230 Royal Society. 



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 Hin 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 hack 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 

 surface 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 converge (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 paral- 

 lelism. This form of object-glass is suitable for the high powers, 

 or such as have a cover adjustment, viz. from the "^-inch " 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 combina- 

 tion 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 indicating causes and results in the microscope and object-glass ; 

 for these lenses are minute, with deep curves and abrupt refrac- 

 tions ; so that if the projection is worked out some fifty times the 

 size of the original, small errors can be detected. The work 

 should be commenced at the back from a long conjugate focus, 

 which, not being a constant distance, may be taken as very near to 

 parallelism. The high powers all have the means of correction 

 within this distance, and perform better with a long posterior focus 

 than with a very short one. The relative indices for the two or 

 more rays should be marked on a large pair of proportional com- 

 passes, the long limb representing the sine of the angle of incidence, 

 and the short one that of refraction. Both the sines ought to be 



