414 
SUMMARY OF CURRENT RESEARCHES RELATING TO 
more convergent by the field-lens L, so as to cross at Q' in the principal 
focal plane of the eye-lens E. 
We then have 
_JL 1_ _ 2. 
LP'"LP 
111 
1-e ‘ f~ LP" Sf' ’ 
since in a negative eye-piece EL = 2/ and/ 1 ' = 3/\ 
LP = |/' and PQ=|p’Q'. 
The focal length of the objective is best determined by the formula 
of Prof. C. E. Cross.* A micrometer scale divided into tenths of a 
millimetre is placed on the stage, and a second, divided into millimetres, 
at the diaphragm in the focal plane of the eye-lens, the field-lens being 
removed. The magnification m of the objective is then given by focusing 
the image of the stage micrometer upon the eye-piece micrometer. 
If p , p denote the distances of the two micrometers from the point 
which behaves as optical centre of the objective, we have 
And if I is the distance between the micrometers 
i = P +p' 
m l 
m + 1 
Then from the formula 
we have 
i 2 _ * 
p + 7~7 
/ = 
m l 
(m + 1) ! 
Determinations, made by use of the above formulas, of the focal 
lengths and magnifications of the eye-pieces and objectives of various 
makers showed how generally erroneous was the labelling. In the case 
of five eye-pieces of one of the best known of American makers, the per- 
centage of error in the value of F varied from 2-7 to 7*4, and in no case 
was f" = 3/' or d = 2f. In ten out of eleven objectives examined, the 
percentage of error was greater than 4, and for two of them it reached 
as high as 41 and 50. Application of the formula M = for various 
combinations was shown to give very inaccurate results as compared 
with determinations of the magnification made by the camera lucida. 
(D -f F) (T — f) 
For the application of the more exact formula M = — ~j =— 
* Jouro. Franklin Institute, lix. p. 401. 
