282 



Lord Ravleigh. On the Intensity of [Nov. 18. 



might suppose the eye (armed when necessary with a focussing lens) 

 to approach without limit the final mirrors. But if we do this we 

 increase the defect of parallelism due to the aperture of the eye. 

 It is true that we may elude the objection by contracting propor- 

 tionally the effective aperture, but only at an expense of brightness, 

 which cannot usually be afforded. In accordance with a universal 

 rule, full brightness requires that the aperture of the eye be filled 

 with light. In this way we see how it is that the aperture of the eye 

 controls the size of the apparatus. 



The employment of a telescope introduces a certain modification, 

 which it may be worth while to state somewhat fully, as the principle 

 is of general application. The extreme angle between the rays of the 

 beam may be regarded as made up of two parts : (1) the angle sub- 

 tended at the object-glass by the aperture in the diaphragm (K) near 

 the final mirrors (upon which the telescope is f ocussed) ; (2) the angle 

 subtended by the object-glass at the diaphragm. If — 



a= diameter of pupil, 

 b = diameter of aperture in diaphragm, 

 r— distance between telescope and diaphragm, 

 m= magnifying power of telescope, 



a= angular diameter of field of view presented to the eye, 



then 



and the extreme angle between the rays of the beam — 



b ma a. a 

 r r mo 



We may here regard a and a as given beforehand ; and we see that 

 with a given b the first term maybe reduced without limit by increas- 

 ing m, and that then the defect of parallelism is proportional to a, the 

 diameter of the pupil. If m and b can both be increased without 

 limit, we may approach as nearly as w^e please to a state of things in 

 which all the rays concerned are parallel. The preservation of full 

 brightness throughout is already secured by the supposition that the 

 effective aperture of the object-glass is ma. 



The reasoning set forth above shows at any rate that the size of the 

 apparatus cannot be reduced below a certain point, but I do not 

 affirm that mine was not unnecessarily large. In addition to its other 

 advantages, the use of a telescope gives facilities for obtaining a good 

 focus upon the division line, an adjustment of great importance for 

 the easy recognition of small differences of brightness. 



The necessarily finite magnitude of the field of view involves a certain 

 imperfection in this, and probably in other methods of photometry. We 



