404 
HOWARD E. PULLING 
devised and has been found to be very satisfactory. These scale 
errors are significant only at high magnifications, and r may be deter- 
mined with a good photographed scale on a stage micrometer under 
low magnification with great accuracy. Having determined r for this 
magnification, another object shoald now be substituted for the ruled 
scale. This object should possess two points that are well defined 
under both this and a higher magnification. When the distance 
between these points is determined r may be found for a higher power 
with which the original ruled scale would be useless. It is thus possible 
to proceed from lower to higher powers, substituting new objects 
when necessary until the desired magnification is reached. Although 
the method is a little tedious, it is no more so than the routine of 
ordinary accurate mensuration and is much more satisfactory than 
the use of photographed scales with the higher powers. 
The presence of the micrometer of course alters the tube-length 
and it is universally known that this must be maintained approxi- 
mately that for which the lenses were ground. Ashe^ has devised a 
very easy and accurate method for determining the tube length 
experimentally. The correct tube length D may be found in milli- 
meters from the equation {B'C)I{A — B) = D, in which A represents 
the number of spaces of a stage micrometer visible in any certain 
interval of an ocular micrometer when the tube length is D. B 
represents the number of such spaces visible in the same interval of 
the ocular micrometer when the tube length is drawn out beyond D 
by a distance C, expressed in millimeters. 
Inaccurate focusing may be the cause of large errors, and it has 
been found that the weight of the microscope and the micrometer 
may in the course of half an hour or less, depending upon the frictional 
resistance of the coarse adjustment, cause such errors in the focus that 
large variations in measurements result. Because distinctness of 
image is not a reliable criterion for judging the focus, ^ I have modified 
a method devised by Cornu and Benoit^ in such a way that it is 
^ Ashe, A., Note on the determination of "optical tube length." Journ. 
Quekett Micros. Club, Series 2. 5: 152. 1892. 
^ See: Apathy, Stefan von, Microtechnik. 2te Abt. Leipzig, 1901. 300 pp., 
and Stephenson, J. W., Observations on Prof. Abbe's Experiments illustrating his 
theory of microscopic vision. Month, Microsp. Journ. 17: 82-88. 1877. 
^ Cornu, A., and J. R. Benoit, Rapport sur la determination de I'Etalon provisoire 
International. Bureau International des Poids et Mesures. Trav. et Mem. 10: 
12. 1894. 
