120 M. E. Pringsheim on the Radiometer, 



in fact, all the theories of the radiometer which rest on other 

 foundations have very soon proved themselves inapplicable. 



If we consider radiometer-motion from this point of view, 

 the first of the above propositions takes the form: — 



An irradiated plane radiometer- vane tends to recede with 

 that side which gives out the greatest quantity of heat to the 

 gas. 



Since it is difficult, in such propositions, to take into account 

 the form of the cooperating bodies, we will rather fall back 

 upon the surface-elements, and say: — 



A surface-element which transfers heat to rarefied air, 

 tends to recede with a force increasing with the intensity of 

 the heat-current. 



We are, indeed, in a position to state the law according to 

 which the quantity of the heat given out increases. For 

 Crookes* has shown, with the aid of a very sensitive torsion- 

 apparatus in which a lampblacked pith bar served as the irra- 

 diated object, that when the apparatus was screened as much 

 as possible from radiation outwards, the deflections increased 

 in the inverse ratio of the square of the distance of the source 

 of light from the pith. Now, as the force necessary for the 

 torsion of the thread is proportional to the angle of torsion, 

 the force produced by the radiation increases likewise in that 

 proportion. The intensity of the radiation incident upon each 

 surface-element of the pith bar, however, increases in pre- 

 cisely the same ratio, if the dimensions of the latter may be 

 neglected in comparison with its distance from the source of 

 light. Hence the quantity of heat absorbed by each element 

 of the lampblack surface, and consequently the rise of tempe- 

 rature of each element, increases in the same measure. Now 

 the quantity of heat given up to the surrounding air in an 

 element of time by an element of surface is proportional to the 

 difference of temperatures between the lampblack and the air; 

 therefore the increase of the heat-current is proportional to 

 the increase of temperature of the lampblack — that is, inversely 

 proportional to the square of the distance of the source of 

 light. But, as we have shown above, the force acting upon 

 the entire pith bar, and consequently that upon each element of 

 its surface, increases in the same proportion. Now, as this 

 force vanishes when the quantity of heat transferred is nil, it is 

 proportional to the quantity of heat given out by the element 

 in unit time. We can therefore enunciate the proposition : — 



An element of surface which is transferring heat to the 

 rarefied air tends to recede with a force that is proportional 

 to the intensity of the heat-current. 



* Phil. Trans, clxvi. pt. 2. 



