Measurements of Rulings on Glass. By EH. W. Morley. 1438 
ceptibly affect only the accuracy of the reduction of the differences 
to fractions of an inch, while such errors could not affect the relative 
magnitudes of these differences except by quantities which may be 
neglected. 
A plate ruled by Mr. Rutherford, of New York, was afterwards 
measured in the same way, but with less care in making contacts. 
Kighteen intervals were measured ; the differences of the two mea- 
surements of the same interval were nothing in two cases, one in 
five cases, two in three cases, three in three cases, four in one case, 
seven in one case, and eight in three cases; the unit is the four 
hundredth of a revolution of the screw head. The probable differ- 
ence of the two measurements of the same interval is sixty-seven 
hundredths of a division. If the measurements be plotted, as in the 
former case, the result is seen in Figure b. If the shorter interval 
in each cycle is subtracted from the longer, half the mean of these 
remainders is the greatest observed displacement of a line by 
periodic error. This quantity is the seventy-six thousandth of an 
inch. This is but four and one-half times as large as the probable 
difference of the two measures of the same interval. The measure- 
ments therefore cannot be used to give the amount of periodic error 
in Mr. Rutherford’s screw, while they conclusively show that it is 
much smaller than in the former case-—Lead before the American 
Association for the Advancement of Science, August 1876, 
VOL. XVII. M 
