38 



THEORY OF THE MICROSCOPE. 



selected as the point of emergence for the determination of the 

 distances of vision. Arithmetical examples would show to what 

 extent the coefficients of amplification found by various observers 

 differ, when they are reduced to the same conventional distance 

 of vision. 



We consider it, however, advisable to put the question to the 

 test of a more complete mathematical examination by referring 

 the action of the objective and of the eye-piece to a single system 

 of cardinal points. As the combination is effected exactly as 

 before, we simply collect the results of the calculation. We will 

 denote the new principal points by E and E*, the focal points by 

 F and F*, and the first and last refracting surfaces of the 

 Microscope, whose distance is equal to 200 mm., respectively by 

 N* and N*. Then 



E = N - 11283 , 

 F = .V- -5174, 



Focal length 



E* = N* + 6-727, 

 F* = N* + 6116, 

 = -611. 



The resulting system is, therefore, as might have been expected, 

 a diverging one, i.e., it forms only virtual images of real objects. 

 The focal points are consequently (in contrast to all former com- 

 binations) nearer to each other than the principal points. 



r 



A" 



V 



FIG. 8. 



Fig. 8 shows how the last paths of the rays are to be constructed 

 in such a system ; a b is the object and a V the* virtual image. 

 The lines indicated by 1, 2, 3 correspond to each other ; they cut 

 the principal planes E Q and U* at equal distances from the optic 

 axis, and their direction is determined by the familiar laws of 

 refraction. 



