120 



B. Galitziue on Radiant Energy. 



We know that a ray of light exerts a certain pressure 

 along its line of propagation, which is numerically equal to the 

 quantity of energy contained in unit of volume of the ray. If 

 the beam is completely reflected the pressure is twice as great. 



Suppose for greater generality s is the area of the radiating 

 surface A, and consider those rays which are emitted with 

 inclination <j) to its normal. According to the laws of re- 

 flexion these will meet the other base B of our straight 

 cylinder at the same angle, as is diagrammatically represented 

 in the figure. The quantity of energy radiated at the angle 

 $ is 



dFt = 2tt6 sin ^ cos </> dcf> s. 



We can assume all these rays to have the same direction. 

 They exert on a b or a' b', which are perpendicular to their 

 direction of propagation, a certain pressure dp', this being 

 equal to dE/abY. 



As ab = s cos cj>, we have 



dp' = -^r- sin </> d(p. 



To every element of a'b' there is a corresponding element 

 of B, which is greater in the ratio of cos $ to 1, and there- 

 fore the force acting on each unit of surface of B is cos <£ 

 times smaller than dp 1 . Besides this, the force acts in a 

 direction making an angle <j> with the normal to B. It 

 follows that the pressure exerted on B is 



dp = dp' cos 2 <f>. 



If B is a perfect reflector we must double the above ex- 

 pression in order to obtain the total pressure, and integrate 



for all values of <f) between and — . Hence 



2 7re c W2 

 P = 2 . -^-1 cos 2 </> sin <£ d(j>, 



or, from (3), 



Formula (14) expresses the required relation. 



P = ie. 



(14) 





