98 CORKESPONDENCE. 



From this it will be seen he used a stop of at least jV*^ of an inch 

 diameter, and that with it he stated he measured the immersion aper- 

 ture as 68° ! 



I need not recapitulate the details of the method employed by 

 him in my presence. In every essential particular the conditions 

 stated in his paper were observed ; the result was that the immersion 

 aperture measured not 68^ only, but upwards of 90° ! 



And again, with the same slit and with another = • 009 inch (less 

 than one-half of the one described by him), and with the lens set at 

 its best adjustment and accurately focussed in each case on the surface 

 of the semi-cylinder in water contact, the apertures shown by the 

 bi-section of the field of the ocular, in rotating the microscope hori- 

 zoutally, were also beyond 90° ! 



I leave Mr. Wenham to explain the discrepancy between the 

 result he published in March 1874 and the results here given. The 

 facts are plain enough : we used the same ^^rth immersion, the same 

 semi-cylinder, a slit opening of the width he describud, viz. -^jjth of .an 

 inch ; but instead of arriving at his former result of 68°, we measured 

 the immersion aperture as beyond 90°. And as, in his paper, he 

 suggested the measiu-emeut would be still more accurate with a 

 narrower slit oj)oning, we tried • 009 inch, — and again obtained 

 beyond 90\ 



Professor Keith has shown in the Joiu'nal for December last that 

 the width of the slit opening cannot aftcct in any way the measure- 

 ment of the immersion aperture. It should, however, be observed 

 that the practical application of a very narrow slit on the plane sur- 

 face of the semi- cylinder involves considerable attention ; but the 

 refinement of the method will only make the experimental proof more 

 nearly c )incide with theory. 



In criticising the position assumed by Mr. Wenham on the im- 

 mersion aperture question, I am compelled to take his utterances 

 in the ' M. M. J.' as representing the views he holds. He has ex- 

 pressed himself unreservedly against the possibility of an object- 

 glass refracting image-forming rays beyond what he terms the limit 

 of 82° from balsam — making that appear to be the natural limit, or 

 '• full aperture." * Professor Keith touched upon this point in his 

 letter to the Joiu-nal, No. Ixiii., p. 132, thus: 



" All see that the limit 82° depends upon the fZz^ej-ewce of refractive 

 power at a plane surface ; that is, upon tivo variables ; and, thei'efore, 

 necessarily changes with a change in either of them. If balsam is 

 substituted for air between the objective and the cover, the refracting 

 surface is practically removed from the cover to the posterior surface 

 of the front lens, from a jj/a»e to a curve, and the limit, which depjends 

 upon the curvature, changes with that variable." 



Mr. Wenham's reasonings have all appeared to ignore this most im- 

 portant view of the question, by which it is shown that the " critical " 

 angle for refraction into air imposes no natural limit when the rays 

 do not go into air at all till they reach the second surface of the front 

 lens, which, far from being parallel to the front, is deeply curved. 



♦ Sec 'M. M. J.; Xo. XXV., p. 117; xxvii , p. 118 ; Ixiii., p. 110; Ixxxv., p. 48. 



