244 



ON THE THEORY OF THE MICROSCOPE. 



observing Pleurosigma angm. and other diatoms, which, seen 

 under polarised light, shew modifications of diffraction which it 

 would be difficult to explain otherwise. However this may be, 

 it is no longer admissible, in an object, for instance, such as 

 muscular fibre, whose structural detail is not dioptrically imaged, 

 to conclude according to ordinary criteria, from observation 

 of changes of the difi'raction image in polarised light, that the 

 various elements possess alternating characters of simple and 

 double refraction ; for if any liomogeneous doubly refracting sub- 

 stance were present with diff'erentiation in its substance sufficient 

 to produce the existing diffracUve eff'ect, then an appearance of 

 striation would arise from interference of the polarised diffraction 

 pencils, shewing exactly the same modifications as muscle fibre 

 does under polarised light. 



XIX. In connection with the foregoing conclusions, which 

 have an important bearing on the scientific application of the 

 microscope, it appears, further, that the limits of "resolving" 

 power are determinate for every objective and for the microscope 

 as a whole. 



^0 particles can be resolved (nor the characters of any really 

 existing structure recognised) when they are situated so closely 

 together that not even the first of a series of diffraction pencils 

 produced by them can enter the objective simultaneously with the 

 undiffracted rays. From this it follows that for every degree of 

 angular aperture there must be a fixed minimum of distance of 

 separable elements, which cannot be stated in exact figures, for 

 the reason that this minimum differs for every colour on account 

 of their unequal wave lengths, and also because the relative 

 significance of the several colours varies greatly. Taking any 

 given colour as a basis, the respective minimum value is found 

 (purely central illumination being employed) by dividing the 

 wave length by the sine of half the angle of aperture, and half 

 that product when, other circumstances being equal, the illumina- 

 tion is as oblique as the objective will admit, whatever be its 

 aperture. As, therefore, even with immersion objectives the 



