402 SUMMARY OF CURRENT RESEARCHES RELATING TO 



where fx sin <f>' = N ; but the principle is the same. The equation to 

 the curve presents some interesting features ; it is 



ad 

 r = C 



y/l - aW 



where C is the distance of the diagram from the lower focal plane of 

 the objective and a is a constant depending on /x and on the number of 

 radial lines in the circle ; for sixteen radial lines, and /x = 1 (drj form), 



a = * The radius representing N.A. = 1*0 is obviously an asymp- 

 tote to the curve ; in the case of the glass form, N.A. = /x will be the 

 asymptote. 



It is of interest to note that the same curve will serve for any 

 refractive index of the medium beneath which it is mounted. If we 

 change the refractive index from 1 to [x, we merely have to close up the 

 radial lines in that ratio, leaving the curve unaltered. For instance, if 

 we had 16 radii for the dry form we could use the same curve, but with 

 24 radii for a plate of glass of fx = 1 ■ 5. 



In practice the instrument proves of great utility, and very reliable 

 and easily used. All that is necessary is to be accurate in centring ; 

 this is easily seen to be correct when the reading of each end of the 

 spiral is the same. 



Dark-ground Illumination with the Greenough Binocular.* — 

 The Greenough pattern of binocular consists, says B. M. Draper, of two 

 separate Microscopes, one for each eye, with paired objectives of very low 

 power. Like other binoculars, it is particularly well-suited for use with 

 dark-ground illumination, and a good way of getting the dark-ground 

 with its higher powers is to put a stop behind the condenser. As, how- 

 ever, the front lenses of the twin objectives stand out some distance on 

 either side of what would be the optic axis of an ordinary Microscope, 

 the stop has to be correspondingly broad from side to side ; otherwise 

 direct rays would enter the objectives and would spoil the dark-ground 

 at the sides of the field. But it is not necessary that the rectangular 

 diameters of the stop should be equally great ; on the contrary, if an 

 ordinary circular stop be used, some rays are needlessly obstructed. On 

 trial, a double or twin stop, corresponding with the twin objectives, gave 

 much better results. This stop consists of two small circular patches 

 placed side by side in the same plane, and touching each other, so as to 

 form a figure of eight. It is used behind the condenser in the same 

 way as an ordinary circular stop, and with almost equal ease. It is only 

 necessary to be careful that the two circular patches shall be placed 

 horizontally, i.e. so as to be opposite the two front lenses of the twin 

 objectives. This position can easily be secured by arranging the stop in 

 the carrier approximately, and then, whilst watching the object, shifting 

 the whole condenser round in its sleeve until the best effect is obtained. 

 A standard low-power condenser such as Swift's Paragon, with its top 

 lens off, gives very satisfactory results. The twin and the ordinary 



* Journ. Quekett Micr. Club, xii. (1914) pp. 313-14. 



