2 64 
Mr. Barlow on the rules and principles for 
Method of practically determining the index of refraction and 
the curvature of the surfaces of any given convex or concave lens. 
2 6. It is frequently convenient for a practical optician to 
be enabled to determine the radii of curvature of a given lens, 
and I am not aware of any rule being given for this purpose ; 
the following therefore may be acceptable. The method of 
measuring the radii of a given concave lens is very well 
known : it is simply to measure the reflected solar focus of 
each of the two surfaces ; then double these numbers will be 
the radii sought. 
The same simplicity of calculation does not present itself 
in the convex lens ; still, however, the following method of 
deducing the radii will be found by no means difficult. 
Obtain, as in the case of the concave lens, the focus by 
reflection from the hack surface of the convex lens, exposing 
first one surface and then the other to the solar rays ; mea- 
sure also accurately the solar focal length of the lens by 
refraction ; and then by means of these three quantities, 
equations may be formed which will give the radii of curva- 
ture and index of refraction. 
Let r, r ' be the radii of curvature of the two surfaces, and 
i -f- x the index of refraction let the lens be exposed to the 
sun’s rays, so that the latter are first received upon the 
surface r. Then by known optical principles the refracted 
focus at the first surface will be 
We may now therefore ( disregarding the thickness of the 
