OP AETS AND SCIENCES. 359 



I tliink from the above results tliat we are not warranted in assign- 

 ing any error of eccentricity in the screw-head, or of sensible variation 

 in value of the different parts of the single revolutions. 



There is a sensible periodic error depending upon the entire number 

 of revolutions. This periodic error is probably a function of the 

 pressure exerted by the springs. It is not the purpose of the present 

 paper to discuss the absolute errors of the screw, but simply to point 

 out their probable amount at arbitrary intervals. 



In this screw, as in all screws adapted to exact measurement, it 

 is preferable in comparing two lengths to set the screw-head at the 

 same zero for the first line in each of the two lengths ; and if the 

 measures are made in the centre of the field the distortion of the 

 microscope lenses is insensible. 



If an eye-piece micrometer is used, it is necessary that all measures 

 be made in the same part of the field. And if that much more exact 

 instrument (in the writer's opinion), the filar micrometer, be applied 

 to the eye-piece of such a microscope comparator as described above, 

 any measure within the field will be executed with the extreme of pre<'i- 

 sion. The errors of the eye-piece micrometer screw are, in this case, 

 approximately multiplied by one-tenth of the focal length of the objec- 

 tive. It is necessary, however, to take the same precautions as with 

 the eye-piece micrometer, in regard to using the same p;irt of the field. 

 It is also better to begin with the same zero of the micrometer head in 

 consecutiv^e measures, and use the same part of the screw ; though of 

 course it is not so important here as in the case of the screw ^tage 

 micrometer. 



The preceding remarks are based upon the following considerations 

 relating to the distance between two lines which are seen in different 

 parts of the field of view at the same time : — 



1^. A distortion of this distance may be caused by the objective, or 

 the eye-piece, or both. 



2°. The lines of an eye-piece filar micrometer may be so illumi- 

 nated that the apparent distance between two lines in the field of view 

 is not truly measured in bisecting first one and then the other.* 



3°. The filar micrometer has errors of its own screw which are 

 variable for different parts of its length, but which probably are sensi- 

 bly the same for the same interval repeatedly used within a short time. 



* Professor Newconib, in his paper on the Uranian and (Neptunian) sys- 

 tems, Wasliington Astr. Obs. for 1873, points out that this source of error may 

 be remedied by using an achromatic eye-piece. It can only occur wlien tlie 

 micrometer lines and the object measured are apparently of different colors. 



