PROCEEDINGS OF THE SOCIETY. 163 



in optical effect the maximum air angle — the whole hemisphere — of 

 180°.* 



Angles, therefore, of different degrees (as 180° in air and 82° in 

 balsam) are shown to produce the same effects, i. e. take in the same 

 rays, while angles of the same number of degrees produce (in air and 

 in balsam) different effects ; Mr. Crisp finally pointing out that the 

 diffraction spectra were one f of the modes in which was demonstrated 

 the inequality of equal angles in media of different refractive indices ; 

 that, for instance, 180° of radiation in air was less than that of 180° in 

 water or oil.] 



"It is the want of appreciation of this fact that lies at the root 

 of the whole of the error into which Mr. Shadbolt has fallen in this 

 question. His fundamental idea is that the angle is alone to be 

 regarded ; that the refractive index need not be taken into account ; 

 that equal angles must represent optical equality whether in air 

 or oil. Hence he regards the table on the cover of the Journal as 

 ' misleading ' inasmuch as it shows 180° in oil and water to be 

 something more than 180° in air; he supposes that it must there- 

 fore be intended to maintain that there can be an angle in excess of 

 180° ; and he considers he has shown that ' no lens can have an 

 aperture of any kind which exceeds that of 180° angular in air.' 



" When it is recognized, however, that the optical effect of the 

 180° in air falls far short of that of the 180° in oil, all the seeming 

 absurdities vanish. 



" That Mr. Shadbolt's erroneous view on this point, and his failure 

 to appreciate that the 180° of the dry lens is not the ' whole,' is the 

 source of his difficulty, may be shown by the following quotations. 

 In his original note p. 1090, he says : — 



" Let us suppose a dry lens of 170° of aperture to have 

 " been placed in position to examine some transparent object 

 " simply laid upon a slip of glass, which object is illuminated 

 " from below ; the lens would now receive and refract from 

 " each luminous point a pencil of 170° [see Fig. 34]. 



" But if that object were mounted in balsam, or other dense 

 " medium, and protected as usual with a thin covering of glass, 

 " the same dry objective could no longer refract the 170° radiant 

 " pencil of light, because certain of the rays of that pencil would, 

 " in their passage towards the lens, fall on the upper surface of 

 " the covering-glass, at and beyond the critical angle, and would 

 " therefore find no exit ; the angular aperture of each pencil of 

 " rays proceeding from the object, would therefore be limited to 

 " an angle equal to double the critical angle for the covering- 

 " glass employed [see Fig. 35], 



" It now becomes apparent why an immersion objective can 



* These demonstrations have been repeatedly published, and are, therefore, 

 omitted here. See the references collected in vol. ii. (1879) p. 651. 



t From the subsequent discussion Mr. Shadbolt appeared to suppose that it 

 was intended to convey that this could only be proved by reference to diffraction 

 spectra. It need hardly be pointed out, however, that it is in principle a purely 

 dioptrical matter, and is established by a simple dioptrical demonstration either 

 ■with or without the Microscope. 



M 2 



