164 A New Formula for a Microscope Object-glass. 



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 

 parallelism. 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 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 indicating 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, 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 compasses, the 

 long limbs representing the sine of the angle of incidence, and the 

 short one that of refraction. Both the sines ought to be set off in 

 the diagram behind, and neither of them in front of the ray in 

 course of projection; this leaves the way clear, with the least 

 confusion of lines. 



At the same time a second or counterpart diagram should be 

 at hand, to which the rays only are transferred as soon as their 

 direction is ascertained ; with these precautions a mistake is scarcely 

 possible. 



Now it is hoped that some improvements may be effected by 

 this investigation, on account of the simplicity attained in the com- 

 bination, in which we have two single lenses of crown, whose foci 

 bear a definite proportion to each other ; while all the corrections 

 are performed by one concave of dense flint, the acting condition of 

 which is not altered by the influence of any other concaves acting 

 in the combination, and hitherto taking a share of the duty. This 

 one flint is now to be considered singly as the heart and centre 



