352 PROCEEDINGS OP THE AMERICAN ACADEMY 



XXIV. 



NOTE ON THE MEASUREMENT OF SHORT LENGTHS. 



By Lkonakd Waldo. 



Assistant at Harvard College Observatory. 



It is often desirable in practical astronomy to determine short linear 

 units with such a degree of accuracy that the errors in the unit may 

 be disregarded, in comparison with the errors of the observations in 

 which it is involved. Such instances as the determination of the 

 errors of micrometer screws, the single divisions of large circles, the 

 apertures of diaphragms and ring-micrometers, the intervals between 

 micrometer threads, may be readily cited, in which tedious numerical 

 computations and considerable observing would be avoided, if such 

 units could be readily submitted to an investigation under the very 

 high magnifying power of the microscope relative to an eye-piece. 



In the usual method of comparing short lengths with the micro- 

 scope by means of an eye-piece micrometer, we meet the difficulty 

 that no greater distance can be measured at one operation than can 

 be included within the two extreme lines of the micrometer in the field 

 of view. In this case, resort must often be had to low-power objec- 

 tives, in which event the micrometer may include a desired space 

 beyond the field of a higlier power ; but, at the best, the microscope 

 eye-piece micrometer fails in all cases where so long consecutive dis- 

 tances as 0.1 inch are to be measured. The expense of the exquisite 

 comparators made by Repsold, Froment, Brunuer Frere, and Trough- 

 ton and Simms, places them beyond ordinary reach. And the cur- 

 rent idea that exact measures must be made with the aid of arbitrary 

 scales, whose divisions may always be assumed to be relatively the 

 same, is apt to cause us to overlook the extreme precision now attained 

 in the construction of short screws, and tlie methods of measuring 

 adapted to the stage of the microscope. 



The screw stage micrometer suggested itself as an available way of 

 submitting short linear units to exact measurement, provided the stand 



