424 KRETZ. 



that quantity, the above formula follows at once. Tables with 

 the argument ^7// may evidently be constructed giving the cor- 

 rections corresponding to any value of 2r. 



Before proceeding to do so, however, let us consider the errors 

 of the screw. These are of two kinds, periodic and non-peri- 

 odic. The former were eliminated during the measurement by 

 always setting the screw to a certain reading (usually 9^^) when 

 pointing at a star during the first half of the day's work, and 

 then, upon reversing the operation, setting it always at a reading 

 differing from the former by 0.5^?. Thus each star was read 

 with the screw in both positions. In order to obviate the effects 

 of non-uniformity of pitch, certain corrections must be applied, 

 however. Investigation showed these to be : 



Corrections in Millimeters. 



ling of Micrometer Head. 



Vertical Screw. 



Horizontal Screw. 



5^ 



0.0000 



0.0000 



6 



-(-0.0004 



-t- 0. 0005 



7 



-I-0.0004 



-|-0.0002 



8 



— 0.0002 



— 0.0003 



9 



— 0.C007 



— 0.0012 



10 



— 0.0014 



— 0.0017 



II 



— 0.0020 



— 0.0022 



12 



— 0.0024 



— 0.0021 



13 



— 0.0023 



— 0.0022 



14 



— 0.0013 



— 0.0014 



15 



0. 0000 



0.0000 



The above quantities are in mm. and must be added to the 

 readings. The vertical screw was used for one plate only, No. 

 II ; the following discussion applies to it as well as to the hori- 

 zontal screw, mutatis mutandis. 



It will be seen that between gR and i iR the increase in the 

 correction is proportionate to the distance from gR. Hence if 

 we start our measures of any star with the original setting of 

 the micrometer head at gR, then the increase in the correction 

 will be proportionate to YzUi, remembering that the maximum 

 value ^7// can have is i.o, which corresponds to 2R. This was 

 always done except in certain cases to be mentioned later. As 

 the coordinates are the difference between the readings on the 



(84) 



