204 Permanence of the Rutherfurd Photographic Plates. 



Final Table of Non-periodic Screw-Corrections. 

 Read, of Screw. First Series. Second Series. Final Mean. 



5 



o.oooo 



0.0000 



0.0000 



7 



— .cxx)8 



+ .0001 



— .0004 



9 



— -cois 



— -0013 



— .0013 



II 



— .0032 



— .0026 



— .0029 



13 



— .0033 



— -0034 



— .0034 



15 



.0000 



.0000 



.OOOQ 



It can be shown mathematically^ that the corrections determined 

 for the various points by the above method possess very nearl}^ 

 equal weight. That the method gives results of extremely high 

 precision, is evident from the agreement of the two entirely inde- 

 pendent series. In examining these, it should be remembered 

 that unity in the fourth decimal place corresponds to one twen- 

 tieth of a micron on the scale, or 0.00005 millimetre. 



In the actual reduction of the observations, it was found con- 

 venient to combine the above errors of the screw with the ordi- 

 wa.vy correction for runs. The latter was always carefully deter- 

 mined by reading the divisions numbered 60 and 65 on the scale. 

 The distance between these two divisions corresponds ver}^ nearly 

 to ten revolutions of the screw, and as no more than two revolu- 

 tions were ever used in the measurements, the error of runs may 

 be regarded as determined with quite sufficient precision. As we 

 shall see further on, the divisions numbered 60 and 65 on the 

 scale have equal errors of division. The error of runs determined 

 from them did not therefore require correction for errors of divi- 

 sion of the scale itself. Runs were always observed at the be- 

 ginning and end of a day's work, which lasted about three hours. 

 As no appreciable variations of the run were, ever obtained, the 

 mean for the day was u^sed for all the observations of that day. 

 The run varied considerablj^ from day to day, however. 



The combined correction for run and errors of the screw was 

 obtained in the following way. Bearing in mind that the read- 

 ings of the screw increase as the numbering on the scale decreases, 

 let us put : 



i2=Eeadiiig on 60 minus Eeading on 65 minus 10.0000, 

 A;==The non-periodic screw-correction already determined, 

 8=Anj reading of the screw, whether taken on the star or scale. 



Then the complete correction for runs and screw-error, which 

 must be added to the readinsr S is : 



