214 The Microscope. 



plane, c^^ of the back lens; we say ahove because both are posi- 

 tive. We have accordingly marked rf^, d^^ at these distances, as 

 the principal planes of the doublet. It will be observed that 

 the second of these planes is some distance external to the lens : 

 yet the second focal length of the doublet ((/ = ft) should be 

 measured upwards from this plane, and would, in fact, be found 

 above the point F^. 



2. — By the same method we measure the mid-doublet B, and 

 again the back-doublet A. Thus we find the trcmsit for the two 

 doublets A and ^, or the distance between the upper principal 

 plane of the lower, and the lower principal plane of the upper 

 doublet; this turns out to be 1.4977. The formulae already used 

 now enable us to combine these two doublets into a low-power 

 Objective, whose two principal planes are found to lie at the 

 lines A B.J, and A B.2 of the figure, and whose focal length is 

 2.1305, measured from these planes. 



Our next step is to combine the low-power objective with the 

 front doublet, having as the transit distance (d^ to A B, in the 

 figure), 2.00428. The principal planes of the objective are found 

 to be at Oj and 0^ of the figure, and its focal length is 2.2162. 



3, — The eyepiece consists of two convex-plane lenses of crown- 

 glass, convex-side downwards ; the lower is 3 thick, and of 

 radius of curvature 40 ; the upj^er is 2 thick, and of radius 30 ; 

 the space between them is 43. By the method already pursued 

 we combine these lenses to an equivalent of the eyepiece, getting 

 as focal length 48, as anteplane 72, postplane 54. Hence the 

 first principal plane is 72 above the lower principal plane of the 

 lower or field lens ; and this measurement carries it 24 milli- 

 metres, or nearly an inch, above the eyepiece ; whilst on the 

 other hand the second principal plane being negative is to be 

 measured downwards from the upper principal plane of the eye- 

 lens, and is 71 below the lowest face of the eyepiece. Thus the 

 principal planes are inverted in the eyepiece, the first one be- 

 coming uppermost. 



4. — Combining the eyepiece with the objective, we use as our 

 transit, the whole distance between the upper principal plane of 

 the objective and the first principal plane of the eyepiece. This 

 (distance depends chiefly on the microscope tube, and on the con- 

 ation of the draw-tube. In the short microscope which I am 



\mining, this transit was found to be 220.8432, and the for- 



