A New Formula for a Microscope Object-glass. 161 



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. Fig. 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 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 change their system, though challenged by a series of high 

 powers constructed on this formula, for the purpose of proving its 

 superiority. Fig. 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 reflexion would take place 

 near the circumference of the contact flint surface, cutting off the 

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

 that practically this would be no disadvantage, as these surfaces 

 are united with Canada balsam, whose refraction is higher than the 

 crown ; so that the rays in this case must proceed with very little 

 deviation. But incidences beyond the angle of total reflexion may 

 be considered detrimental, as they imply excessive depth of curva- 

 ture ; this can be discovered by looking through the front of an 

 object-glass held close to the eye, any air-films in the balsam near 

 the edge of the lens appearing as opaque black spots. 



At the commencement of the present year the author caused a 

 few object-glasses to be made, with a middle of the form of Fig. 5, 

 the performance of which was very satisfactory. In this the 

 extreme rays pass at more favourable incidences, and within the 

 angle of total reflexion. The upper lens is of dense flint. 



When the experiments on the single front were concluded, and 

 the remarkable corrective power of the triple back in conjunction 

 therewith had been proved, the next attempt was to make the 

 middle also a single lens, leaving the entire colour-correction to be 

 performed by the one biconcave flint in the back. After numerous 

 trials it was found that, though something like over-correction or 

 negative aberration could be obtained with the back, in the degree 

 requisite for balancing the under-correction of the single middle 

 and front when set at the prescribed distance of the aplanatic 

 focus, yet by trial on the mercury globule all the results invariably 

 displayed two separated colour-rings : these could not be combined 



