PROCEEDINGS OF THE SOCIETY. 729 



Stokes's early papers in which the resolution is distinctly enunciated. 

 Stokes's words are : "... , for we may represent an arbitrary disturbance 

 in the medium as the aggregate of series of plane waves propagated 

 in all directions."* He does not give a proof of the theorem, nor a 

 reference to where a proof may be found, from which the natural 

 inference is, that the theorem could be referred to as a well-known 

 theorem so long ago as 1845, when Stokes published the paper in which 

 this incidental reference occurs. Dr. Stoney desired to call special 

 attention to this, lest it should be supposed that he claimed the dis- 

 covery of the theorem. "What he did was only to re-discover it when 

 it seemed to be forgotten, and to show its great value as a means of 

 investigating optical problems. 



It may be of special interest to some Fellows of the Society to know 

 that it is possible to see resolved equidistant lines of which there are 

 140,000 to the inch. Grayson's second set of rulings consists of twelve 

 bands of lines, of which the closest are 120,000 to the inch. By taking 

 the seventh of these bands, which consists of lines 70,000 to the inch, 

 and examining it with an objective of N.A. 1*35, used in conjunction 

 with a condenser of N.A. 1*30 — the admirable immersion condenser 

 computed by Mr. Conrady — it was found possible to form a visible 

 image of the band with its lines duplicated, so that the image as seen 

 was an image of lines 140,000 to the inch. To accomplish this, all light 

 of longer wave-lengths was excluded by admitting only light from the 

 violet end of a solar spectrum, which formed by a two-inch lens of short 

 focus an image of the sun, as the source of light. A slit was then 

 placed under the condenser in such a position that the direct light from 

 it was seen at the edge of the " concentration image " — i.e the image 

 seen on looking down the tube of the Microscope — accompanied by the 

 first and isecond spectra formed by the ruling. The first spectrum was 

 then shut out by a narrow strip of copper foil placed over the objective, 

 and in this way the direct light and the light of the second spectrum 

 were alone allowed to pass up the tube and form the microscopic 

 image near the top of the tube. Under these circumstances, as Abbe 

 pointed out, the image of the band as seen had twice as many lines 

 as are in the object on the stage. 



To succeed in this experiment it was found necessary to adjust 

 carefully the tube-length, and the distance between the condenser and 

 the image of the sun, which was the source of light. 



Nobert's celebrated nineteenth band was of lines 120,000 to the old 

 Paris inch, which is the same as 112,594 to the English inch. It is, 

 therefore, not as close a ruling as Grayson's twelfth band, and of course 

 falls far short of being as fine as a ruling of lines 140,000 to the English 

 inch. 



Mr. Gordon spoke in answer to Mr. Conrady, and handed in the 

 following note upon the mathematical part of Mr. Conrady's paper : — 



The main position in Mr. Conrady's paper, the position by establish 

 ing which he proposes to re-establish the Abbe theory, is contained in 

 the following sentence, which occurs on page 620 : " The first spectrum 



* Stokes's Collected Papers, i. p. 102. 



