402 
HOWARD E. PULLING 
however, that the difference in level is o.i cm. The construction for 
this source of error is shown in figure 3, in which c is assumed lower 
than & by a distance of o.i cm. and h 
Hes in the plane a-h-d which is per- 
pendicular to the axis of the micro- 
scope. Since this is the plane in 
which the protractor should move, 
the angle a-d-b is the true angle which 
should be used in all calculations. 
The angular error is obviously the 
difference between angle a-d-b and 
angle a-d-c. 
Let angle a-d-b = 15°, the maxi- 
mum angle which may be read from 
the protractor of the micrometer now 
in use. Let b-c be drawn perpendic- 
ular to the plane a-b-d and be equal 
to O.I cm. Let R = 17.5 cm. Then 
ab = 2i^-sin 7° 30' = 4.568 cm. In 
the triangle b-a-c the angle a-b-c = 
90°. Hence, bc/ab = tan b-a-c = 
0.1/4.568 cm., and bac = 1° 15' 14''. 
Since bc/sm bac = ac and sin {adc/2) 
= acl2R, then aJc/2 = 7° 30' 9". It 
must be [concluded that the error is 
negligible for even this extreme case as the instrument is sensitive 
only to minutes. 
b 
Fig. 3. Construction for the error 
caused by tilting the vernier. 
V. Errors Caused by Tilting the Ocular in Its Sleeve 
Since the protractor-carrier rides upon the vernier-arm and since 
each has a broad surface of contact with the other, there would be no 
tilting of the ocular even if it fitted rather loosely in its sleeve. 
VI. Errors Caused by the Lateral Play of the Ocular in Its 
Sleeve 
This may best be detected by setting up the instrument with the 
tip of the line in the ocular at the edge of some object in the field, 
and then attempting to move the ocular back and forth in its sleeve by 
