48 gray: micrometer microscopes 



.". Lj^ — L^ = 1168.0 divisions. Since the magnification by the 

 microscopes was such that 1 division = f m 



L^ - L^ = i oi 1168.0 = 876.0 m. 



The accuracy that can be obtained with microscopes having 

 errors even as large as those Hsted under A in Table 1 is shown by 

 measuring three times with each of a pair the same interval of 

 999.05 M = 1332 (f m). The results are recorded in Table 2 

 below. In each series the center of the field was located consec- 

 utively near the right edge, the center, and the left edge of the 

 image, so as to obtain wide variations in the corrections, which 

 were taken from a correction table of the type described. Part of 

 the deviations from the averages are to be ascribed to inaccurate 

 focusing and another part (perhaps )to linear interpolation, which 

 is not altogether justifiable with such large and irregular periodic 

 errors. Nevertheless, the agreement is even better than would 

 have been predicted. 



The calibration of a microscope by one of the processes usually 

 described involves such laborious computations and least-square 

 adjustments that it is no wonder to find it attempted only as a 

 last resort when the demands of high accuracy compel. While, of 

 course, the complete calibration of any divided scale requires con- 

 siderable time, it is, however, possible to determine microscope 

 corrections more accurately and with less labor than would appear 

 from previous accounts. The whole procedure can be made one 

 of direct measuremxcnt and simple graphical addition. 



In determining the screw errors it is customary to use the ocular 

 of the microscope under investigation for viewing the displacement 

 of the spider-lines. An enormous gain, however, is secured by 

 removing the ocular and measuring the displacements by means 

 of a second micrometer microscope.^ 



•• The use of an auxiliary microscope for this purpose was first brought to my 

 attention by Mr. E. D. Tillyer, of the Bureau of Standards, to whom I am indebted 

 for many valuable suggestions and criticisms. He informed me that it was the 

 regular practice at the United States Naval Observatory. (See J. C. Hammond : 

 Introduction to Publications of U. S. Nav. Obs. 6, A XIII. 1911.) Sir David Gill 

 (Roy. Astrom. Soc. Monthly Notices 45, 65. 1884) also employed a compound 

 microscope in a simple apparatus he designed for rapidly and accurately investi- 

 gating screw-errors; but his method is in several respects inferior to that of the 

 Naval Observatory. 



