1873.] 



for a Microscope Object-glass. 



117 



being affected by every change of eyepiece, length of tube, or adjustment 

 for thickness of cover ; therefore a correction for a fixed point cannot be 

 maintained. Achromatism in the microscopic object-glass, like that of 

 other perfectly corrected optical combinations, must be the reunion of 

 the rays of the spectrum close to the final emergent surface of the 

 system. The remedy suggested by these experiments appeared to be in 

 a transposition, that is, in placing the over-corrected triple in the middle 

 of the entire object-glass ; this would at once cause a convergence of the 

 blue and red rays. A single lens of longer focus at the back would then 

 bring these rays parallel at the point of final emergence. 



By projection in a diagram this condition was apparently realized. The 

 dispersive power of the flint (density 3* 686) was taken by the refractive 

 index 1*76 of line H in the blue ray of the spectrum, and 1*70 of line B 

 in the red ray. The refraction of the corresponding rays in the crown 

 (density 2*44) was 1*53 H and 1*51 B. "With these indices the rays are 

 traced in fig. 6. The radii in the right-hand half section are those of an 

 " eighth " of the new form drawn twenty times the size of the original. 

 The single front is of the usual form, as this is much alike in all cases. 

 The radius or focus of the single plano-convex back is about four and a 

 half times that of the front, and the focus of the middle (triple) three 

 times. The passage of the blue and red rays at the extreme of the pencil is 

 shown in contrast with the preceding, the separation from the same front 

 being alike. 



The inner and outer, or blue and red rays, after passing the first sur- 

 face of the triple middle, meet the concaves of the flint, which refract 

 the blue rays to a greater extent than the red, and cause them to con- 

 verge (instead of diverging, as in the opposing half diagram), so that at 

 their exit from the triple they meet and would cross, effecting what is 

 known as " over-correction ;" but this is so balanced and readjusted by 

 the single back of crown glass, that the rays are finally united, and 

 emerge in a state of parallelism. This form of object-glass is suitable 

 for the high powers, or such as have a cover adjustment, viz. from the 

 " -|-mch " upwards ; perfect colour-correction is equally to be obtained 

 in all of them. 



It may be asked by some who have devoted their attention to the 

 higher branches of optical mathematics, why the above result should 

 have been worked out entirely by diagrams. But it has been found 

 such a difficult task to calculate the passage of the two rays of greatest 

 and least refrangibility through a combination having sixteen surfaces of 

 glass of three different densities and refractions, that even first-class 

 mathematicians have hitherto shrunk from the attempt. 



Diagrams, however, are surprisingly accurate in their capability of in- 

 dicating causes and results in the microscope and object-glass ; for these 

 lenses are minute, with deep curves and abrupt refractions ; so that if 

 the projection is worked out some fifty times the size of the original, 



