184 TESTING THE MICROSCOPE. 



VIII. 

 DETERMINATION OF THE CARDINAL POINTS. 



LASTLY, the problem remains to be solved of examining a given 

 objective with regard to the position of the cardinal points, both of 

 the separate double-lenses and also of the whole system, i.e., to dis- 

 cover empirically the distances of the principal and focal planes 

 from each other and from the refracting surfaces in a manner 

 analogous to that which we have above obtained, under definite 

 assumptions, by calculation. In order to solve this problem with 

 approximate accuracy, the following method may be adopted : 



(1.) The focal lengths of the separate double-lenses, then those 

 of the two posterior lenses of the system, and, lastly, that of the 

 whole objective, are determined. For greater accuracy it is ad- 

 visable to make repeated measurements with higher powers, and 

 with a different scale, &c. 



(2.) We determine the distances of the first and second focal 

 points from the anterior and posterior surfaces of the double-lens, 

 or of the system. For this purpose we place it upon the stage 

 with the surface in question turned upwards, and adjust the plane 

 mirror of the Microscope so that the image of a distant object 

 (e.g. y of a tree, or a cloud, &c.) is visible in the focal point of the 

 combination. The Microscope being focused as sharply as possible, 

 we mark a fine line on the body -tube at the upper or lower edge 

 of the socket in which it slides, and then lower the focus until the 

 surface of the system to be investigated (which is turned upwards) 

 appears in the field of view; to aid the focusing, the surface 

 may be slightly marked with the tip of the finger. This position 

 of the body-tube is registered by marking a fine line. The dis- 

 tance of the two lines, which is obviously the magnitude required, 

 can be micrometrically determined, either by the compasses, or, if 

 very small, by a second Microscope of low power. 



(3.) We measure the thickness of the double-lenses or of the 

 system that is, the distance between the first and last refracting 

 surfaces. Since the anterior surfaces of the double-lenses gene- 

 rally lie exactly in the same plane with the edge of the cell, 

 the measurement is most easily made in the manner above de- 



