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Mr. P. H. Wenham on a new Formula [Jan. 16, 



rendered its use in a pair objectionable. The highest density at this time 

 known, quite free from this defect, was 3*686. By means of the triple 

 back, the final corrections were rendered less abrupt, a greater portion of 

 the marginal rays could be collected, and the aperture of an " eighth " 

 was at once brought up to 130° or more. 



At this time the author had been making some experiments in the 

 construction of an object-glass in the form of fig. 2. Mr. Lister having 

 favoured his " eighth" with an examination, was good enough to com- 

 municate his late improvement of the triple back. No time was lost in 

 giving this a trial, the result of which proved that excessive negative 

 aberration or over-correction could readily be commanded with lenses of 

 shallow contact-curves. During these trials all chromatic correction was 

 obtained by alterations in the triple back;- for it was found that the 

 colour-correction could not be controlled by a chauge 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. Por 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 combinations 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 correction. 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. Pig. 3 represents a front lens suitable for 

 bringing the back rays to a focus. The dotted fines indicate the effect 

 of this difference, showing that with a lens of less thickness 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 chauge 

 their system, though challenged by a series of high powers constructed 

 on this formula, for the purpose of proving its superiority. Pig. 4 re- 

 presents the curves of the first successful " eighth " on this system, having 

 an aperture of 130°, enlarged ten times. On tracing the passage of 



