376 



Transactions of the Society. 



Fig. 82. 



But if subdued light be substituted for the direct lamp -light, a point 

 is easily reached which corresponds pretty much to the lighting which 

 commonly obtains on the stage of the Microscope, in which three 

 images are clear and conspicuous, the rest but feebly luminous and 

 more or less invisible in consequence. These invisible images may 

 become visible when they overlie and so reinforce one another, under 

 which conditions they do, in fact, give rise to the familiar intercostal 

 points and fictitious markings of very minute and regularly formed 

 objects such as diatoms. But for the broad effect with which we are 

 in this experiment concerned, they are of no importance. 



We shall have presently to consider the physical law of the 

 formation of this image of a point of light ; but for the moment I 

 desire to draw your attention to the fact that this is the truly focussed 

 image of a poini of light seen through this particular aperture. 

 Every aperture, however extended, has its own proper point image, 



and the condition assumed for the pur- 

 pose of elementary dioptrics, that the image 

 of an object produced by a lens corresponds 

 point for point with its original, is never 

 realised in fact. Every luminous point 

 of an object focussed by a lens is focussed 

 in some definite shape, which shape has 

 nothing to do with the correction of the 

 lens, but is determined solely by the form 

 and curvature of the wave-front which 

 the lens transmits ; determined therefore in 

 part by the size and dimensions of the 

 effective surface of the lens, in part by the 

 form of the wave-front when received by 

 the lens, and in part by the refractive index 

 of the lens in relation to the surrounding 

 medium. 



The law is not a complicated one, but 

 for the moment it will be simpler to assume, 

 as we may, that our point pattern is the 

 three-image pattern of fig. 8 1 than to work 

 out the theory of its formation. As it will 

 be necessary to refer frequently in what 

 follows to the geometrical properties of this 

 focussed image of a point of light, it will 

 be convenient to have a word by which to 

 designate it. I propose to call it the 

 antipoint of that point, or in general the 

 antipoint simply, meaning thereby the form given by the particular 

 segment of wave-front in question to the focussed image of the point 

 in which it has originated. Assuming then that we have to represent 

 a simple geometrical figure by means of antipoints such as are shown 



