410 Mr. R. W. Cheshire on a ^eio Method of Measuring 



too small therefore to permit of a prism being cut from it 

 with which to conduct the ordinary examination ; on the 

 other hand, it may be considered undesirable to deface or 

 injure the lens in any way which would militate against its 

 subsequent use in an optical system. One of the most 

 obvious methods of solving the problem is to measure one or 

 more of the optical lengths associated with the simple lens, 

 the principal focal length or the back focal length for some 

 specified wave-length, and to supplement this information 

 with measurements of the radii of curvature of the lens 

 surfaces and the axial thickness at the vertex. A knowledge 

 of these quantities is theoretically sufficient to enable one to 

 calculate the index of refraction of the glass for the wave- 

 length employed, but a little consideration will suffice to 

 show that the limitations of practice restrict the accuracy 

 possible in the determination of the retractive index to a 

 figure appreciably higher than one in the fourth place of 

 decimals, with a corresponding greater relative inaccuracy 

 as regards the partial dispersions. In the first place, the 

 ordinary type of spherometer in which the three fixed points 

 lie on a circle of diameter 1^ in. to 2 in. is, in many cases, 

 useless for the measurement of the curvatures of the surfaces. 

 The small lenses used in the construction of micro-cope 

 objectives, eyepieces, and the smaller sized telescope ob- 

 jectives require to be examined on a special optical sphero- 

 meter designed to deal with these small apertures. Various 

 optical devices involving the use of the lens surfaces as 

 reflectors have been suggested and employed from time to 

 time, but none of these methods aim at or secure an accuracy 

 of the order of 1 in 5000 which is the present desideratum. 

 And it should further be remembered that even this accuracy 

 is not sufficient for the determination of the partial dispersions. 

 Secondly, as regards the determination of focal lengths or 

 of back focal lengths, the presence of spherical aberration in 

 the simple uncorrected lens very seriously limits the reliance 

 to be placed upon the observations. In the most favourable 

 case, that of a convexo-plane lens, the ratio of the longitudinal 

 spherical aberration for the extreme ray to the focal length 

 may be taken to be approximately represented by (A//) 2 , 

 where / denotes the focal length and h the semi-linear 

 aperture of the thin lens. But, in order to secure reasonably 

 good definition and an absence of depth of focus, a semi- 

 aperture of at least// 4.0 is advisable, corresponding to axial 

 spherical aberration amounting to about 1 part in 1500. 

 When all these factors are taken into consideration it will 

 be seen that the accuracy to be expected in the determination 



