THE PRESr DENT'S ADDRESS. 27 



distance from B to D must, therefore, be increased. The calcula- 

 tion of the distance between D and B (Fig. L), when the object- 

 glass is circular, is a much more laborious and complicated 

 problem. It was first solved in 1834 by Sir Gr. Airy,* the late 

 Astronomer Royal, who was the originator of this theory, of 

 which the above is a mere outline. He found that with a 

 circular objective, 8 the distance between D and B, was equal 



1'2197 A. F 



to r * It is not my intention to trouble you this evening 



with any dry mathematical formulae, or repeat what I have 



demonstrated elsewhere, but you may take it as correct that the 



. ■ X F, . 

 formula for a square aperture given above, viz., 6 = —r~ * s 



practically the same, that it yields the same numerical 

 values as Abbe's formula for microscopic vision, with which you 

 are all well acquainted. 



Unfortunately, however, the apertures of both telescope and 



Fig. 5. 



In Fig. 5 the three triangles are superimposed ; it is a simple and easily 

 remembered picture which contains the whole germ of the theory. Let 

 A C be the diameter of the object-glass, A I its focal length, and A O the 

 distance of the object. Then when C W is one wave. length, I M is the size 

 of the minimum visible image at the focus, and O B is the size of the object. 



This result I have expressed in a simpler and more handy form in 

 another place thus : — " One unit of Aperitive resolves one unit of Interval 

 at a distance equal to the Reciprocal of the Ware-length." Example: — 

 Let a wave-length be chosen between lines C and J), viz., ^o^eo iuch. Then 



Aperture resolves Interval at Distance. 

 1 inch 1 inch 42,260 inches. 



1J inch 1 inch 1 mile. 



3 inches 1 inch 2 miles. 



3 inches | inch 1 mile. 



This table agrees with practical results obtained for terrestrial objects 

 seen by reflected light with the best telescopes. 



When a wave-length of ^fIto (between lines 1) and E) is taken for bright 

 celestial objects the above rule agrees with Dawes' empirical formula for the 

 separating power of astronomical telescopes, viz., 4"56", divided by the 

 aperture of the object-glass in inches. 



* "Cambridge Philosophical Society's Transactions," Vol. v. (1835). 



