Mr. Wenham's new Formula for a Microscope Object-glass. 227 



good enough to communicate his late improvement of the triple 

 back. JSTo time was lost in giving this a trial, the result o£ which 

 proved that excessive negative aberration or over-correction could 

 readily be commanded with lenses o£ shallow contact-curves. 

 During these trials all chromatic correction was obtained by altera- 

 tions in the triple back ; for it was found that the colour-correc- 

 tion could not be controlled by a change in the concave surface 

 of the triple front, as the negative power of the flint here ap- 

 peared to be feeble, requiring a great difference in radius to give a 

 trifling result. For this reason the front concaves were formed 

 of very dense and highly dispersive flint ; the cause of this was 

 analyzed by a large diagram, with the passage of the rays projected 

 through the combination, starting from the longest conjugate focus 

 at the back. This proved that the rays from that focus passed 

 through the concave flint of the front nearly as a radius from its 

 centre, or in such a direction that its negative influence was almost 

 neutralized. It is well known that a lens may be achromatic for 

 parallel rays, and under-corrected for divergent ones. The utmost 

 extent of this condition was apparent in the object-glass under 

 consideration. 



This led the author to the idea of the single front lens of crown 

 glass, which gave a fine result at the first attempt, as the back com- 

 binations to which it was applied happened to have a suitable 

 excess of negative or over-correction existing in the triple back 

 alone, the middle being neutral or nearly achromatic. Still there 

 was a defect remaining as positive spherical aberration ; and this 

 was afterwards cured by giving additional thickness to the front lens, 

 which is now recognized as a most essential element of correc- 

 tion. In a " fifteenth," for instance, a difference of thickness of 

 only -002 of an inch will determine the quality between a good 

 and an indifferent glass. Eig. 3 represents a front lens suitable 

 for bringing the back rays to a focus. The dotted lines indicate 

 the effect of this difference, showing that with a lens of less thick- 

 ness the marginal rays fall within the central, producing positive 

 aberration as the result. 



The single front introduced by the author is now used by every 

 maker ; for several years he could not induce the leading opticians 

 to change their system, though challenged by a series of high 

 powers constructed on this formula, for the purpose of proving 

 its superiority. Eig. 4 represents the curves of the first successful 

 " eighth " on this system, having an aperture of 130°, enlarged ten 

 times. On tracing the passage of the marginal rays through the 

 combination, it will be seen that, though the successive refractions 

 are nearly equalized, the contact-surfaces of the middle pair are 

 somewhat deep, though no over-correction existed or was needed 

 here, for this would have required a shorter radius still (the density 

 of the flint in this was 3*686). If this pair of lenses were not 

 cemented with Canada balsam, total reflection would take place near 

 the circumference of the contact flint surface, cutting off the mar- 

 ginal rays at a, and limiting the aperture. It might be argued that 



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