346 



SUMMAEY OP CDRKENT RESEARCHES RELATING TO 



(2) An identical object O (Fig. 87) cemented to the under surface of 

 a glass plate, will apijear at a somewhat higher plane 0*, but neither 

 amplified nor reduced. The pencil u, however, which is gathered 

 in from the radiating object, is less in angle than u* in the ratio 

 approximately of 1 : 1 • 5 ; and if, therefore, equal pencils in air and 

 in glass were equivalent the quantity of light emitted from any square 

 millimetre of the object and received by the pupil would be less in 

 the proportion of 1 : (1 • 5)^ = 1 : 2 • 25. The object would therefore 

 be seen less bright in the same proportion. 



Fig. 87. 



Fm. 86. 



Fig. 88. 



(3) The same object, separated by air from the under surface of the 

 plate, would emit once more pencils of the aperture u* (Fig. 88). The 

 circumstances will be the same as in (86). As the loss of light at a 

 polished glass surface with perpendicular incidence is not more than 

 about 6-7 per cent., this case, 88 ^if the hypothesis were correct) 

 would show the object brighter than (87) at least in the proportion of 

 2:1. Any one may satisfy himself at once that this is not the case, 

 and that the difference in brightness between (88) and (87) is not 

 appreciable. Therefore the smaller pencil u in glass must contain as 

 much light as the wider pencil u* in air. 



If instead of the eye a microscope objective (dry) which takes in any 

 wide pencil — say 140° — is used, the above considerations must equally 

 apply; iiu* = 140°, m = 2 x 38° 50' = 77° 40' (n being 1-5). The 

 second case (87)would be that of an object cemented to the under surface 

 of the covering-glass. The third case (88) would be that of an identical 

 object with the cover-glass laid on only. If 140° in glass were the 

 same as 140° in air, the 77° 40' in glass would be very much less, and 

 as the quantities of light must be estimated by the squares of the sines, 

 there would of course result a very great difference of brightness in 



