304 



PROCEEDINGS OF THE AMERICAN ACADEMY 



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By means of this formula, the value of f was computed for every 5° 

 for n = 1.5; and the results, callingy:=: 100, are given in column 2 of 

 Table III. Column 1 of the same table gives the corresponding angle 

 of incidence, and column 3 the rate of change of y for small changes of n, 



or -^. This is only serviceable if we wish to compute the foci of lenses 



of various indices, but it is applicable only for value of n near 1.5 or 1.6. 

 As an example, suppose we wish the focus of a lens having an index 

 of refraction = 1.57, and inclined 45°. Then /' = 40.6 -f- .07 X •(> 

 = 41.0. The values in column 4 are computed in this way, and give 

 the foci for the lens actually employed, whose index was assumed to 

 be equal to 1.55. To compare these results with observation, the last 

 column of Table I. was reduced by dividing by 25.5, the principal 

 focal distance. The differences or errors are given in column 6, which 

 show the close agreement with theory. From these it appears that 

 the deviations are probably mainly due to accidental errors, the pre- 

 ponderance of negative values rendering it probable that the focal dis- 

 tance 25.5 was taken as too small. 



TABLE III. 



The case of the horizontal slit is more comjjlicated, since the rays 

 no longer remain in one plane. Considering only those rays in the 

 vertical plane passing through the axis around which the lens turns, 



