Transpiration and Radiometer Motion. 483 



accordance with these conditions, but if the vane is steadily 

 irradiated, conductivity soon establishes a steady distribution 

 of temperature through the vane from front to back with 

 permanent temperatures 6 2 and 6 X , so that the first deflexion 

 alters until it attains the fixed value due to these steady con- 

 ditions. Suppose the black face to be irradiated by a candle, 

 and let Q be the amount of heat it absorbs per unit area per 

 unit time, and E the corresponding amount emitted by the 

 clear face ; then if we ignore loss of heat by the edge, and 

 denote the conductivity of the substance of the vane by k, 



Q = A J (^-^ l )//8=B (26) 



Now in (25), (v 2 — «i)/( w 2 + v i) mav be written 



or 



(0 2 -0i)/(0t+0i) 2 , 



in which the denominator is nearly ^(O 2 -\-0 1 ), since the diffe- 

 rence of 2 and 6 1 is small ; and as in the experiments (6 2 -f- #i)/2 

 was always an ordinary temperature it may be taken as con- 

 stant, so that {v 2 — v } )/(v 2 + Vi) was always closely proportional 

 to 6 2 —6 1 and therefore to Q(Z/k; but Q is inversely as the 

 square of the distance of the candle from the vane and directly 

 as the number of candles at that distance (the candles being as 

 nearly as possible in the normal to the centre of the vane), 

 thus the deflecting force varies as the number of candles and 

 inversely as the square of their distance from the vane, which 

 is the experimental result (Crookes, ' Nature/ xiii.) ; the 

 deflecting force is proportional to the thickness of the vane 

 and inversely proportional to the conductivity of its material, 

 hence the advantage of using a substance such as mica for the 

 vane, and the disadvantage of using metal. 



To show that this theory of the radiometer is in harmony 

 with the experimental facts, we will briefly describe the 

 general results of Crookes's numerous experiments, and it 

 will be seen that they accord with the deductions from our 

 formulse. 



Crookes obtained his most valuable quantitative results 

 with an apparatus such as the one of which we have just 

 considered the theory. The bulb was continued into a 

 vertical tube for containing a torsion fibre nearly a metre 

 long, and the rectangular plate of roasted mica was attached 

 directly to the fibre so that its plane was vertical and its 

 centre at the centre of the bulb ; a continuation of the line of 

 the fibre divided one face of the plate into two equal halves, 



