Dr, Wollaston's Microscopic Doublet. 265 



placed in contact, and that their aberration will also be equal 

 to one quarter of that of the equi-convex lens. In Mr. Cod- 

 dington's treatise on the reflection and refraction of light 

 (which contains the substance of Professor Airy's papers on the 

 achromatism, and on the spherical aberration of eye-pieces), 

 g,rti,<:le 1 17, page 156, is to be found this combination, which 

 i§,,tbe best for a microscopic doublet on Martin's principle, 

 because the lenses being in contact, the full power of each tells^ 

 only as the thickness of microscopic doublets must be very 

 considerable, on account of the enormous angle of aperture 

 they require, it will be necessary to make the focus of the se- 

 cond lens shorter than that of the first in the ratio of its thick- 

 ness, otherwise the rays cannot di-aw to the same point. 



It is evident, therefore, that the distance selected by Dr. 

 WoUaston for the distance between his lenses, namely 1-^^ or 

 1 J of the length of the shorter focus is wrong, and does not 

 give the minimum of aberration, it should have been 2, more 

 especially if the distance is measured from the plane surfaces. 

 I here give a table of the foci and distances of plano-convex 

 lenses for doublets, in which the unit may be supposed to re- 

 present the one-hundredth part of an inch, the constant lens, 

 therefore, is one-tenth of an inch focus. 



Con. 10, 10, 10, 10, 10, 10, 10, 10, 10, 10 

 Var. 10, 9, 8, 7, 6, 5, 4, 3, 2, 1 

 Dis. 0, 1, 2, 3, 4, 5, 6, 7, 8, 9 



I On trying any of these doublets by the well known rule, 

 ^**^^ultiply the foci together, and divide the product by their 

 sum minus their distance, the quotient will be the focus of a 

 lens of the same power with the combinations,^^ which are all 

 equal to 5 or one ^^^j of an inch; their spherical aberration 

 is also equal to -^-^ of the thickness of an equi-convex lens 

 of the same power and aperture. The only mistake which 

 caa well be made in this sort of doublet is, to place the 

 lenses at wrong distances ; for any two plano-convex lenses 

 ^ay be combined toother in their best position, (if I under- 

 ,^t^^, Martin rightly^ and their aberration «^ill always be 

 ^qjL^pl to one quarter of that of an equi-qonvex lens of the 

 same focus. As I look at every thing in a practical point of 

 view, I consider all those combinations of glasses, whatever 



