142 Measurements of Rulings on Glass. By EH. W. Morley. 
error may be computed in another way. If we subtract the mean 
of the whole twenty-three measurements from the successive mea- 
surements, we get the following column of residuals. If now we 
add all the successive residuals which have the same sign, we get 
the total measured displacement of the last line before the change 
of sign. In this way we obtain the column of displacements. 
ate Mean. Residuals. Displacements, 
12,237 12,299 =) (92 
12,375 a ae. ae 
12,335 . + 36 i se os 
12,200 _ Log 
12,285 ” - U4 — 117 
12,295 e He 
12 425 ” + 126 | 
12,312 f ti. i} +389 
12,210 ~ merce) 
12,185 < = ANd i = ae 
12,320 99 + .21 | 
12,352 m1 Eee: \ + 74 
12,215 Pa me | 
12.237 | ee 
12,360 a5 + 61 | 
12,375 + + 76 |$ +4 145 
12,307 if 4a 
12,230 % =; S| dae 
12,317 a BY ati | hm 
12,385 » + 86 | 
| 12,880 z + 8i + 191 
12,305 | - eer 
12,240 » — 59 | — 121 
aT 
The mean displacement, without regard to sign, is thirteen 
divisions and two-tenths ; this quantity is the eleven thousand two 
hundredth of an inch, or 0°000089 inch. This quantity is twenty- 
four times as large as the probable difference of two measurements 
of the same interval. It is identical with the previous value. 
This agreement shows that the error is proportional to the chord 
of the arc of the screw which corresponds to the measured 
interval. It may be said that since the measured intervals were 
not all absolutely consecutive, the first method probably is the 
more accurate. 
Mr. Rogers, who did not for a time admit the conclusiveness 
of the foregoing measurements, thought that the periodicity shown 
in my results was most probably due to periodicity in the micro- 
meter screw employed. But it is obviously impossible to suppose 
that to such a cause could be due inequalities amounting to a fifth 
part of its pitch. And further, the measurements were so made 
that the effect of periodic errors in the micrometer could per- 
