156 On the Focal Length [sea ee 
adjusted for glass covering, which will explain the greater dif- 
ference in the corresponding extreme values of f in the last 
column. 
The measurements in the preceding Table were made with the 
second form of apparatus, so that the length of 7 varies slightly from 
the normal length of 10 inches. The extreme values are 276 mm. 
(10-87 inches) for No. 16, and 235 mm. (9°25 inches) for No. 7. 
To ascertain the effect of this variation on f, the computed focal 
distance, the following observations were made. Ist. A Smith and 
Beck 4} inch (No. 14) was measured, first with 7 = 279 mm. 
(10°98 inches), and then with 7 = 412 mm. (16°22 inches). The 
computed values of f in these two cases were— 
7 = 279 mm., f = *2102 inch; 7 = 412 mm, f = *2035 inch, 
giving a difference of only ‘0067 inch in f for a difference of 
133 mm. (5°24 inches) in 7. 2nd. A Tolles second quality + inch 
(No. 26) was measured in the same way, giving values of f as 
follows :— 
1 = 259 mm., f = -2424 inch; J = 414 mm, f = ‘2395 inch, 
a difference of but ‘0029 inch, corresponding to a difference of 
155 mm. (6°10 inches) in 7. From these results it was inferred 
that with the maximum deviation (in No. 16) of 22 mm. (0°87 inch) 
from the normal value of /, the correction required to reduce the 
value of f to that standard length would be within the limits! of 
probable error, and in most of the objectives the deviation of / is far 
less than in this case. . 
An examination of the Table will show that the focal length of 
the objectives of some makers differs considerably from the length 
marked upon them. For example, No. 34 marked } inch is really 
a 4 inch objective; No. 33 marked } inch is really a 4 inch; 
No. 29 marked +45 inch is a 4. Lens No. 14 marked } inch is 
really a + inch; but Nos. 13,15, by the same makers, are correctly 
designated 4 inch, § inch. Differences of this kind must of neces- 
sity lead to a great confusion in comparing objectives with one 
another. I would therefore suggest that each objective made should 
be measured before being offered for sale, that this confusion may 
cease to exist. A convenient arrangement would be to fix a glass 
scale divided to 5 or +} inch in the draw-tube, sliding in the tube 
of the microscope, and measure as I have already described. The 
draw-tube should be moved till the front of the ruled glass is 
exactly 10 inches from the micrometer used as the object. Or it 
would be more convenient still to have an apparatus similar to the 
first form, but arranged with a suitable stage and stand so that it 
can be set at any desired angle. The distance 10 inches (254 mm.) 
suggested as a standard is chosen because it is the normal distance 
