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XVI. — Note on Diagrams {Plate XII.) exhibiting the Path 

 of a Bag through Tolles \ Immersion Objective. 



By Professor R. Keith. 



{Read 9th April, 1879.) 



I HAVE sent with this note additional diagrams (Plate XII.) to 

 aid in localizing the symbols and following out the formulae used 

 in the computation of the ^ immersion objective made by Mr. 

 R, B. Tolles and owned by Mr. Crisp.* The lines are not drawn 

 to any scale, although the elements of the objective are entered 

 upon the lines corresponding to those in the objective itself. 



It will be observed that the ray of light finally emerges from 

 the plane surface of the small lens without refraction. It is, of 

 course, supposed to enter material of the same refractive power as 

 the lens itself: meeting the point in discussion upheld by Mr. 

 Wenham, viz. that there is some interior impossibility of using 

 more than 82^ of aperture in balsam. It will be further observed 

 that the ray meets the plane surface at an angle of over 55^, and 

 therefore if that surface divides the glass from air, it cannot pass 

 out of the lens ; since at 41° and upwards the effect of the great 

 difi'erence of density between glass and air is to stop the light. It 

 is thus seen that the limit of aperture in air does not indicate the 

 limit of aperture in any denser material, the limiting angle being 

 greater the denser the material ; being 90^ when the densities are 

 equal. 



* See vol. i. Plate VII. Professor Keith notifies the following errata in the 

 lithographed computation : — 



In the elements furnished by Mr. Tolles, r — • 29 shoidd be »• — • 029, and 

 in the fourth column of figures, seventeenth line from the top, 55° 5' 51" should 

 be 55° 5' 21". 



