876 



RECOKD OF CUKRENT RESEARCHES RELATING TO 



lower refractive index, the radiant spaces will become wider, and can 

 therefore no longer be contained in the semicircle, as is shown in 

 Fig. 93. The fan will have opened out, and instead of the original 

 30 spaces there will be only 26f , the other 3^, outside the semicircle, 

 being excluded. 



If we now substitute air, we shall have a further widening of the 

 radiant spaces; the fan will have been yet further expanded (as 



Fig. 93. 



Fig. 92 



Water. 



Fig. 94, 



Air. 



shown in Fig. 94), arising from the still lower refractive index of air, 

 and the semicircle will contain no more than 20 spaces, 10 of them 

 being now beyond the 180°, 



It will therefore be seen that while an aperture of 180° in aii- 

 includes (in the illustration given) only 20 radiant s])aces, 180° in 

 water and oil include respectively 26f and 30, these numbers repre- 

 senting the respective apertures in air, water, and oil, the smallest 

 number (20) rejiresenting, as before stated, 180° in air. 



The whole confusion has arisen from not getting beyond the 

 simple and obvious fact, about which there can be no dispute, that a 

 dry lens cannot have an aperture of more than 180°. That which is not 

 appreciated is the fact that by substituting for the air of the dry lens 

 either water or some other more refractive medium than aii\ the condi- 



