1877.] 



Magnifying -power of the Half-prism, 



33 



Slant side 



i in. 



lin. 



2 in. 



3 in. 



4 in. 



6 in. 



CO 



No. of Prisms. 



Brightness. 



1 



•084 



•16 



•29 



•40 



•50 



•65 



1-00 



2 



•080 



•145 



•25 



•325 



•375 



•44 



0-50 



4 



•073 



•125 



•19 



•22 



•235 





0-25 



8 



•063 



•095 



•118 









0-125 



16 



•048 



•059 



•062 









0-063 



Brightness: 



These figures show how little is gained by increasing the breadth of the 

 prisms in a long train ; in fact the 



Absorption through the bases of all the prisms t 



Number of prisms 



and this absorption, as it approaches its limiting value 1, increases very 

 slowly with the thickness of glass when that exceeds 6 or 8 inches. The 

 height of the prisms may, however, be increased with advantage up to 

 the limit determined by the condition that the height of the emergent 

 pencil (after passing through the eyepiece) shall not exceed the diameter 

 of the pupil of the eye. Thus with a magnifying-power of 10 on the 

 viewing-telescope it is useless to make the prisms more than 2 inches in 

 height. 



The coefficient — ^ — shows the variation of the brightness with the 

 2/ tan a 



absorptive power of the glass and the angle of the prism. 



The above formula has been obtained on the supposition that the whole 

 of the prism is utilized right up to the refracting edge, which is assumed 

 to have no sensible thickness. In practice, however, this is rarely the 

 case, and the most valuable part of the prism is lost, from the difficulty 

 of working a surface true up to the edge. In a long train of prisms this is 

 a matter of some importance, where light is of consequence ; and there is 

 in such a train the further objection, that the pencil falling on the viewing- 

 telescope is in fact rendered excentrical, and its effective breadth dimi- 

 nished, by the greater absorption in passing through the thick parts of 

 the prisms. 



2. Compound Prisms. 



Here, as the breadth of the prism is increased, there will be a point 

 where the increased absorption makes up for the increased brightness 

 of the incident pencil ; and when this is the case 



h -{fqe-M-cq'e-^^Q, 



dB 



whence 



VOL. XXVI. 



fa-cq 

 .-. fqe- fqk =cq'e- C9,k , 



-f9 + C( l fa 



