218 Mr. S. T. Preston on Action at a Distance. 



responding to an assemblage of luminous points is propor- 

 tionally impaired. 



The truth is that, so far as it is possible to lay down any 

 general law at all, the definition depends rather upon the area 

 than upon the external diameter of the aperture. If A be this 

 area, the illumination at the focal point, where all the secondary 

 waves concur in phase, is given by Il = A 2 /X 2 / 2 , the primary 

 illumination being taken as unity. The whole illumination 

 passing the aperture is on the same scale represented by A. 

 Hence if A' be the area over which an illumination lo would 

 give the actual total illumination, AA / = X 2 / 2 ; and A', being 

 in some sense the area of the diffraction-pattern, may be taken 

 as a criterion of the definition. 



In the case of an annulus we saw that the minimum focal 

 length allowing a lens to be dispensed with is also depen- 

 dent upon the area of aperture — 7r(r^— rj). so that it, would 

 appear that if the object be to form at a given distance, and 

 without a lens, as well-defined an image as may be, it is of 

 comparatively little consequence whether or not an annular 

 aperture be adopted. A moderate central stop would doubt- 

 less be attended with benefit ; but it is probable that harm 

 rather than good would result from any thing like extreme 

 proportions. 

 January 29. 



P.S. — Reference should be made to a paper by Petzval on 

 the Camera Obscura (Phil. Mag. Jan. 1859), in which the 

 definition of images formed without lenses is considered. The 

 point of view is different from that above adopted. 

 February 18. 



XXX. On Action at a Distance. By S. Tolver Preston*. 



ALTHOUGH I am far from admitting the propositions 

 contained in Mr. Walter R. Browne's recent reply 

 and previous article (as he seems to assume), some of which 

 appear to partake somewhat of the nature of assertion, I will 

 nevertheless notice one or two points in his last communica- 

 tion, as illustrative of the paradoxical kind of reasoning em- 

 ployed by those who attempt to support " action at a distance." 

 On page 130 of the last Number of the Philosophical 

 Magazine, Mr. Browne remarks, " Nothing is fully explained 

 until it has been brought under an inexplicable law." This 

 "inexplicable law " is exemplified by Mr. Browne's theory of 

 " action at adistance"as applied to gravity — which accordingly, 

 * Communicated by the Author. 



