On the Limits of Resolving Power. By E. M. Nelson. 527 



4" ' 55 

 practical limit of to remain, or is a new value to be found ? 



a 



In reply, first, the theoretical limit may be dismissed at once, as 

 being quite hopeless. The physical nature of the image at the 

 focal point is not yet fully understood, consequently the mathe- 

 matical deductions do not agree with the practical results. 

 Secondly, it is probable that Dawes' limit, which has proved 

 serviceable for so many years, will require a very slight modifica- 

 tion on account of the improvement in the correction of modern 

 telescope object-glasses. It might be suggested that 4" ■ 5, divided 

 by the aperture of the object-glass in inches, would more nearly 

 represent the separating power of the best telescopes at the present 

 time — this gives c a value of ■ 988. With regard to the micro- 

 scope limit, it is not to be expected that objectives, possessing 



such a large -^ ratio as those of a microscope, can have 



a limit equal to those for a telescope, with a ratio which is ten, or 

 twenty, times smaller. 



Now the microscope limit, printed at the end of the Journal, 

 is a limit for a certain class of physical experiments performed 

 with a microscope when used in a certain manner, and it in no 

 way represents a limit for a microscope when legitimately used for 

 the purposes for which it is intended. A microscope objective 

 differs from a telescope object-glass, inasmuch as a telescope 

 object-glass is always used at full power, not so a microscope 

 objective ; the greater part of practical work is done with a half 

 or three-quarter cone of illumination, and only in exceptional cases 

 is this last amount exceeded. Excepting very low powers, it is 

 only objectives of the highest excellence that will stand a § cone, 

 and the best oil-immersions will not stand even this. No physicist 

 has, so far as I am aware, offered any explanation of the pheno- 

 menon. They have all, with the exception of the late Professor 

 Abbe, treated the microscope lens as if it were a telescope object- 

 glass, with the light spread over its entire surface. Professor 

 Abbe, on the other hand, ignored the centre (in fact, he went so far 

 as to recommend for the highest class of work that it should 

 be stopped out), and confined his investigation to the two small 

 areas at either extremity of a diameter of the aperture. It is 

 upon this investigation that the table of limits, printed at the end 

 of the Journal, is based. 



A biologist reports to a society the discovery of some minute 

 structure, stating that it was made with a ^ °f 1*3 N. A., with- 

 holding the important fact that he had only used a third of 

 the aperture of his lens, having illuminated the object with a 

 cone of 0*4 N.A. from an ordinary Abbe condenser. This is a 

 typical case of daily occurrence. Suppose, now, an astronomer 



