422 KRETZ. 



by using an inaccurate value of the division errors was still 

 further reduced. 



In the table on p. 423 the corrections, which must be added 

 to the measured 3^ ni. with the sign shown, are given in milli- 

 meters. The argument is the number of the line. When two 

 lines were used, the mean of the corresponding corrections was 

 applied to ^ ?«. 



Corrections for Runs and Screw Errors. — As has already 

 been stated, observations were made for runs twice a day, once 

 by each observer. A complete observation always consisted of 

 two determinations, made as follows : The screw being set at 

 about 5 R (the R representing revolutions), the spider-threads 

 were set on the line 70, and the micrometer head was read. 

 Then, without moving the microscope, the screw was turned 

 until the threads bisected line 65, and a reading was taken. 

 Then once more on 65, and back to 70, and the observation 

 was completed. The lines 65 and 70 were selected as they 

 have nearly the same division errors. Since the screw makes 

 two complete revolutions while the threads cover the distance 

 of one millimeter on the scale, and since the screw readings in- 

 crease when the threads are moved in a direction opposite to 

 that of increasing numbers on the scale, it is evident, that, if it 

 were not for runs, the readings on line 70 would be less than 

 those on line 65 by exactly 10 R. If that is not the case, then 

 the correction to be added to any observed % w in order to 

 reduce it to the case of no runs of the screw, is 



y 



— {)4"') ^ millimeters, 



where • 



2r = Read, on line 65 — Read, on line 70 — loA". 



Thus 2r is the total error of runs on ten revolutions ; for each 

 day of observation it is evidently equal numerically to the "Runs 

 in mm." of Table II. For one millimeter the error will evi- 

 dently be i/^- 2r/5, the factor ^ reducing the quotient to mm. 

 And since the correction to each ^ 7n must be proportional to 



(82) 



