784 PROCEEDINGS OF THE SOCIETY. 



Thus, if our investigation requires us to describe the light which 

 traverses the space between the cover-glass over a microscopic object 

 and the front lens of the objective, which space is filled with some 

 uniform medium, usually air or oil, then the correct theory appears to 

 be, that this light is a mass of undulations, the waves of which consist 

 of alternating electro-magnetic stresses ; whereas, it is the usual practice 

 to substitute for this the vastly simpler hypothesis that the light consists 

 of rays. Nobody supposes, or at least ought to suppose, that these 

 hypothetical rays are what really exist ; but the substitution of their 

 easily studied machinery for the much less manageable machinery of 

 nature is legitimate, inasmuch as it can be shown that it leads to correct 

 results in a great number of the problems most commonly met with. 

 This hypothesis, upon which the whole of the science of Geometrical 

 Optics is built, is one of the most useful hypotheses of the physicist. 



Nevertheless it is desirable that the study of this branch of nature 

 shall also be carried on by making use of the theory of light, and this 

 the speaker had found to be practicable by availing ourselves of a new 

 method of resolution. It is possible to prove that however complex 

 may be the mass of luminous undulations which traverse a space filled 

 with a uniform medium, the whole of this light can be resolved into 

 simple undulations of flat wavelets, one advancing across the space in 

 every direction in which light traverses it, and each travelling across it 

 without having undergone change while doing so. 



The theorems required for mathematically handling this method of 

 resolving light have been worked out, and it has been found that not 

 only can it deal with problems of optics which lie beyond the grasp of 

 geometrical optics, but that it enables us to treat many problems that 

 have been investigated by the older methods in such a manner as to 

 present to the scientific imagination a singularly distinct picture of 

 what really occurs. 



There is no class of problems in which the advantages of the new 

 method are more conspicuous than when we are dealing with the 

 resolving power of Microscopes. It at once shows (1) that the limit of 

 resolving power for each wave-frequency of the incident light depends, 

 so far as the instrument is concerned, not on the objective but on the 

 combination consisting of the objective and condenser ; (2) that the 

 resolving power has different limits according to the kind of object 

 presented for resolution ; (3) that amongst these the only object in 

 respect of which the resolving power is accurately definite is a ruling of 

 equidistant parallel lines or a straight row of equidistant dots ; and (4) 

 that the limit of resolution of each other kind of object bears an ascer- 

 tainable relation to this resolution of equidistant lines or dots, which 

 may be called the standard resolution. It also shows the conditions 

 under which the detail upon an object ceases to present the appearance 

 of ' spherules,' and exchanges this appearance for one in which the 

 shape and size of the specks is presented. The limit of the conditions 

 under which this latter appearance is presented is the limit of fully 

 satisfactory microscopical vision. It also shows that a single pair of 

 close objects can be seen as two under conditions which are insufficient 

 to resolve a ruling of which the spacing is the same as that of the two 



