28 the president's address. 



microscope objectives are not square, but circular, and referring 

 to the formula for circular telescope objectives we see that it is 

 a trifle more than one-fifth larger than that for square apertures. 

 It therefore comes to this, that so long as the telescope objec- 

 tive is square, and the microscope objective is circular, the 

 mathematical formulae for both are numerically identical, 

 although the reasonings by which those formulas are obtained 

 lie along""wholly different paths; but when we have circular 

 objectives in both cases, the resolving power of a telescope, 

 according to the physical theory, is about one-fifth less than 

 that of a microscope, according to the diffraction theory. Now, 

 we know that it is impossible that light should act in one way 

 in a tube because it is called a telescope, and in another way 

 when it is called a microscope, and it was this glaring 

 discrepancy between the telescopic and microscopic theories 

 which led me to publish in 1893 a pamphlet on " The Theory 

 of Telescopic Vision." Thus it was my endeavour to bring the 

 theory of telescopic vision into harmony with that of the 

 microscope. This evening you have before you the converse 

 problem in Mr. Wright's articles, bringing the microscopical 

 theory into consonance with that of the telescope. There is 

 one thing for certain, that sooner or later either the Airy or the 

 Abbe theory will be abandoned, for both cannot possibly be 

 correct. 



You must now know that with regard to these articles in the 

 11 English Mechanic " 1 am in a somewhat better position than 

 you, because, in reply to some notes, Mr. Wright most kindly 

 wrote to me at great length explaining several of his points, 

 and giving me fuller information concerning others. What 

 follows next with regard to the resolving limit will therefore 

 have more reference to his letter than to what has appeared in 

 print. 



Lord Rayleigh, whose work on the undulatory theory is so 

 well known and appreciated by all, made careful experiments 

 with a telescope,* and obtained a somewhat smaller limit for 

 circular apertures, viz., one lying about half-way between those 

 calculated by Airy for circular and square apertures. 



* " The Resolving Power of Telescopes," bj Lord Rayleigh. " Pliilo 

 gophical Magazine," August, 1880. 



