305 



the 4 portions of the measuring har with the metre, while standing 

 on one side of the comparator, repeated the observations standing 

 on the other side. 



To distinguish the observation-series from each other, we shall 

 call those which were made while the observers were in their original 

 position with respect to the comparator, A, those in which thej were 

 on the other side. B, the series in which the mark on the metre 

 lay to the right of the observer r, tliat in which it was on the 

 left /, while the first of two identical series we shall call 1 and 

 the second 2. For each portion of the measuring bar each observer 

 therefore took 8 series of observations A)\ , Ar,, Al^ , Al^, Br^ , B?\, 

 Bl^, BI^. Care was taken, that when the first series was begun 

 with the metre, the second identical series should begin with the 

 measuring bar. 



5. Rims and errors of the micrometer screws. For the purpose 

 of determining any possible changes in the runs of the micrometer 

 screws, the length of the millimetre divided into 10 marked on the 

 measuring bar near the end lines was measured every day before 

 and after the measurements, with both of the microscopes. From 

 the results it appeared, that the value of the run, which \vas approxi- 

 mately 200 micromillimetres, did not change perceptibly. As, however, 

 it was not certain, that the millimetres on the measuring bar were 

 of exactly the correct length, the absolute value of the run was 

 afterwards determined by measuring out a distance of 1 centimetre 

 divided into millimetres on a measuring rod of nickel-steel belonging 

 to the Observatory in Leiden, supplied by the Société Genevoise, 

 the errors of division of which had been accurately determined in 

 Breteuil. For all the measurements the same value of the run is 

 assumed, viz. 198.69 micromillimetres for the microscope marked I 

 and 199.82 micromillimetres for the unmarked microscope. 



Moreover the periodic errors of the micrometer screws were 

 determined in tlie observatory at Leiden, by measuring distances 

 equal to a half and a third of a turn. The continuous errors were 

 determined by measuring a larger distance, with portions of the screw 

 situated symmetrically with respect to the zero. 



For micrometer 1 the correction formula of the readings in parts of 

 the divided head, was found to be: 0.18 /S'w (z* + 17°); the influence 

 of the term dependent on the double of the reading was imperceptible. 



In the unmarked microscope no periodic errors could be detected 

 by the observations. 



The continuous errors were imperceptible in both microscopes. 



