gray: micrometer microscopes 47 



negative of the total correction to the reading R'. Reversing the 

 sign of aR is merely a matter of convenience. It is usually suffi- 

 cient to enter the corrections for every tenth of a turn and to 

 obtain those for the hundredths by interpolation. A convenient 

 arrangement is one similar to that followed in most mathematical 

 tables: the whole turns are indicated at the side and the tenths 

 at the top. 



The displacement corresponding to one division ( = 0.01 turn) 

 of the microscope may differ so little from 1 n that only small cor- 

 rections will be required to reduce the readings to microns. It may 

 however, well happen that reduction to the desired length unit 

 might require corrections so large as to be inconvenient. It then 

 becomes advisable to select an auxiliary unit corresponding to 

 the average screw-value, and to express all corrections in terms 

 of this unit, which should be the same for both microscopes.^ It is 

 further advantageous to minimize the magnitude of the correc- 

 tions by adjusting both microscopes to give almost the same mag- 

 nification — if possible one that permits a simple reduction factor. 

 Then all computations can be made in terms of the auxiliary unit, 

 multiplication by the reduction factor being deferred until the end. 



Another gain is effected by recording obser^'ations in such a 

 form that the corrections can be added directly without any copy- 

 ing of figures. For example, the complete record and computation 

 for a single comparison of two bars A and B would appear about 

 as follows: 



' All these considerations apply with increased force to a larger group of micro- 

 scopes, for example; a group of four used to read a divided circle, or several used 

 to step off a considerable length by means of a bar reaching from one microscope to 

 the next. 



