440 



Transactions of the Society. 



Fig. no. 



niaining pairs 3. . .3 and 4. . .4. If now we add these four resultant 

 curves together in order to obtain a grand total light curve, we produce 

 a curve which being reduced to a convenient scale, takes the form shown 

 in fig. 110, V. Now here it is to be observed that between the maxi- 

 mum and minimum points the difference is not 19 p.c, as in curve 



No. 109, but 50 p.c. Lord Kayleigh 

 supposes that a difference of 19 p.c. in 

 brightness in the interval between two 

 bright lines is just sufficient for resolu- 

 tion. If so, then it is clear that with 

 two groups of lines such as we have here 

 the resolution would be complete. 



It is to be further remarked that the 

 figure which yields this result does not 

 really represent even a colloquial line, but 

 rather a small aperture, of which the £ A 

 with which we have credited it is the larger dimension. For it is clear 

 that if there were other antipoints seated along these lines before and 

 behind the plane of the paper, they would push their toes — so to speak 

 — under the summits of the antipoints bisected by the plane of the 

 paper on their own side of the division and so produce a further in- 

 crease in the maximum brightness. It is of course true that they would 

 raise the brightness of the minimum to some extent in the same way, 

 but not to the same extent, for not even the front row of antipoints 

 could add quite one-half as much to the brightness of the minimum 

 as to the brightness of the maximum, and the hinder rows would add 

 much less than half. Hence, although the antipoints from both sides 

 combine to raise the brightness of the minimum, whereas those only 

 from one side contribute added brightness to the maximum, the effect so 

 produced when there is an interval of h A between the nearest lines of 

 the two systems must be to heighten the resolution of the bright lines. 

 It appears certain, therefore, that these two bright " lines " lying at an 

 interval of i- X from one another would be fully and even brilliantly 

 resolved in the image formed of them by a perfectly corrected lens. 



The matter thus set at large de- 

 mands fresh and attentive considera- 

 tion, and perhaps I may be permitted, 

 without attempting an exhaustive 

 treatment of it, to contribute the fol- 

 lowing observations to its discussion. 



Assume for the sake of simplicity 

 that the light-intensity curve of the 

 antipoint has the simple form shown 

 in fig. 111. (This form does actually 

 for the antipoint of a square aper- 

 the sides of the square.) 



Fig. 111. 



correspond to the light-curve 



ture along a section parallel to one of 



Further, for the sake of simplicity again, let us ignore the bright rings 



denoted by dotted lines, and assume that the section represents a solid 



of rotation, so that the antipoint curve will present the same contour — 



as in the case of the antipoint formed by a circular aperture — on all 



