378 PROCEEDINGS OF THE SOCIETY. 



80° at the radiant, while tlie other was 170° at the radiant. As 

 a small j)art could not equal a greater part of the same whole, 

 Mr. Shadbolt's contention was established in a simple manner with- 

 out the hemisphere, always supposing that the assumption with which 

 he started was correct. 



Unfortunately, as the further Note showed, Mr. Shadbolt was still 

 involved in exactly the same fallacy as at the December and January 

 meetings, viz. first, that the aperture question could be rested on the 

 basis of photometry simply, and secondly, that radiation in air and 

 radiation in balsam were the same things. On this supposition, he 

 (Mr. Shadbolt) of course could not regard the small balsam-jDencil of 

 80° in Fig. 35 as the equivalent of the large air-pencil of 170° in Fig. 34 ; 

 but treating the former as less, it necessarily followed that when ex- 

 panded into 170° after refraction it still was less (or was " diluted ") 

 in comparison with the original unrefracted pencil of 170°. It was 

 indeed diluted, but what Mr. Shadbolt had failed to gras^j was 

 that it was first equally "compressed" (using his expression), 

 so that " compression " and " dilution " balancing one another, the 

 pencil, notwithstanding refraction, did contain the same amount of light 

 as the unrefracted pencil. It was singular that Mr. Shadbolt had not 

 seen the inadequacy of such a photometrical test of aperture, even if 

 he had been right in his application of it, but if he insisted on its 

 adequacy the first step he must necessarily take was to get rid of the 

 notion that the small balsam-pencil of 80° in Fig. 35 did not contain 

 the same amount of light as the large air-pencil in Fig. 34. 



(2) In the next place, Mr. Shadbolt suggested that " nothing had 

 been shown to disprove the view he enunciated " as to aperture. 



Now, Mr. Shadbolt had formulated his conclusions in his original 

 paper in such unusually emphatic words as these : — " I have therefore 

 demonstrated beyond dispute that" &c. ; and his demonstration was based 

 on two things : (1) a diagram, and (2j a i^hotometrical j)roposition. 



As to the diagram, that was dis2:»osed of by one of the simplest 

 and most elementary of optical considerations (see j). 334), which 

 had been entirely overlooked by Mr. Shadbolt ; and not only so, but 

 it was further shown that no other diagram could be drawn in support 

 of his view, unless an angle were foimd whose sine was greater than 1 ! 

 The diagram was in fact another of those curious instances which 

 had so often occurred in the angular-aiierture discussion, of its 

 supporters being so certain that their view must be right, that it 

 never occurred to them to test the proof which they sui)posed they 

 had given, by an apparatus which was in the possession of every one, 

 and which was so simple and free from complication as a plano- 

 convex lens ! 



On the photometrical question, Mr. Shadbolt himself rested his 

 view on the equivalence of radiation, no matter what the medium was ; 

 and his whole argument from first to last could only hold good on the 

 supposition that that view was correct, as he himself admitted with 

 perfect candour. Leaving out of account any comment upon the 

 strangeness of basing the aperture question solely on quantity of 

 light, the difficulty in supporting the second point was, however, 



