ZOOLOGY AND BOTANY, MICROSCOPY, ETC. 



401 



of radial lines are drawn from a common centre, making equal angles 

 with one another ; the precise number is immaterial, but it has been 

 found convenient to divide the circle into sixteen equal parts. One of 

 these (preferably that lying horizontally) is selected as a zero, and points 

 are marked off along the others at distances equal to a constant length 

 (usually 25 mm. or 1 in.) multiplied by the tangent of the semi-angle of 

 aperture, i.e. the tangent of the angle whose sine is the numerical aper- 

 ture. This is done for every " 1 of N. A., and a spiral curve drawn 

 through the points thus obtained ; this curve being repeated turned 

 through 180°. The curves are shown with fair accuracy in fig. 38. 



The diagram is used precisely as the Cheshire Apertometer : either 

 the objective is focused on the upper surface of a cube of wood, as in 

 the Cheshire instrument, or else a pinhole in the centre of the diagram 

 is focused, and the body racked back 25 mm. or 1 in., this being 

 measured easily enough with a scale. This latter method is preferable 



6 



for objectives of high aperture. A low-power eye-piece is employed. 

 On examining the Ramsden disk with a hand-lens (a watch-maker's eye- 

 glass does well) the appearance in fig. 39 is seen, and the method of 

 estimating the value of the N.A. is fairly obvious. We have only to 

 start from the zero and count in the direction of the spiral " 1 for each 

 radial line passed over. The second figure is found by estimating the 

 position between two adjacent radial lines of the point where the spiral 

 cuts the margin of the back lens. In fig. 39, for example, the N.A. is 

 about 0*73. 



The procedure is the same with the form suited to immersion lenses ; 

 the upper surface of a plate of glass is focused, and the diagram is 

 balsamed to the lower surface. It might be preferable to have twelve 

 radial lines instead of sixteen, and read like a clock ; this is a matter 

 for experiment. 



Of course the value of the radius vector of the curve for a diagram 

 in optical contact with glass will not be quite the same as before. 

 Instead of r = C tan </>, where sin <£ = N, we shall have r = C tan <f>' 



