
\mlocity perpendicular to the surface. So that, in the steady state, N = Avhere 
u = du = ; whence N = 
^ tt ■ Jo V 2w7r V 2mTT 
Avhich is the same formula as lias lieen deduced above Avithout postulating the 
existence of a steady state. 
By folloAving up the analogy betAveen the emission of corpuscles and evaporation, 
the preceding formuhe, connecting the corpuscular pressure Avith the tenqierature, can 
be obtained thermodynamically in a manner involving still feAver assumptions. 
IT. The Eijuilihrium of Corpuscles rear a Plane Surface of Hot Metal of 
Infinite Extent. 
§ 4. Both tin’s problem and the coi'responding problem in spheres are of consider- 
alde inqjortance, not only in connection Avith experiments in vacuum tubes, but also 
Avith regard to the behaviour of hot celestial bodies in space. For instance, the 
aurora borealis and allied phenomena indicate that large quantities of ions continually 
reacli the earth from some extraneous source, Avhile certain A^ariations of the earth’s 
magnetic held and other meteorological plienomena seem to be intimately connected 
AAuth eA-ents Avliich take place at the surface of the sun. Tlie jiresent papier does not 
attenqit to soh'e these ipiestions, hut the alioAm facts indicate tliat tlie subject of the 
ionisation produced by hot Ixxlies is not Avithout inq)ortance in regard to meteorology. 
The problem under consideration may Ije specihed in the following terms :—Given 
an irdinlte quantity of hot metal lx)unded on one side by a plane surface of infinite 
extent Avliicli is maintained at a given potential, hnd the charge on unit area of the 
metal surface and the potential at any point in the space outside the metal when the 
steady state has been attained. 
Let us take tlie surface of separation perpendicular to the axis of x, and let 
the suffix 1 refer to points inside the metal, the suffix 2 referring to points in the 
