198 Dr Searle, The determination of the effective 
readings the track may be slightly moved so that the next pair 
of readings is quite independent of those already taken. If the 
microscope has a micrometer scale in the eyepiece, a different 
dividing line may be used for each pair of readings for the two 
ends of the diameter. 
The focal length, f; of the system is then found by any 
method—the goniometer method or the revolving table method 
is convenient *—and the value of n=f/a is calculated. 
§5. Second method. If a luminous point were placed at the 
focus F, (Fig. 2), the rays from it, after passing through the 
system, would form a beam of rays parallel to the axis AF,. If 
a glass scale were placed against the mount of the lens, as A BC in 
Fig. 2, the diameter of the beam of light could be at once read off, 
provided that the face of the scale which rests against the mount 
has a suitable matt surface, 2.e. a surface which will so scatter any 
light which falls upon it that it is easy to distinguish the parts 
which are illuminated from the parts which are not illuminated. 
The divided face of the glass scale should rest against the mount. 
The diameter of the bright patch on the scale is equal to the 
effective diameter of the stopt. 
The practical method of obtaining a beam of rays from a small 
area in the focal plane is to allow light from a flame to pass 
through a small opening in a thin metal plate placed in that 
plane. The source of light must, of course, be near enough to 
the plate to ensure that the stop is filled with light; it need not 
be so near as to burn the support of the plate. But, since the rays 
do not now proceed from a point, the emergent beam will not be 
made up only of rays which are parallel to the axis and conse- 
quently the diameter of the bright patch on the scale ABC will 
no longer be equal to the effective diameter of the stop. The 
necessary correction is, however, easily found. 
Let G be a point, in the plane of the diagram, on the edge of 
the circular opening in the plate in the focal plane, let WV, be 
the nodal point of the lens system corresponding to F,, and let WV, 
be the other nodal point. Then, if a ray from @ is directed towards 
NV, before it strikes the lens J, it will, on emergence from the lens 
L, proceed in the direction V.K as if it came from NV,, the two 
directions GV, and V,K being parallel, by virtue of the property 
* For a description of these methods see G. F. C. Searle, “ Demonstration of 
Laboratory Apparatus and Experiments,” Proceedings of the Optical Convention, 
1912, p. 161. 
+ A matt surface may be obtained by aid of paraffin wax. The scale is gently 
heated over a flame until it is warm enough to melt the wax. A thin layer of wax 
may be obtained by wiping off most of the melted wax by a piece of: paper with 
a straight edge. With a little practice, a suitable coating of wax is easily obtained. 
Mr R. Whiddington found that a good matt surface may be obtained by dabbing 
a piece of putty against the glass. 
