426 KRETZ. 



One plate was measured, beginning with ^.yR during the 

 first half, and g.2R during the second half of each morning's 

 work. This required the construction of a third table. The 

 method was entirely similar to the above, so that I need not 

 enter on it here. 



In the foregoing it has been shown that the screw cor- 

 rection may be put in a form to be directly proportionate to 

 y^in. But we have seen previously, that, from the nature of 

 things, the correction for runs is proportionate to the same 

 quantity. We can therefore construct a table with the argu- 

 ment y^vi, which will give at once the combined effect of both 

 corrections. For example, let us consider the case of Dec. 

 14th, 1897. From Table II we find that 2r on that date was 

 — 0.0069 mm., /. e., the means of the four differences 



Read, on 65 — Read, on 70 — loR 



was — 0.0069 mm. The screw therefore registers less than the 

 true distance, and a certain quantity must be added to each 

 i^w. By the general formula this quantity is 



(j^w) X0.0138/10 millimeters. 



Giving y^m the values o. i, 0.2 . . . i.o, and combining 

 with the corresponding screw corrections, we get the table 



^w. 



Beg! 



nning at 9.0 



Beginning at 9.5 



0.0 



+ 



0.00000 



+ 



0.00000 



O.I 





.00004 





. 00004 



0.2 





.00008 





00008 



0.3 





.OOOH 





.00011 



0.4 





.00015 





.00015 



o.S 





.00019 





.00019 



0.6 





.00023 





.00023 



07 





.00027 





.00027 



0.8 





.COO30 





.00036 



0.9 





.00034 





.00052 



1.0 





.00038 





.00068 



Tables like the specimen were constructed for each observed 

 value of the runs. The columns headed " Beginning at 9.0" and 

 "Beginning at 9.5 " give the corrections in mm., to be applied 



(86) 



