FOCAL LENGTH. 181 



view contracted by a small diaphragm) is inversely as the magni- 

 fication, and the ratio is again proportional. These relations afford 

 us a means of determining by calculation the values for different 

 objective-systems in connection with the same eye-piece, if this 

 value is known for a single one of them. If, for instance, the 

 numbers of the divisions of a stage-micrometer, which are seen 

 in the diminished field of view with four different objectives, are 

 respectively, 60, 45, 20, and 12, and if the total magnification 

 in obtained with the first = 50, with the other three it will amount 

 to ff, f, and ff times 50, that is 66f , 150, and 250. 



It is in many cases advantageous to know not only the magni- 

 fying power, but also the exact diameter of the field of view. Its 

 determination is effected simply by measuring the apparent 

 diameter on the plane of projection at the distance of distinct 

 vision, and dividing by the magnification. The measurement may 

 also be effected directly with a micrometer, which occupies the 

 whole of the diaphragm in the eye-piece, or which is movable 

 laterally. 



Similarly, we may require to know the objective-amplifications. 

 The field-lens is removed from the eye-piece micrometer, which 

 is then adjusted until the given objective-image is clearly seen. 

 As, however, the divisions of the micrometer are at a known 

 distance, generally *1 mm., the diameter of the real image may be 

 measured thereby. The ratio of the latter to the diameter of the 

 object evidently gives the objective-amplification. 



2. FOCAL LENGTH. 



In the determination of the focal length, special attention is 

 required in the application of the mathematical formulae given 

 in the Introduction, in order to obtain a result as accurate as 

 possible. Since the principal points of the objective-system are 

 unknown, the direct measurement of the focal lengths or of the 



conjugate foci is impossible. The formula - H ^ = - , in which 



p and p* denote the conjugate foci, and / the principal focus, 

 cannot be immediately applied. We may assume that we know 

 the relative magnitude of image and object, and one of the two 

 foci, provided that it is taken so large that merely an approximate 



