ZOOLOGY AND BOTANY, MICROSCOPY, ETC. - 817 



Then 

 and 



Again, 

 and 



f - p = ^,- V = p{%,-^)- 



9 ^9 



By substituting in equation /? these values, 



from which 



and lastly, 





9" 

 n = 1 4-—^ -(n' - 1), 



This calculation is for Brewster's instrument, m which the artificial 

 lens is plano-concave. In Smith's apparatus, in which the lens is piano - 



1 ,111 



convex, the fraction -—j- changes sign, so that ~ = -^ -\- -jr • 



In the two equations which express the law of conjugate foci, 



^' + P - F ' p + P ~ / 

 1 1 11 _l_i 



i _ 1 -1- ^ 

 p' ~p-F f' 



Substituting for - its value we get 



1 1 _1_ 1 _l_ L 



by subtraction 



