Mtvichestcr JMemoirs, Vol. Iv. (191 1), No. *i\. 5 



reading will give i/z', hence their numerical sum will be 

 ijf. In the example shown /^ = 04, and i/«-2'5 ; ^' = o•25 

 and i/^' = 4. Hence D^6'5. 



For concave lenses there is more difficulty in finding 

 focal length, for there are no good direct methods available. 

 The best way is to combine the concave lens with a more 

 powerful convex lens. In optological practice this is 

 accomplished by the help of a box of lenses — called a 

 " test case " — from which a convex lens can be selected so 

 as to neutralise the negative lens. 



A very useful and interesting method of investigating 

 the power of a lens is to observe a uniform scale through 

 a small pin-hole, and to notice the displacement of the 

 scale divisions when a lens with a stop of definite aperture 

 is interposed. The use of the pin-hole prevents errors due 

 to parallax and no focussing is required, but the scale 

 must be well illuminated. Since the images formed by the 

 lens are not observed, only the deviation of the rays being 

 measured, the method is applicable to both converging 

 and diverging lenses. The power in dioptries may be 

 read off directly from any uniform scale in the following 

 way : Observe the scale A {Fig. 4) through a pin-hole H 

 and a circular aperture EG in a disc DD. Let the radius 

 of the aperture be a scale divisions, the distance from the 

 pin-hole H to the centre C of the aperture be y metres, 

 and the distance from C to the centre N of the scale x 

 metres. The point M of the scale will be on the boundary 

 of the field of view, and the number of scale divisions 

 visible on each side of N will be : — 



«HN/HC = a(x- + r)/j. 

 Let the scale division at M be marked zero. Place the 

 lens to be tested in contact with the disc DD, with its 

 axis in the line HCN, then the rays of light entering H 



