1885.] 



MICROSCOPICAL JOURNAL. 



143 



ing distance, it is found to be .295. 

 Taking this from .885 gives .59 as 

 the distance of o back of the front of 

 the objective. This position corre- 

 sponds to a value ofr'(; = 9.925 inches, 

 which differs from 10 by .075 inch. 

 Now, if greater accuracy is desired, 

 readjust the draw-tube so that the 

 screen shall be at 10.59 inches from 

 the front of the objective ; that is, at 

 10 inches from the determined posi- 

 tion of 0. Now. repeating the meas- 

 urements, we find rc'= 10.8S3 and a' U 

 = .113; 



10.883 X. 01 QQ O 



hence, c = = .0640, 



.123 



and c o = 10.S83 — .8848 = 9.9982. 



This differs from 10 inches by 

 .0018 — a quantity unappreciable in 

 such measurements. Taking again 

 the ^vorking distance, we find it to be 

 .293 inch, which, taken from c o, 

 gives .5918 inch as the corrected dis- 

 tance of o from the front of the ob- 

 jective. This may safely be taken as 

 the desired position, correct within 

 the usual observational error in such 

 work. As may readily be seen, an 

 attempt at a recorrection of this might 

 be made in the same way that this 

 was corrected from the first ; but the 

 errors of observation would probably 

 be greater than the proper correction, 

 so that such observations would pos- 

 sess no additional weight. 



The magnification, as above stated, 



,10 .... 10 



equals equals, m this case, ^-^ 



c o .8040 



= 11.3, though this has been found 

 previously by the actual measure- 

 ment of a' b' compared with a b. 



It may be of interest to compare 

 this result with those derived from 

 some of the other formulae in use as 

 approximations. First, there is the 

 common rule, ' Divide 10 inches by 

 the focal length of the objective' or 



o = 135. This rule assumes that 



the objective is exactly a |^, and that 

 the object is placed at the principal 

 focal distance from the centre, in order 

 to form an image at 10 inches dis- 



tance. The first assumption may or 

 may not be true, as objectives often 

 difier considerably from their rated 

 ^•alues. The second is inaccurate, 

 as the distance is always greater than 

 the principal focal distance. 



/ 

 . , . 10 — ^ 



or, m this case, ;// = 



Next, there is the formula /;/ 



T '>J- 



This assumes the rating of the ol> 

 jective to be correct, and makes use 



of the formula -A- ., = , which is 



. f f '' 

 only approximately correct. 



Another method proposed is to 

 measure the distance 10 inches from 

 the front of the objective, and then to 

 measure by a screen the magnified 

 divisions of the micrometer. Per- 

 forming these operations, we find in 

 this case m -- 10.55. This method 

 will always give a result too small, 

 and varying with objectives of tlie 

 same focal length coming from dif- 

 ferent makers. 



Next, as to the rating of the objec- 

 tive. This is usually defined as the 

 principal focal length of a simple 

 lens, which, under the same circum- 

 stances, vyould produce the same 

 magnification. That is, it is the 

 principal focal length of a double 

 convex lens of equal curvature on 

 each face, such that if substituted for 

 the objective, and so placed that the 

 distance from the image to the centre 

 of the lens is the same as that be- 

 tween the image and optical centre of 

 the objective, the magnification will 

 be the same as that produced by the 

 objective. The principal focal length 

 of such a simple lens depends, how- 

 ever, on four elements: ist, the ra- 

 dius of curvature of the faces ; 2d, the 

 refractive index of the material of 

 which it is made ; 3d, the thickness 

 of glass ti^aversed by the ray ; 4th, the 

 distance from the principal optical 

 axis to the parallel ray. Within the 

 limits for ordinary glass lenses, how- 

 ever these elements may vary, the 

 principal focal length is not far from 



