68 



THE AMEKICAN MONTHLY 



[April, 



The large, clear marginal space caused 

 a little glow of diffused light within 

 the lens, so that as the draw-tube was 

 closed a gauzy mist covered the clear 

 part of the field. 



The clear front of the ^-inch ob- 

 jective measured .36-inch. A stop 

 .3-inch in diameter allowed no part 

 of the object to be seen, though light 

 enough was admitted to define the 

 margin of the field. Smaller stops al- 

 lowed more and more of the object 

 to be seen, and one of .2 -inch only 

 appeared as a very small, indefinite, 

 black point in the centre, with the 

 usual penumbra about it. 



The following table gives the dia- 

 meter of the portion of the front lens 

 included by the angle at the princi- 

 pal focus, both of the telescope and 

 the microscope, as well as the full 

 size of the clear front of each: — 



In comparing these figures it will 

 be seen that in the case of the single 

 lens one-inch objective, the "avail- 

 able" front is the whole front when 

 used as a telescope, and as a micro- 

 scope when used with the standard 

 length of tube. It is cut down when 

 the shortening of the tube makes the 

 mounting of the lens act as a dia- 

 phragm and prevents the marginal 

 rays from reaching the field-glass of 

 the ocular. 



It will also be noticed that in the 

 two system glasses, the construction 

 of the objective is such as to dimin- 

 ish this " available " front most in the 

 widest angled glass, viz.: in the ^- 

 inch which has 38° angle by telescopic 

 and 39/^° by microscopic measure- 

 ment, being what is properly consid- 

 ered a wide-angled glass for its power. 

 In this case the full field of .36-inch 

 is reduced to .20 in telescopic use, 

 and even to .08 in the microscopic use. 

 It would be a very great mistake, 

 however, to suppose that the remain- 



der of the front is not useful, for we 

 have seen that a paper stop .30-inch 

 in diameter was required to shut out 

 the whole field. Referring to the fig- 

 ures 25 and 24, it will be seen that the 

 whole cone of rays m b I' contributes 

 to make the image of the point b at its 

 conjugate focus b' , and of this cone 

 the portion m b n would only be one- 

 quarter Qti m b I when m n is half of 

 m /, for the circular areas will be to 

 each other as the squares of the dia- 

 meters. In using it as a microscope, 

 therefore, nearly four times this so- 

 called " available " field is useful in 

 transmitting irriage-making pencils 

 which go to perfect the image at the. 

 conjugate focus in the ocular, and 

 nearly sixteen times if we reckon the 

 the areas of sections of the cones of 

 rays. In other words, the maker of 

 the objective has combined his lenses 

 so as to use, or make available, the 

 whole front except the narrow annu- 

 lus .03-inch in width at the very mar- 

 gin of the lens, or only one-twelfth of 

 the whole. It should be further no- 

 ticed that the difference between the 

 true front and the so-called " avail- 

 able " is greatest in the widest angled 

 glass and least in the narrowest. Con- 

 sequently when compared with work- 

 ing-distance, a measurement of the 

 angle at principal focus seems to 

 make less of the front available than 

 in inferior glasses, which is not true. 

 Still another point of importance is that 

 the shortening of the tube acts con- 

 versely in its effect upon this '' avail- 

 able " front in the case of the two uses 

 of the instrument. Used telescopi- 

 cally, the shortening of the tube in 

 the two-system glasses enlarges this 

 part of the front, whilst it is dimin- 

 ished in the microscopical use; and 

 both these results are such as follow 

 directly from the elementary princi- 

 ples referred to at the beginning. 



These considerations may fairly be . 

 regarded as indicating: First, that the 

 measurement of the telescopic angle 

 of field is not the true measurement 

 of the angular aperture of the micro- 

 scope. Second, that in low-powers 



