210 The Microscope. 



our general formula to find the character of the lens as a whole. 



The formula is f = ■ where / is the required principal 



focal length of the lens, tz is the thickness of the lens, and the 

 other terms are as already explained. The second focal length 

 of the lens, g, is equal to/ with the sign changed, when the same 

 medium is on both sides, but may be got separately by the for- 

 mula 



— 9i 92 



9 = 



/2 — gi + t[ 



These focal lengths are to be measured from the principal 

 planes, / from the first plane, g from the second plane of the real 

 or imaginary lens. I propose to designate the three segments 

 depending on the principal planes, by the names anteplane, inter- 

 plane, postplane, and the interval between the second principal 

 plane of one lens and the first principal plane of the following 

 lens (real or imaginary) by the term transit (indicating it in the 

 formula by t, as in combining two lenses it has the same function 

 as thickness ti has in one). 



The formulae for determining the anteplanes and postplanes, 

 and thereby determining the principal planes are 



ay. (anteplane) = — — ; 



h—gi + t 



— 92t 

 a2 (postplane) = 



/2 — ^1 + < 



(where t is either thickness or transit in different cases. It may 

 be marked as t', thickness of crown-glass lens, f^ transit of doub- 

 let, tf transit of objective.) 



It will be observed that all the formulae have the same form 

 of denominator. 



In all cases conjugate focal lengths (ji and J2) can be got 

 from each other and the principal^focal lengths by the equation 



/ 9 

 — + ^ 1. 



ii J2 



III. For the DmihUts, The imaginary lens that is equivalent 



