24 



THE PRESIDENTS ADDRESS. 



i.e., there will be darkness. If the point D is moved a little 

 further from B, so that A D is longer than W D by one whole 

 wave-length (see dotted isosceles triangle ADC), there will 

 be another reinforcement of light at that point, and so on. 



Hitherto we have only been considering the effect of the 

 wave-action of light at a small spot on either edge of an 



objective ; we must now take 

 into account its action over 

 the whole area. Let us, in 

 the first instance, suppose 

 that the object-glass is square, 

 and let us divide this square 

 into equal rectangular spaces 

 by drawing lines parallel to 

 one of the sides of the square 

 (Fig. 2) ; we can then easily 

 see that the light passing 

 through one rectangle will 

 Fm. ^- oppose that passing through 



another; thus, if we divide our square objective into eight rec- 

 tangles, and name them consecutively EFGHIKLM, E will 

 oppose I, F will oppose K, Gr — L, and H — M. The case being that 

 of thedotted triangle AD C(Fig. 1), where the light passing at the 

 E or A edge of the object-glass to the point D has one wave-length 

 further to travel than that passing at the AC or W edge, therefore 

 that passing at the centre of the square, viz., at the line 

 between H and I to the point D, will have half a wave-length 

 less to travel than that at E, and half a wave-length more than 

 at M. Moreover, the rectangles being all equal to each other, 

 the opposition of the rays will consequently be equal in effect. 

 From this we learn that the image of a bright point, such as a 

 star, at the focus of a telescope is made up of a bright disc in 

 the centre of a dark ring, encircled by a bright ring, etc. 

 Now, so long as the objective is square, it is easy to calculate 

 the distance the dark point D is from B. When F is the focal 

 length of the objective, A its aperture, and A. the wave-lenoth, 



A F 



then the distance between D and B, $ is equal to . This 



A 

 means that the least separable distance in the image at the 

 fouus bears the same propori ion to the local-length, as the wave- 

 length does to the diameter of the objective. But the ratio of 



