Dr. Gr. J. Stoney on Microscopic Vision. 441 



32. Criticism of the Abbe and the Airy methods. — The proof 

 which we have just gone through is instructive in many 

 ways. In the first place, it carries the analysis of the image 

 down to rulings of the simplest kind that are known. In the 

 second place, it makes the flexibility and Protean character 

 of the whole process conspicuous ; for although we followed 

 one particular order in combining the secondary beams in 

 pairs to form rulings, it is manifest that this order was in no 

 degree necessary, and that the secondary beams might have 

 been grouped in an infinite number of different ways, the 

 only condition being that whatever order we adopt we must 

 take care to use up all the light. This means that the set of 

 rulings which form an image is not unique : that there are 

 an infinite number of such sets, any one of which will suffice 

 to form the image. 



But, above all, the proof given in the last section brings 

 well into view the source of the advantage which is found in 

 employing Abbe's mode of procedure as our instrument for 

 searching out the causes of the phenomena presented by 

 microscopic vision. By the process we have followed the 

 light sent forward from the objective field has been analysed 

 into beams of plane waves. Now this is only one of number- 

 less possible ways of analysing that light. It is an analysis 

 which may be made, not which must be made. But it has 

 the advantage over every other analysis, that the resulting 

 waves are uniform waves, exactly alike in every respect over 

 the whole extent of each wave surface and each wave retaining 

 its form and intensity unchanged during its advance. 



This sets us free from a sea of difficulties that embarass 

 our progress when we attempt to employ any other resolution. 

 If the analysis be made into curved waves of any kind — into 

 those of Airy's method or any others — the resulting waves 

 are not uniform over each wave- surface ; and as the law of 

 this want of uniformity is not yet known, we can only 

 legitimately employ Airy's method in the cases where this 

 want of uniformity has an inconspicuous effect upon the 

 result of our inquiry. This is the case, for instance, in the 

 treatment of telescopic vision to which Airy applied it. Here 

 the sector of each hemispherical wave that we have to deal 

 with is sufficiently small for the want of uniformity within 

 its small extent to be of negligible amount. 



It has sometimes been supposed that we can investigate 

 microscopic vision by applying Airy's analysis to the light 

 sent forward to the eye from the image of the microscopical 

 object which is formed by the objective close to the eyepiece. 

 This light as it comes from each point of that image is confined 

 within a cone which is a continuation upwards of the narrow 



