312 Mr. Gr. J. Stoney on Crookes's Radiometer. 



three forces seems in all the experiments to have been opposed 

 to Crookes's pressure. 



21. At any particular degree of exhaustion it is only the 

 difference between this resultant and Crookes's pressure which 

 becomes apparent. It is easy to see that as the rarefaction 

 proceeds convection-currents will become in some degree more 

 active, but this occurs in a degree sufficiently moderate to 

 allow the resultant force to diminish continuously as the ex- 

 haustion proceeds. On the other hand, what I have called 

 Crookes's pressure does not exist at all until such a degree of 

 rarefaction has been attained as will cause the gradient to ex- 

 tend from the disk beyond the walls of the chamber ; after 

 this is once effected, if the exhaustion be still continued, 

 Crookes's pressure first rises to a maximum and then steadily 

 diminishes. It is evident, therefore, that there is a certain 

 tension, depending in some degree upon the form of the ra- 

 diometer, at which the excess of Crookes's pressure over the 

 force arising from the convection-current will be a maximum. 



22. If we assume that the chamber is of such a considerable 

 size as compared with the size of the disk that the general 

 temperature of the air within it is but slightly raised above 

 that of the glass, the following formula will approximately 

 give the value of Crookes's pressure : — 



Crookes's pressure per square centimetre 



= 2 8 i>, 273 + *' 



where = means is nearly equal to, and where p is the out- 

 standing tension per square centimetre within the chamber, 

 h* the length of gradient corresponding to p and At, d the 

 distance of the disk from the glass in front of it, t the tempe- 

 rature of the glass and of the back of the disk, regarded as 

 approximately the same, and finally At the excess of tempera- 

 ture imparted to the front of the disk. 



23. Let us suppose, as in my former paper, that — ~ — will 

 be equal to § t when p is 1 of an atmosphere. Then the 



* The value of S at any tension is given by the formula 



where k is the length of gradient, i. e. the thickness of the thin layer 

 of warmed air, when air at the temperature t and at the pressure of one 

 atmosphere is in contact with a body whose temperature is £-4-1° (see 

 Philosophical Magazine for last month, p. 180, § 7). The assumption I 

 venture to make in §§ 6 and 22 amounts to this — that k is as much as 

 -giro of a millimetre. 



t This follows from the assumption referred to in the last footnote. 



