Luminous Intensities- of Sun and Sky. 559 



sun, be placed symmetrically with respect to the optic axis 

 of the system, and at a sufficiently great distance from L. If 

 the dimensions of the source of light be not excessive, every 

 point of it, P, will produce a luminous cone CCO on the other 

 side of the lens L, o£ approximately uniform intensity, and 

 within this cone will be comprised the screen S. Provided 

 the luminous cone is uniform, each point of the source will 

 contribute the same amount towards the illumination of S. 

 Thus the amount of light falling on S is always the same, 

 whether the source of light be of finite dimensions, or a 

 point-source. It is evident that in order that all this may 

 hold, certain conditions must be satisfied. It is, in fact, 

 necessary that the focal length of the lens L should be short 

 in comparison with the length of LS ; and that the luminous 

 source should, besides being of sufficiently small dimensions, 

 be at a sufficiently great distance from the external focus Q. A 

 preliminary test of the apparatus is sufficient to show whether 

 these conditions are fulfilled in every respect. If they are, then 

 it is possible to regard the dimensions of the luminous source 

 P as arbitrary, and to suppose, for instance, that it subtends 

 the same angle of 32' as the sun. For the sky is substituted 

 a circular uniformly luminous screen, of intensity i. Let 

 this screen be sufficiently large in comparison with its distance 

 from the first ground-glass screen in the tube T (see fig. 3) . 



Fig. 3. 



V 



It is next necessary to vary the intensities of the two 

 sources in order to calibrate the instrument. But since we 

 are concerned merely with the ratio of their intensities, it is 

 evidently sufficient to vary one of them only. The screen 

 representing the sky may be allowed to remain in a fixed 

 position, while the distance of the source representing the sun 

 is varied. 



In doing this we may still suppose, as explained above, that 

 the source subtends an angle of 32' ; while its intensity 

 depends on its real distance from L. 



In order to graduate the photometer, it is necessary to 

 determine the ratio of the intensities of the two sources, and 

 for this purpose an ordinary photometer may be used. If I 

 stand for the intensity of the source representing the sun, and 



