DIOPTRIC INVESTIGATION BY GAUSS 



107 



scientific work may be done by such men, and it will promote the 

 accomplishment of this, in our judgment, if the frequently expressed 

 desire be met which will enable 

 such students to understand in a 

 general but thoroughly intelli- 

 gent manner the principles in- 

 volved in the employment of 

 systems of lenses. 



Many such either have scanty 

 knowledge of algebra, or in the 

 continuous pressure of other 

 rl.tims have lost much that they 

 once possessed. We believe that 

 in these cases the following ex- 

 position of the dioptric system 

 of Gauss, with a following ex- 

 ample worked out in full and 

 with every step made clear, will 

 be of real and practical value. 

 Without some intelligible under- 

 standing of the ultimate prin- 

 ciples of the microscope no re- 

 sults of the highest order can, at 

 least with moderate and high- 

 power lenses of the best modern 

 construction, be anticipated. On 

 this ground we commend the 

 study to the earnest reader. 



Let R N, S N' (fig. 86) be 

 the spherical surfaces of a lens 

 of density greater than air, and 

 let P R S p be the course of a 

 ray of light passing through it ; 

 C, C', the centres of the spherical 

 surfaces. 



Let PR, R S be produced 

 to meet the perpendiculars 

 through C and C r in A and A'. 



Let C R=r, C' S=/, 2 //,== 

 index of refraction out of air 

 into the medium. N N'=tZ, the 

 thickness of the lens. N R=>, 

 N' S=6'. These may be con- 

 sidered as straight lines. 



Let the equation to P R be 

 y-b=m(x ON) . . (1) 



Let the equation to R S be 

 y b=m'(x ON) . . (2) 



1 This figure is greatly exaggerated for the sake of clearness. 



2 If either of the curvatures be turned in the opposite direction the sign of the 

 corresponding r must be changed. 



