NOTES AND MEMORANDA. 75 



required direction, and the analyzer is turned a few degrees to the 

 right and left. Two cases then present themselves : — 



1. If this section is by accident exactly in the required position, the 

 transition from partial to total extinction will be gradual, and no 

 difference in intensity will be perceived between either of the two half- 

 disks in any position of the analyzer. 



2. If the section of the polarizer is not exactly in position, if it 

 makes even an excessively small angle with the line of separation, 

 variable ditferences will be found between the two half-disks. 



If the analyzer is stopped in a position near to total extinction, 

 one half-disk will be seen to be darker than the other ; the polarizer 

 should then be turned gradually till equality in tint is established, and 

 that will be the position sought. This should be tested by turnin^' 

 the analyzer, when the two half-disks ought to be found perfectly 

 equal in intensity, this intensity varying with the rotation of the 

 analyzer. 



The position of the polarizer is marked ; then to determine that of 

 the section of the analyzer the polarizer is gently displaced about 1^°, 

 which destroys the equality of the intensities ; this is afterwards 

 restored by the analyzer. The principal section of the latter will be 

 found at exactly 90^ from this last position. 



This method can also be used to determine the principal sections 

 of quarter and half undulation plates, and that of plates parallel 

 with the axis. It gives much greater precision than the ordinary 

 methods. 



The margin of the half-plate, which separates the two half-disks, 

 is perfectly clear, and without thickness ; we have then to compare 

 two surfaces of different intensities which are strictly tangent. If the 

 adjustment is made with care, the slightest difference will be appre- 

 ciable ; and this detail contributes much to increase the precision of 

 the method.* 



Improvements in Object-glasses.— Mr. Gundlach, of Rochester, 

 New York, has patented a method of constructing object-glasses for 

 astronomical telescopes and other purposes, by which both aberrations 

 are corrected to a higher degree than has hitherto been attained. The 

 common double objective, consisting of a negative flint-glass lens and 

 positive crown-glass lens, is deficient by reason of chromatic over- 

 correction at the outer edge, and chromatic under-correction towards 

 the centre. This is caused by the flint-glass lens, as usually shaped, 

 not having the proper form to remove this defect. Nor can it be 

 perfectly removed by any alteration in shape, except at the expense of 

 increased spherical aberration, the correction of both aberrations 

 depending on the same factor (the flint-glass lens), and on opposite 

 conditions of this factor, the best form for the complete correction of 

 the one producing the maximum of the other aberration. 



The difficulty is obviated by constructing an object-glass, in which 



both the chromatic and the spherical aberrations are corrected by 



special means independent of each other, leaving the flint-glass lens 



to perform exclusively its legitimate function of correcting the 



* M. L. Laurent, in ' Comptes Kendus,' vol. Ixxxvi. p. 662. 



