MEASUREMENT OF OBJECTS 123 



and the greatest diameter of the outline of the Bacillus tuberculosis as sketched 

 with the camera lucida to be T5 mm. : then, from the formula 



D=J^ =0-003 mm. = 3/4, 



we find the length of the tubercle bacillus to be 3/4. 



A table can be readily drawn up showing the magnification obtained with 

 any combination of lenses, and such a table will save considerable time in 

 the measurement of microscopical objects. 



B. Measurement with the ocular micrometer [see footnote p. 122]. 1. The 

 stage micrometer is examined through the ocular micrometer, and the number 

 of divisions on the ocular micrometer corresponding to one on the stage 

 micrometer determined for each objective. For example, supposing that with 

 objective No. 8 one division of the stage micrometer cover five divisions on 

 the ocular micrometer, then five divisions on the ocular micrometer are 

 equal to T J^ mm., and one division to ^-^ mm., that is to 2/4. 



2. Replace the stage micrometer by the object to be measured. Suppose 

 it occupies n divisions on the scale. 



3. Now, knowing that one division is equal to 2/4, and using D to denote 

 the diameter of the object, 



T>=n x2/4. 



If the object cover for example two divisions, then 



D=4/4. 



Note. A table giving the value of each division of the ocular micrometer when 

 used with any objective can be drawn up. It is then only necessary to multiply 

 this figure by the number of divisions occupied by an object. For example, using 

 Reichert's lenses 



With objective No. 2 one division on the ocular micrometer scale =21 /j. 

 No. 4, =11,,. 



No. 8, =2-2/4. 



No. 9, =l-9/x. 



i^sth, =1*8/4. 



Thus : Suppose, using objective No. 8 (Reichert), an object covers two divisions 

 on the ocular micrometer ; then 



D =2-2/xx2 = 4-4/4. 



Similarly, an object seen through a f^th immersion lens covers three divisions ; 

 then D = 1 -8/4 x 3 = 5 '4/4. 



It will be readily understood that the higher the magnification the more 

 exact the measurement. With high powers the errors of observation are 

 reduced. 



SECTION VI.^DARK-GROUND ILLUMINATION. 



It has already been shown (p. 113) that it is impossible even with the best 

 microscopes to distinguish, i.e. to resolve, any two points less than about 

 O p l/4 apart, or to see any details of smaller dimensions than 0*1/4. 



To render small delicate objects more readily visible under the microscope, 

 Siedentopf and Zsigmondy have utilized the fact that very fine particles 

 placed on a dark back-ground and powerfully illuminated are rendered much 

 more easily visible than when examined on a brightly illuminated surface. 

 Everyone is familiar with tKis fact in connexion with the stars the darker 

 the night the brighter the stars. This is the whole principle of [the dark- 

 ground illuminator, or, as it sometimes unfortunately is termed] the ultra- 

 microscope. The dark-ground illuminator does not increase the resolving power 



