342 



SUMMARY OF CCTRRENT RESEARCHES RELATING TO 



radiation in all directions, is seen projected as a sui-face of equal 

 brightness. 



If there were equal intensity of emission in all directions, what 

 Fig 80 would be the necessary result ? Compare two equal 



portions of the surface, one a (Fig. 80) perpen- 

 dicular to the line of vision, and the other b greatly 

 inclined. Every infinitesimal surface-element of b 

 sends to the pujiil of the eye a cone of the same 

 angle u' as a similar point of a (the slight difference 

 \ of the distance from the eye being disregarded). 

 If the intensity of the rays were equal, as supposed, 

 the whole area b would send to the eye the same 

 quantity of light as the equal area a, since both 

 areas contain exactly the same number of elements. 

 But the icliole quantity of light from b would be 

 projected upon a smaller area of the retina than that 

 from a (as b appears under a smaller visual angle, 

 being diminished according to the obliquity, or as 

 1 : cos U-). Consequently, if the assumption were true, b must appear 

 to be brighter than a, and the sphere would show increasing bright- 

 ness from the centre to the circumference. Close to the margin the 

 increase ought to be very rapid, and the brightness a large multiple 

 of that at the centre. 



This, as is well known, is not the case — the projection of the 

 sphere showing equal brightness. The quantity of light, therefore, 

 emitted from b within a given small solid cone u' in an oblique direc- 

 tion, must be less than that which is emitted from a within an equal 

 solid cone u in a perpendicular direction : and the intensity of the 

 rays must decrease in the proportion of 1 : cos w when the obliquity 

 10 increases. 



Therefore Fig. 81 is not a correct diagram of the rays emanating 



Fig. 81. 



Fig. 82. 



from a surface-element, but Fig. 82 — the density of the rays decreasing 

 continuously from the vertical.* (Cf. also Figs. 59 and 60.) 



This subject bears also upon the question of the loss of light with 

 dry objectives. It was seen that immersion objectives gave a great 

 increase of light over dry objectives. As the true explanation of this 

 was not appreciated, it became necessary to account for the increase 

 otherwise, and the reflection at the plane face of the lens was taken to 

 be the reason. A large amount of loss is supposed to be accounted for 

 by the following reasoning : — A pencil of light is assumed to be pro- 

 perly shown in Fig. 81, the density of the rays being imiform, whether 

 they are close to or removed from the perpendicular. If this pencil 



* The thickened lines indicate the greater amplitudes. 



