A Top Stop for the Microscope. Bij J. W. Gordon. 9 



cliiced this effect are tilted to one side relatively to the remain- 

 ing surfaces of the diatom. It is not difficult to determine the 

 angle of tilt necessary to produce the observed effect, and of 

 course the orientation of the facets is given at once by the axis 

 of the refracted beam. Thus we may obtain by means of a very 

 simple operation of stop analysis an orographical representation 

 of the surface, and so trace irregularities of contour which, ]:)eing 

 developed along the line of vision, are not to be seen except by 

 oblique illumination, and require for their detection the peculiar 

 discriminating power of the much-disparaged narrow aperture. As 

 to the exact adjustment of aperture and stop employed in these 

 experiments, I may refer you to the photogxaph of the Eamsden 

 disk which is appended to every photograph. By means of such a 

 photograph, and a scale such as is shown projected upon it, the 

 exact adjustments used are accurately recorded. The scale, I may 

 say, is, when fully divided, graduated to decimal subdivisions of 

 the equivalent focal length of the Microscope taken as a whole. 

 Thus, if the magnifying power is 1000 diameters with a camera 

 focal length of 10 in., the scale unit is y^Q in. and the degrees 

 inscriljed upon it are yooq ^^- sach. In figs. 4 and 5, however, 

 the scale is too small for useful sidjdivision, and the graduations 

 stand at distances equal to / apart. The photographs, being en- 

 largements, show both the Ramsden circle and the scale itself of 

 proportionately increased dimensions. It will, of course, be evident 

 that this employment of the equivalent focal length to measure 

 the aperture gives a systematic value to the readings. That is 

 to say, all the apertures with which we are concerned are stated 

 in terms of /. Photographers and astronomers unfortunately 

 express their measurements in terms of the full aperture, not of 

 the semi-aperture, and as an expression for the full aperture, that is 

 to say, for double the diameter of the mean zone, would be almost 

 unintelligible when used to denote the breadth of an annular 

 opening I have not been able to adopt their notation. Microscope 

 makers, on the other hand, although they employ the diameter of the 

 mean zone for expressing the angle of a lens, speak of their readings 

 under the superfluous and obscure name " numerical aperture," and 

 pedantically suppress all reference to the conventional symbol /. 

 This form of expression therefore, although it signifies exactly 

 what I have done, is so little suitable for scientific use that I have 

 hesitated to adopt it, and, choosing a middle course, have written my 

 magnitudes thus : S.A. =?i/; the letters S.A. denoting semi-aper- 

 ture and the symbol n standing for the numerical coefficient which 

 expresses the diameter of the mean zone in terms of the equivalent 

 focal length — the value which lens makers call the numerical 

 aperture. To translate this into the language of opticians generally, 

 the numerical value must be doubled and the equation written 

 A = 2 nf, whereas it may be taken as it stands for numerical 



