JOIJENAIj 



OF THE 



ROYAL MICROSCOPICAL SOCIETY. 



OCTOBER, 1906. 



TRANSACTIONS OF THE SOCIETY. 



X. — On the Limits of Resolving Power for the Microscope 

 and Telescope. 



By Edwakd M. Nelson. 



(Read March 21st, 1906.) 



It cannot be admitted that the theoretical resolving limits, both 

 for the telescope and the microscope, are as satisfactory as the 

 science of to-day requires. As the telescope and the microscope 

 are mere variations of the same optical instrument, the theoretical 

 resolving limits should be the same for both. Few, however, will 



recognise the identity of the telescope limit of _ 



aperture m inches 

 with the column at the end of our Journal headed "Limit of 

 Resolving Power in Lines to an Inch for White Light." To make 

 this subject at all intelligible to microscopical readers, it will be 

 necessary to trace, very briefly, the position of the telescope limit, 

 and we may well take this first, as its investigation predates that 

 of the microscope by some forty years. 



A point of light, such as a star, is imaged both in a telescope 

 and in a microscope as a bright disk surrounded by alternate dark 

 and bright rings. It has been the received opinion that the radius 

 of the first dark ring is the measure of the limit for the separation 

 of a double star by a telescope, so that it is this radius which must 

 for the present occupy our attention. The method of calculating 

 this radius, when the aperture of the telescope is square, is quite 

 simple, but it will suffice for our present purpose to accept the 

 result, and refer the reader to text-books for the proof. It has 

 been found that, when the aperture is square, the radius of the first 



Oct. 17th, 1906 2 m 



