206 



THEORY OF MICROSCOPIC OBSERVATION. 



foci I -- 1 j = ~] , which are proportional to these magnitudes. 



\P P* ft 



If M is the diameter of the diaphragm,^ its distance from the 

 object, and m the diameter of the image, and finally n and n the 

 refractive indices ; then we find 



n = 



_, or, approximately, n' = " p 



m' m 



where it is assumed in the latter formula that p is very large in 

 comparison with r. 



In applying these formulae to spheres with negative foci, the 

 second term of the denominator must be taken positive. Thus 

 we should have 



_; and hence = (l + 

 \ 



n . 



m 



3. HOLLOW SPHERES AND HOLLOW CYLINDERS. 



The following consideration is generally applicable to tubular 

 cells, globules of oil, and nuclei with vacuoles, starch-grains with 



spherical cavities, &c. For the sake 

 of brevity, we will limit our discussion 

 to the case of hollow cylinders. Of the 

 pencils of light, which influence the 

 microscopic image with an object of 

 this kind, we have, (1) marginal rays 

 which pass through the walls of the 

 cylindrical tubes without reaching the 

 lumen ; (2) marginal rays which meet 

 the inner surface of the cylinder very 

 obliquely, and are there reflected ; 



(3) rays which enter the lumen, are 

 reflected on the walls, and then after 

 two refractions reach the objective ; 



(4) rays which traverse the lumen in 

 a direct line, and undergo in conse- 

 quence a four-fold refraction. 



The marginal rays, which are only refracted twice, behave 

 exactly in the same way as in the solid cylinder. It here 



/ 



FIG. 112. 



