50 gray: micrometer microscopes 



vals; those of the next five (opso, 20^40, 40P60, eoPso, soPioo) are the 

 lengths of the one-fifth turn intervals in proper order. The next 

 step is to adjust these curves so that they are mutually consistent, 

 that is to say, the progressive corrections found by adding five 

 consecutive ordinates of Cioo should agree with the corrections 

 represented by Co, and any ordinate of Cioo should equal the sum 

 of the corresponding ordinates of the curves 0P20, .... 

 soPioo- If the curves are plotted to a suitable scale the additions 

 are quickly made by marking off the distances on strips of paper. 

 These adjusted curves afford a fairly safe means of interpolation 

 to obtain the corrections for intervals not actually measured. The 

 curve plotted from the sums of the components of each interval 

 is likely to lie above or below that plotted directly from the entire 

 intervals. This divergence can 'proceed from progressive error 

 or gradual change of scale value in the screw of the auxiliary mi- 

 croscope, or from thermal expansion of S; but it is of no conse- 

 quence. The adjustment is first directed towards rendering the 

 two curves parallel, then any distance separating them is divided 

 among the curves representing the components of the interval by 

 merely shifting the base lines from which the deviations would be 

 measured.^ 



After the adjustments have been completed, the curves for the 

 one-fifth turn intervals are added graphically to form a new set 

 (C20, C40, Ceo, Cso) yielding the corrections at the beginning of each 

 fifth. If interpolation is necessary, it is readily accomplished 

 graphically with sufficient accuracy. The interpolating curve 

 for any selected turn will exhibit the corrections at every drum 

 reading within this turn. Five points besides the initial zero are 

 obtained from the correction curves just mentioned. If inter- 

 polating curves are plotted for several turns evenly distributed 

 along the course of the screw, sufficient data can be obtained for 

 plotting curves (Cio, C30, C50, C70, C90) to give the correction at 

 every tenth of a turn, or oftener, as functions of the comb readings. 



5 Altho adjustments of this kind made by different computers would prob- 

 ably differ slightly, a least-square solution would be a sheer waste of effort, since the 

 differences in almost any case would affect the final corrections by considerably less 

 than the accidental error of a pointing in using the micrometer of which S forms 

 a part. 



