398 
HOWARD E. PULLING 
the microscope-tube in order to maintain the center of gravity of the 
instrument near the axis of the tube, and, to increase the ease of 
manipulation, the milled head of the screw should be large. 
The glass slip, c, may be either cemented to the annular disc in 
the ocular and remain there permanently, or it may be cemented to a 
short tube closely fitting the ocular but removable. The first method 
is preferable, since it maintains r constant for a given objective. 
This arrangement does not interfere with the ordinary use of the 
ocular because the line is very fine, very short, and in no way confuses 
the vision; almost the entire field remains unobstructed and a slight 
rotation of the ocular changes the position of the line. In default of a 
photographed line, one may be scratched on a thin, circular cover-slip 
with a fine cambric needle; such a Hne will serve equally well, since 
only its tip is used and the straightness and slope of the line are of no 
importance. The tip should be sharp and distinct because the exact- 
ness with which it may be placed against the object-image controls 
the accuracy of all measurements. The first micrometer that has 
been constructed on this plan was built at a cost of $23.00. This 
instrument however did not possess the adjusting screw, e, which 
would of course add to the cost. On the other hand, because various 
alterations in the design of the instrument were found necessary during 
the progress of the work the figure given should include a large part 
of the cost of the adjusting screw. 
The errors to which the angular micrometer is subject by reason 
of its construction may next be considered. 
I. Failure to Center Protractor and Vernier 
Case I : Centers of protractor and vernier on a line at right angles 
to the zero radius of the vernier. (See construction in figure 2.) In 
the figure the circle A-A' is that of the fixed scale upon which the 
angles are read. B-B' is the circle traced by the protractor as the 
pointer in the ocular moves across the image of the object to be 
measured. The angles 182, 183 are the angles as read, being those 
through which the pointer in the ocular apparently moves. The 
angles 71, 72, and 73 are the true angles corresponding to the first 
mentioned, and are those through which the pointer in the ocular 
actually does move. The center of the vernier, a, and the center of 
the protractor, h, lie on a Hne perpendicular to the zero radius of the 
vernier a-d. 
