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Il.—Measurements of Rulings on Glass. 
By Evwarp W. Mortey, Western Reserve College, 
Hudson, Ohio, U.S.A. 
Puate CLXXV. 
In November 1875, Mr. Rogers, while employed in perfecting the 
details of his engine for ruling lines on glass, asked me to measure 
the intervals between the lines on a plate which he ruled for the 
purpose and sent to me. It contained a hundred heavy lines ruled 
twenty-four hundred to the inch, forty heavy lines ruled four 
hundred and eighty to the inch, forty light lines ruled like the last, 
ten lines ruled twenty-four to the inch, and a hundred light lines 
ruled twenty-four hundred to the inch. My attention was given 
to the detecting and measuring any periodic errors occasioned by 
periodic errors in the screw of the ruling engine, by eccentricity of 
the screw head, and by other causes producing similar results. To 
determine this kind of inequality with the smallest probable error, 
it was obviously proper to measure, not intervals produced by a 
hundredth of a revolution of the screw, but intervals ten or twenty 
times as large. ‘Twenty-three intervals of the hundred and twen- 
tieth of an inch as nearly consecutive as possible were therefore 
measured. After several preliminary trials with objectives of foci 
ranging from two inches to the sixteenth of an inch, a nominal 
inch objective, whose focal length is really eight-tenths of an inch, 
was selected for the work. It had been found that the same care 
with this objective gave results with a less probable error than any 
other tried. Mr. Rogers afterwards suggested that even a quarter- 
inch objective was too low a power to afford the required accuracy. 
While I cannot undertake to say what instrumental appliances are 
best suited to the habits, methods, and predilections of another ob- 
server, the fact remains that for myself the work in hand could be 
done with this objective so that a given amount of care made the 
probable error of results less than when the work was done with 
either a half, quarter, eighth, or sixteenth. The fine adjustment 
of the stand was screwed hard down and left untouched throughout 
the measurements. ‘The micrometer employed was a cobweb mi- 
crometer by Troughton, having two movable wires. The screw 
heads have each a hundred divisions; the fourth part of a division 
was read by estimation. Two readings were taken for each interval 
measured, between which the screw heads were both moved several 
divisions. ‘The wires were brought to the edges of the images of 
the lines of the glass plate, till the minimum visible bright line 
between the image and the wire was the same for each wire. As 
each interval was measured only twice, one can hardly compute the 
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