The Hehnholtz Theory of the Microscope. By J. W. Gordon. 



395 



Fig. 84. 



the standing wave-fronts, correctly imaging in shape and dimen- 

 sions those two gaps in the surface of the mirror. The images 

 which would be found clinging round the inner surface of the 

 mirror need not detain our attention, but it concerns us to note 

 that the glass globe is exactly half filled with the central images, 

 of which the largest therefore is 6 in. in diameter, and the rest 

 are gradually smaller in size, having intervals of half a wave- 

 length between them. Fig. 83 illus* 

 trates this state of things. 



Next suppose the glass globe to 

 be taken out, but the apparatus to 

 be used otherwise in the same way 

 as before. We shall now have the 

 same number of images as in the 

 first case, and they will be ar- 

 ranged on the same plan, that is 

 to say, with one set clinging to 

 the surface of the mirror, and the 

 other set clustered at the centre. 

 The set clinging to the mirror is 

 exactly the same as before, but the 

 set clustered at the centre is now a 



set of larger images than the first. For every one encloses the 

 next inner one at a distance of half a wave-length in vacuo and, 

 therefore, the largest is now not 6 in. in diameter, but 6 X 1 • 5 

 = 9 in. Similarly with all the rest. Every image of the series is 

 larger than the corresponding member of the series formed in 

 glass in the ratio n — 1 • 5 in this case. 



These images have been formed in a very special way, and it 

 is perhaps not obvious that the same law of relative magnitudes 

 would apply to images not of an aperture, but formed by an aperture 

 of an object lying outside it. It should then be observed that these 

 standing wave-fronts, although manifestly images of the mirror, are 

 images of the focus also, and really formed by the ordinary and only 

 method of image-formation, that is to say, by the interference of 

 crossing and coincident wave-fronts. The distances at which 

 repetitions of these interference phenomena can occur depend 

 manifestly on the wave-length in the medium in which they 

 occur, and if the distance apart of successive images is propor- 

 tional to the wave-length, the magnitude of the smallest and 

 of every image in the series must be proportional to the same 

 magnitude, for the radius of the smallest and of every other image, 

 is only its distance from the zero point of the scale. It follows that 

 the law which determines the relative magnitudes of these images 

 must equally apply to all images which are formed by the inter- 

 ference of wave-fronts by regular projection through an optical 



