84 Prof. F. L. 0. Wndswortli on the Optical Efficiency 



of rotation, and X the mean wave-length of light. It is 

 readily seen that this movement is just that required to 

 separate the superposed images of two lines, one of which is 

 fixed, the other seen by reflexion in the mirror, by the 

 amount necessary for "resolution"*. 



The corresponding expression for the microscope is deduced 

 on the assumption that the smallest linear movement that can 

 he observed with this instrument is also equal to the limit of 

 resolving power. This, according to the researches of Helm- 

 holtz f, is 



e=iM (2) 



The angular movement corresponding to this linear movement 

 at the end of a pointer of length I is 



a m = e/l= £j, (3) 



from which at once follows the conclusion already stated, that 

 the two methods are equally accurate when 



l = b. 



It will be noticed in the first place that both of these 

 expressions are based on the assumption that the smallest 

 measurable angle or distance is the same as the corresponding 

 angular or linear resolution. But in general there is a 

 difference between these two quantities. The smallest 

 measurable quantity depends not on the resolution of one 

 object from another, but on the accuracy with which one 

 object can be located with respect to another. According to 

 Miehelson this " accuracy " for any optical instrument is 

 directly proportional to the resolving power, and is therefore 

 represented by an expression 



A = aR, 

 where A represents the accuracy (the reciprocal of the 

 smallest length or angle that can be detected) ; R is the reso- 

 lution (the reciprocal of the angular or linear resolvino- 



* The term " resolving power " has been erroneously applied by some 

 to the expression (1). In its commonly accepted meaning the term 

 resolving power refers simply to the capacity of an optical system to 

 separate two or more lines or points whose positions with respect to 

 each other are fixed, A mirror, therefore, whether used alone or with a 

 telescope, has exactly the same resolving power as a telescope of the 

 s.xme aperture. 



t Pogg. Ann. Jubelband, 1874. See also paper by Rayleigh, " On the 

 Theory of Optical Images, with Special Keference to the Microscope," 

 Phil. Mag. Aug. 1896. 



4. In Rayleigh's first paper this limit is given, probably through a 

 typographical error, as £\ instead of f A. 



