gray: micrometer microscopes 49 



With this second microscope the following distances are deter- 

 mined: (1) That traveled by the spider-lines as the screw (S) 

 under investigation is advanced five whole turns. (A different 

 number of turns may sometimes be more convenient.) (2) That 

 traveled during each single turn. (3) That traveled during each 

 fifth (or tenth) of a turn. It is not necessary that the screw of 

 the auxiliary microscope (A) be very accurate, because all the 

 pointings will be confined to the same portions of this screw, 

 each only a fraction of a turn long. Besides, any irregularities 

 here will be rendered negligible by choosing an objective that 

 will magnify the interval to be measured sufficiently to make its 

 image nearly fill the usable portion of the field of view. The 

 measurement of consecutive five-turn intervals for the entire 

 length of the screw is not necessary, but it is advisable in order to 

 reduce the acumulation of errors by addition in determining the 

 progressive corrections; and the extra time consumed is a small 

 item. Again, it is hardly worth while to carry out measurements 

 (2) and (3) with everj^ turn. It will usually be found sufficient 

 to measure the first and the last turn of each five-turn interval. 

 Since adjacent turns are not hkely to differ much, this grouping 

 in pairs will check blunders. 



After all the intervals have been measured, a length close to 

 the average for one turn of S is selected as a basis of comparison. 

 A multiple of ten divisions of A is convenient. By simply adding 

 the deviations of the measured five-turn intervals from five times 

 this basis, we compute the progressive corrections at the beginning 

 of each five turns, choosing the point of zero correction at the 

 middle of the screw. These corrections will be expressed in divi- 

 sions of A, and the same unit is retained in all stages of the compu- 

 tation until the end, when the correction curves are read off by a 

 scale which automatically translates into the numbers to be en- 

 tered in the final table. 



We now plot a series of curves the abscissae of which are the 

 whole turns of S, that is, the comb readings of the micrometer to 

 which it belongs. The ordinates of the first curve (Co) are the 

 progressive corrections mentioned in the preceding paragraph; 

 those of the second (Cioo) are the lengths of the one-turn inter- 



