EADIATION IN AIK AND BALSAM 57 



air almost to the entire hemisphere, and it then utilises a definite 

 opening double its focal length. But when the radiant is in balsam 

 (without any other alteration), the same opening is seen to be utilised 

 by the rays which are within a smaller cone of not more than 82. 

 and rays which are outside this cone require a surplus opening which 

 is never required for rays in air. 



This holds good whether there be refraction or no refraction at 

 the front surface of the system ; the difference is based solely on the 

 difference of the medium. Consequently we arrive at the conclusion 

 that the solid cone of 82 in balsam embraces the same rays which, 

 in air, are embraced by the whole hemisphere, and every wider cone 

 in balsam exceeding the 82 conveys more rays from the object than 

 are admitted by the whole hemisphere of radiation in air. 



It follows, therefore, that the same rays which in air are spread 

 over the whole hemisphere are closed together or compressed in 

 balsam within a narrower conical space of 41 around the perpen- 

 dicular, and all rays which travel in balsam outside this cone con- 

 stitute a surplus of new rays, which are never met with in air that 

 is, are not emitted ir/ie/i the object is in air. The loss which takes 

 place in the latter case can never be compensated for by increase of 

 illumination because the rays which are lost are different rays 

 physically to those obtained by any illumination, however intense, in 

 a medium like air. 



In the paper of Professor Abbe there is an elaborate and careful 

 elucidation of this change in the angular distribution of the radiating 

 light when the medium is changed ; but to Mr. Crisp's paper on the 

 same subject, giving an exposition and simplification of Abbe's de- 

 monstration, the novice will look with the utmost profit. 1 The 

 following extract will give clearness and emphasis to the above 

 deductions of Abbe : 



' If we take the case of refraction, then one of the most funda- 

 mental of optical principles shows that the same rays which in air 

 occupy the whole hemisphere 

 are compressed in a medium of 

 higher refractive index within 

 a smaller angle, viz. twice the 

 critical angle. If in fig. 39 

 the object is illuminated by an 

 incident COlie of rays of nearly Fiu. 39. Comparative compression of 

 82 within the slide, and the i; 8 ht y* in two different media, 



slide has air above in the first 



case and oil in the second, it is obvious that the same ray which is 

 incident on the object at nearly 41 will always emerge in air at an 

 angle of nearly 90 ('), and in oil at nearly 41 (a"), so that the 

 same rays which in air are expanded over the whole hemisphere are 

 compressed into 82 in oil, and, therefore, rays beyond 82 in oil 

 must represent surplus rays in excess of those found in the air- 

 hemisphere. 



' If, on the other hand, the case of dijf ruction is considered, then 

 Fraunhofer's law shows that the same diffracted beams which in air 

 1 Jouni. R.M.S. ser. ii. vol. i. p. 303. 



