Transpiration and Radiometer Motion. 481 



With these results we can now state what ought to be the 

 behaviour of a radiometer, and as Crookes and Pringsheim 

 found the best form of instrument for investigating the laws 

 of the radiometer experimentally to be one in which a single 

 vane of mica blackened on one side was attached with its 

 planes vertical to a horizontal arm attached to a vertical 

 torsion fibre, the whole being suspended in a glass bulb 

 capable of being filled with any gas at any pressure, we will 

 discuss the theoretical laws of such a form. Let D be the 

 mean distance of the edge of the vane from the glass wall 

 immediately opposite it, b the perimeter of the vane, s — b the 

 perimeter of the glass wall opposite, E the area of each face 

 of the vane, E + S the sectional area of the bulb (S being small 

 compared to E) in the plane of the vane, and j3 the thickness 

 of the vane ; when the black face is irradiated let its tempera- 

 ture become 2 , that of the clear face being l9 then there is a 

 fall of temperature 2 — x through the thickness of the vane, 

 and thus the thickness of the vane becomes a surface capable, 

 along with the surface of the bulb opposite it, of starting 

 thermal transpiration from the cold edge to the hot, with 

 elevation of the pressure in front of the hot face to p 2j and 

 depression of that behind the cold face to p x ; when a steady 

 state is established the total traction on the surface of varying 

 temperature must be approximately equal to SQt> 2 — pjb/s, and 

 the excess of total pressure on the black face over that on the 

 clear face is 'E(p 2 —p 1 )b/s, so that the total force deflecting 

 the vane whose moment is to be balanced by the torsion 

 couple of the fibre is (E -f $)(p 2 — pi)b/s. Thus the total 

 deflecting force is 



(E + B)- *'7\ IV i „ \ — ^m t— i ( 25 ) 



or 16?7o 2 (v2 + ?;i) 4 VoiVi + ViY Pz+pi 



e/{AJp + W + 1/p}, where p is the mean pressure (/?2+j0i)/2. 

 This equation contains all the theoretical laws of radiometer 

 motion when S is very small compared with E. If everything 

 is kept constant except the mean pressure (p 2 +pi)/2 there is 

 a value of the mean pressure of the gas in a radiometer for 

 which the deflecting force is a maximum, a very important 

 point in radiometer construction. When the pressure is high 

 enough the last two terms in the denominator may be neglected 

 and the deflecting force is inversely proportional to the 

 pressure, and when the maximum is passed and the pressure 

 becomes small enough the first two terms may be neglected 

 and the deflecting force becomes proportional to the density 



