1897.] near the focus of a Telescope. 267 



its greatest maximum between v = V2 and v = 13 which will be 

 within a small fraction of the radius, it then diminishes to its least 

 minimum between v= 1*8 and 1"9. Afterwards it passes through 

 a series of maxima and minima until at length it becomes practi- 

 cally constant and equal to unity. The appearance on a screen 

 would be that of a bright ring surrounding a series of fainter rings, 

 within a very small distance from it, these latter rings gradually 

 disappearing into a uniformly illuminated space. The outer ring 

 would be most conspicuous, not only by reason of its greater 

 intensity but also because of its greater width. On a photographic 

 plate exposed with a view to showing the existence of this outer 

 ring the probability would be that the light from the inner rings 

 would hardly affect the plate at all ; in any case the maxima and 

 minima would be so close together and differ so little from each 

 other that they would be indistinguishable, except perhaps the 

 first two or three. Moreover, unless the light used were of a 

 single definite wave-length, the maxima and minima for different 

 wave-lengths would overlap. If the light were confined to a small 

 portion of the spectrum, this might not affect the outer ring very 

 much, since it is separated from the next inner ring by a wider 

 and darker interval than exists between any of the others, but a 

 very small range of wave-length would be sufficient to fill up 

 nearly all the other minima. 



The curve if 2 only represents the variation of the intensity for 

 points which are near the outer ring in comparison with its radius, 

 for points nearer the centre the terms which have been neglected 

 would become more and more appreciable until the regularity of 

 the curve was entirely destroyed. These terms were of order 

 T V(1 - Kf (2P 2 + 2Q 2 - 1), and 1/Vz, of which however the first is 

 always small, since P and Q become ultimately equal to \ ; even 

 the second would not make much alteration in the shape of the 

 curve unless z were as small as 100, so that the curve will represent 

 the intensity for a considerable distance towards the centre when 

 y is large. At the centre itself, as is well known, 



S 2 M 2 = 4 sin 2 % , 



4 



or the intensity varies with the position of the plate from zero to 

 4. From the centre outwards the intensity varies irregularly 

 until 1 — k and l/*Jz become small enough to allow the application 

 of the preceding results. 



The figure (Fig. 2) gives some idea of the shape of the intensity 

 curve from the edge of the image up to the centre, the variation 

 near the centre being quite irregular in the sense of varying rapidly 

 with the position of the screen, while the constant ■ part and the 

 variation at the edge are the same for all positions of the screen so 



VOL. IX. PT. V. 21 



