144 



THE AMERICAN MONTHLY 



[August, 



the radius of curvature, but only 

 equal to it under special circumstan- 

 ces. If, then, a comparison with 

 such a lens were necessary in order 

 to find the rating of an objective, 

 there would need to be established a 

 standard to which the last three ele- 

 ments above should conform ; the 

 variation in such standard lenses be- 

 ing only in radius of curvature. Of 

 course such a system of lenses is out 

 of the question, and some other 

 method is necessary. The principal 

 focal length might be measured prac- 

 tically but for the trouble in carrying 

 out some of the details. It would be 

 the distance from the optical centre 

 for parallel rays to the point where 

 they are brought to a focus. The 

 first we do not know exactly, and 

 cannot find in the same way as its 

 position for diverging rays. The 

 second calls for personal judgment 

 on just when parallel rays are at a 

 focus, w^hich will admit of a slight 

 variation on either side of the true 

 position. Furthermore, the short 

 working distances of higher powers 

 would prevent the spot of light from 

 being readily observed. 



The function of focal length in gen- 

 eral is to determine magnifying power, 

 and, for all purposes of comparison, 

 it seems but natural and just to base 

 the rating on magnifying power, and 

 on that alone. Such being the case, 

 opticians seem to have generally come 

 to use for such purposes what is vir- 

 tuallv a kind of hypothetical lens pos- 

 sessing such properties that the com- 

 mon formula -.-(- -,, = - holds exact- 



f f '' 

 ly for it. It may be said, in passing, 

 that in such a lens the thickness of 

 the material would be entirely unap- 

 preciable in comparison with its ra- 

 dius of curvature, and the index of re- 

 fraction of the material woidd l)e 1.5. 

 Such being the hypothetical stand- 

 ard, the formula above holds exactly, 



and solving fory we havcy= ^, 



If, now, y represents co in the figure 



above, f will represent c' o = 10 

 inches. Therefore, we have 



10 r 



f = c o^ . 



-^ 10 — r 



But ma";nification equals — ; and sub- 



^ ^ CO 



have 



That 



is, the principal focal length of such 

 a hypothetical lens as would pro- 

 duce the same magnification as the 

 objective under the same circum- 

 stances equals 10 divided by one plus 

 the magnification of the objective : 

 and this is taken as the rating. As 

 seen, it depends entirely on magnifi- 

 cation under a standard set of condi- 

 tions, and cannot but be fair as a 

 means of comparison between objec- 

 tives of various powers from the same 

 or difterent makers. 



Applying this rule to the example 

 above, we have 



10 10 ^1 



11.3 -|- I 12.3 



This objective, on this method of 

 rating, then, would rather be called 

 an eight-tenths than a three-quarters, 

 and a variation from the true value as 

 large or larger than this will often be 

 found. 



If the objective has collar adjust- 

 ment the optical centre and equiva- 

 lent focal length vary with the posi- 

 tion of the collar, so that if an exact 

 knowledge of them is desired for any 

 given position of the collar the opera- 

 tions must 1k' performed with it in 

 such position. 



An idea of the range of power is, 

 of course, obtained by taking it at 

 the uncovered and extreme covered 

 points ; and these, with one or two 

 intermediate positions, would proba- 

 bly g-ive a sufficiently extensive knowl- 

 edge of the powers of the objective. 



In closing, it may he well to notice 

 that the above method of measure- 

 ment provides a practical way of using 

 the lo-inch tube length. This term 



