102 



THE AMERICAIS^ MONTHLY 



[June, 



the angle taken from the focus 

 to the line of the top where it 

 intersects the curve, at the apex 

 of the parabola to 155°, the 

 extent to which the upper section 

 of the figure can reflect rays, as 

 shown by the lines CC. The line 

 D represents the critical angle 

 from glass to water, limiting the 

 degrees to 120. Now, unless 

 oil is used, rays included between 

 the lines D and C^ are lost ; 

 but if the water-angle {If) is 

 raised to C^ the convergent surface 

 of the top of the paraboloid, at the 

 corresponding angle of incidence 

 that will admit C^ is represented by 

 the line E. A perpendicular ^taken 

 from this at the point A will inter- 

 sect the axis at G^ representing the 

 radius of the concave re<|uired in 

 the top for admitting all rays with 

 a water-contact. 



By this illustration it will be 

 seen, that a shallow concave top 

 of -^-^ of an inch radius, will be 

 sufficient for an immersion parabo- 

 loid of -^-^ of an inch focus. This 

 is shown full 

 size in Fig, 20. 

 A is the para- 

 boloid ; B the 

 focal point ; G 

 the center of 

 curvature of the 

 hollow top. Of 

 course a deeper 

 concave top will 

 perform efjually 

 well, but is not 

 so convenient to 

 use on account of the larger body 

 of water required for filling it. The 

 hollow-topped paraboloid is free 

 from the troublesome adhesion that 

 sometimes takes place between the 

 flat surfaces at the top and slide, 

 which prevents the free use of the 

 stage movements and a concave 

 surface is not liable to be scratched 

 by intervening particles of grit. 



The immersion j)araboloid is most 

 useful in cases where dry or non- 

 immersion object-glasses are em- 

 ployed, as it is only with these that 

 total reflection can be obtained from 

 the top of the cover on objects 

 mounted either in balsam or nuid. 

 But if immersion object-glasses are 

 used on objects mounted dry and 

 adherent at the top of the slide, 

 this, under the circumstances, being 

 the total reflecting surface, the 

 contact of the object prevents total 

 reflection at the part where light 

 is admitted and shows the object 

 brilliantly luminous in a black field. 

 From the above it may be 

 inferred, that if the front of an 

 object-glass, in cases when the aper- 

 ture is supposed to be limited by 

 water from rays reflected back and 

 increased by an intermedium of oil 

 of cedar or cloves, if the first sur- 

 face is also made concave, it would 

 be the means of dispensing with 

 the objectionable use of oil. I have 

 tried some experiments this way : 

 Fig. 21 is the 

 front lens of an 

 immersion ^^- 

 inch object-glass. 

 At first the con- 

 cave surface of 

 the front was 



made much shallower than is shown, 

 without any appreciable difl'erence 

 in effect from that of a flat plane. 

 The concave was then deepened 

 till it reached to near three times that 

 of the hemispherical back radius, 

 with a slightly improved result in 

 the way of increase of light and 

 flatness of field. The experiment 

 was not carried further. The radius 

 of the back convex is .045. That 

 of the concave, .13. Of course if 

 oil of the same optical properties as 

 the glass were to be used, the effect 

 of the concave surface would be 

 simply nil. It would then act like 

 a flat front. 



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