108 Transactions of the Royal Microscopical Societtj. 



This subject has been treated of in a very complete and satis- 

 factory manner by Helmlioltz,* whose authority on such a question 

 few of us would venture to dispute. In his essay he maintains 

 that the size of the smallest objects visible does not depend simply 

 on their size, but veiy much on the susceptibility of the eye for 

 faint differences in the intensity of light. For this reason the 

 ultimate defining power of the microscope cannot be so well deter- 

 mined by the examination of single bright points or lines on a dark 

 ground, or of single dark points or hnes on a white ground, as by 

 the use of fine gratings, which have alternate bright and dark 

 stripes, as on Nolert's test-plate, and on the frustules of Diatom aceae 

 and the scales of insects. He contends that in the case of such 

 objects the smallest distance that can be accurately defined de- 

 pends upon the interference of the light passing, as it were, 

 through the centres of the bright spaces, and that when this inter- 

 ference is of such a character that bright fringes are produced at 

 the same intervals as the dark lines, and are superimposed on 

 them, the lines can be no longer seen, and the normal limit of 

 perfect definition has been reached. He, however, points out that 

 by a favourable overlapping the dark portions of the fringes may 

 occasionally so coincide with the true lines as to make it possible to 

 see still smaller intervals, but that a certain and unequivocal per- 

 ception of such hnes would scarcely be possible. He then proceeds 

 to show that this Hmit of true and distinct vision depends upon the 

 angle of divergence of the light, entering the object-glass of the 

 microscope, and on the wave-length of the light, according to 

 the following relations : 



d = the distance between the lines ; 



a. = the angle of divergence ; 



X = the length of the wave of the light ; 



then we have 



d = 



2 sin. a 



This angle of divergence is equivalent to one-half of the true angle 

 of aperture, when illuminated by an equally large pencil of light ; 

 but at the same time one cannot but think that in actual practice 

 the results must be made somewhat more complex, owing to the 

 presence of light having a less angle of divergence than the extreme. 

 All the calculations are also made for true focal adjustment and 

 correction of the lenses, and if these be not actually correct the 

 combined effect of all the disturbing causes must necessarily give 

 rise to many appearances not easily explained. Of course these 

 remarks do not in any way apply to minute bright points. 



The formula given by Helmholtz is entirely different from that 



* I'oggcndorff's 'Annalen,' Jubelhaud, 1874, p. 573. 



