An Optical Parados. 779 



indefinitely in the minerals, and therefore be a known 

 element. The choice it would seem must rest between 

 bismuth (208 o) and lead (206*9). Boltwood calls attention 

 to the persistent appearance of lead as a constituent of the 

 uranium-radium minerals, and cites certain evidence in favour 

 of the view that it is one of the final products. Owing 

 to the rapid rate of change of polonium, and to the refined 

 methods of separating it from the mineral on a large scale 

 introduced by Marckwald, the experimental identification of 

 the ultimate product would seem to be now mainly a matter 

 of cost. 



LXXIV. An Optical Paradox. 

 By Lord Rayleigh, O.M., FM.S* 



CONSIDER the following combination : — A point source 

 A of approximate^ homogeneous light (X) is focused 

 by the lens LL upon the object-glass of a telescope T. In its 



turn the telescope is focused upon L. According to geome- 

 trical optics the margin of the lens L should be seen sharp by 

 an eye applied to the telescope ; but when we consider the 

 limitation of aperture at the object-glass of the telescope, 

 we come to the conclusion that the definition must be very 

 bad. The image of A at C constitutes the usual diffraction 

 pattern of which most of the light is concentrated in the 

 central disk. The diameter of this disk is of the order 

 X . LC/LL. If this be regarded as the effective aperture of T, 

 the angular resolving power will be found by dividing X by 

 the above quantity, giving LL/LC ; so that the entire angular 

 magnitude of the lens LL is on the limits of resolving power. 

 If this be admitted, we may consider next the effect of 

 enlarging the source A, hitherto supposed to be infinitely 

 small. If the process be carried far enough, the object- 

 glass of T will become filled with light, and we may expect 

 the natural resolving power to be recovered. But here we 

 must distinguish. If the enlarged source at A be a self- 

 luminous body, such as a piece of while-hot metal or the 

 carbon of an electric arc, no such conclusion will follow. 

 There is no phase-relation between the lights which act at 



* Communicated bv the Author. 



