192 THE MICROSCOPICAL NEWS, 
new aberrations introduced thereby. But if this is properly com-. 
pensated by any of the ordinary means, and the Jesf correction for 
the new position of the image is obtained, the residuary aberration 
will be reduced to an amount which will exactly correspond with 
the change in the amplification according to the above rule.* 
This statement leads now to several inferences of practical 
importance, which are :— 
(az) The total effect of the aberrations (therein including the 
strictly residuary aberration, as well as the irregular dissipation of 
the rays in consequence of technical faults of the lenses) in the 
ultimate image of the entire microscope is, with every given objec- 
tive, always proportional to ¢he total amplification of the image, and 
does zo¢ depend on the length of the tube alone, or the depth of 
the ocular alone, with which that amplification may be obtained. 
This is easily seen if it is borne in mind that the ocular merely 
effects an enlargement of the objective-image, together with the 
dissipation-circles which are inherent therein. For if a certain 
total amplification N—say 500 diameters—is obtained with the 
whole microscope, the objective amplifying the object by N’ dia- 
meters, and the ocular amplifying the objective image by N” (say 
50 and ro respectively), then will N’ N” = N, and the linear 
diameter of the dissipation-circles in the wdémate image will be 
N”. «, if « denote the diameter of the dissipation-circles in the 
objective-image. If now the same total amplification N should be © 
obtained with the same objective by means of a longer tube and 
a lower eye-piece, N’ will be increased (say to 100), and in the 
same proportion « also, but N” will be diminished in the inverse 
ratio (to 5). The product N” « therefore retains its former value. 
But if, on the other hand, the total amplification N should be 
increased (either by increasing the length of the tube, and there- 
fore the value of N’, or by increasing the amplification of the 
ocular N”), the product N” e¢ will vary in the ratio of N, because in 
the one case the second factor, and in the other case the first 
factor, are increased in that ratio. 
( Zo be continued. ) 
A biographical dictionary of physicians, edited by Dr. Hirsch 
of Berlin and Dr. A. Wernich, is to be published by Urban and 
Schwarzenberg. 
* The tacit assumption which is implied in the proposition that the compen- 
sation for change of the conjugate foci is always possible, without introducing 
new aberrations and without altering the new focal length and the aperture, 
may be readily shown to be true under the restrictions in regard to the distance 
of the images which have been indicated above. 
