82 



THEORY OF THE MICROSCOPE. 



the image a b', but suffers no further loss through the succeed- 

 ing refractions. 



Defective centering of the objective-system may further arise 

 from the fact that the optic axes form small angles with the 

 axis of the Microscope and this is a second case which we have 

 ^ to discuss. Let E^ and E 2 (Fig. 38) be again 



the principal planes of the first and second 

 double-lenses of a perfectly concentric system, 

 P Q the common optic axis, a b the object 

 and a' V the virtual image of the first lens, 

 and therefore the object to the second. If 

 the latter is now turned round one of its 

 principal points, without otherwise altering its 

 position, while the optic axis o 2 o 2 changes 

 its position with regard to P Q, the portion 

 a'x of the virtual image comes into a more 

 unfavourable position, just as in the preced- 

 ing case. The action is, therefore, similar to 

 the case of a lateral displacement of the optic 

 axis ; but the error due to the difference of 

 angle increases with the distance of the 

 object. It should be added, that in con- 

 sequence of the inclination of the lens, the 

 image formed by it appears to be inclined 

 also, from which circumstance the final ob- 

 jective-image, even if the inclination were 

 compensated for by opposite aberrations, must 

 necessarily be deteriorated. In general, then, 

 the deviation of the optic axes acts more 

 disadvantageously than their mere lateral 

 displacement ; at the same time it should be observed, for 

 example, that an angle of about 2 is required in order that with 

 an object-distance of 7 to 8 mm., as was supposed for the second 

 lens, the above assumed displacement of '25 mm. may be equalized. 

 It must, consequently, be decided by experiment which kind of 

 deviation is easier to correct. 



If both kinds of error are present in a system of lenses, the 

 effect is exactly the same as if first a displacement of the axes 

 parallel to their own direction had taken place, and then a 

 deflexion, or vice versd. The arithmetical expression of the errors 



-f 



a 



FIG. 38. 



