218 Praesepe Group; Measurement and Reduction 



and by estimation to twentieths of a micron. The details of the 

 operation of observing runs were to set the micrometer head at 

 about 5- r o and to read on the scale as follows : 



Line 70, Line 65, Line 65, Line 70. 



These two lines were selected because they have practically the 

 same division errors, thus avoiding an extra correction, and also 

 because they happen to have more accurately determined division 

 errors than most other lines. The correction for runs need not 

 be applied to the separate readings on the stars and on the scale 

 but may be applied to the quantity ^ m directty ; for let us put 



2R= reading on Line 65, minus reading on Line 70. minus 

 10/0000. 



Dividing by 2 we obtain R, the quantity given in Table II ; we 

 must then add to ^m the correction 



T> 



— (w m) — millimetres. 



5 



This correction may conveniently be combined with the cor- 

 rection for non-periodic errors of the screw or variations in its 

 pitch ; investigation showed that the following quantities must 

 be added to observed readings of the micrometer head in order 

 to reduce them to what they would have been had the screw been 

 of uniform pitch, but of the same total length : 



Reading of the Micrometer Head. Correction in Millimetres. 



r 

 50 O. 



6.0 , , 4- 0.0005 



7.0 -)- 0.0002 



8.0 — 0.0003 



9.0. . . , — 0.0012 



10.0 — 0.0017 



11. o — 0.0022 



12.0 — 0.0021 



13.0 — 0.0022 



14.0 — 0.0014 



150 o. 



The screw is actually longer than ten turns, but as only this 

 length was used in the determination of the error of runs the rest 

 of the screw was not investigated. It will be observed that the 

 corrections progress uniformly in the interval from 9. r o to n. r o; 

 advantage was taken of this fact to make the application of the 

 corrections a simple matter. For if the micrometer head be set 

 at 9/0 when the microscope is pointed at a star, then the reading 



