THE ANGULAR MICROMETER 
397 
The vernier arm is clamped to the microscope and remains fixed during 
the progress of any measurements. The protractor-arm, h, is clamped 
to the ocular so that by turning the screw, e, attached by swivel joints 
to a and h, the system, vernier-ocular, is rotated about the common 
center. In making a rneasurement the tip of the line in the ocular 
is brought against the edge of the image formed by the object to be 
measured, as in figure 2, c. The protractor is then read with the aid 
of the vernier to minutes of arc. The ocular and protractor are then 
rotated about their common axis until the tip of the line in the ocular 
appears at the outer edge of the image. The position of the protractor 
is again read and the difference between the two readings is the 0 of 
the equation given above. 
The other quantity in the equation which must be known in order 
to determine x is the radius, r. Since the line in the ocular is fixed 
in its position relative to the axis of the microscope, one determination 
of r is all that need be made for each system of lenses. To determine 
this radius a suitable scale is placed on the stage of the microscope 
and 6 is determined for some convenient interval of the scale, as 
described above. The value of the interval in units of length is sub- 
stituted for X in the equation, the corresponding value of 6, as read 
from the protractor, is introduced, and r is determined algebraically. 
This value of r may then be used, with the same system of lenses, 
for future measurements. 
The micrometer is constructed of an alloy of aluminium which 
is very rigid, is light enough to avoid tipping the microscope 
tube, and whose coefficient of thermal expansion is very low. This 
alloy, known as a "White Metal" mixture, is composed of 92 per- 
cent aluminium and 8 percent copper. The graduated members, 
vernier and protractor, are of coin silver and must of course be as 
accurately graduated as possible with very fine lines. The screw with 
its milled head is fixed to a swivel block attached to the vernier-arm 
and works in a threaded bearing attached to the protractor-arm by 
another swivel joint. This screw may be dispensed with, although it 
adds to the ease with which delicate adjustments may be made and 
reduces the pressure on the vernier-arm during the time of making 
these adjustments. Pressures of the hands in moving the vernier 
tip the microscope tube, and this changes the path of light through the 
lenses, the focus, and the apparent position of the object to be meas- 
ured. This adjusting screw should be affixed as close as possible to 
