| | | | | |
| Step. | 1 | 2 | 3 | 4 | 5 | 6 | 7 | 8 | 9 | 10 |
+----------+-----+-----+-----+-----+-----+-----+-----+-----+-----+-----+
| Ends of |+.010|-.016|-.020|-.031|+.016|+.008|+.013|+.017|+.004|-.088|
| thread. |+.038|+.017|-.003|-.022|+.010|+.005|+.033|+.018|+.013|-.003|
| | | | | | | | | | | |
| Excess- |-.028|-.033|-.017|-.009|+.006|-.003|-.020|-.001|-.004|+.005|
| Length | | | | | | | | | | |
| Error of |-17.6|-22.6|- 6.6|+ 1.4|+16.4|+ 7.4|- 9.6|+ 9.4|+ 6.4|+15.4|
| step. | | | | | | | | | | |
| Correc- |+17.6|+40.2|+46.8|+45.4|+29.0|+21.6|+31.2|+21.8|+15.4| 0 |
| tion. | | | | | | | | | | |
+----------+-----+-----+-----+-----+-----+-----+-----+-----+-----+-----+

In the preceding example of the method an interval of ten degrees is
taken, divided into ten steps of 1 deg. each. The distances of the
ends of the thread from the nearest degree divisions are estimated by
the aid of micrometers to the thousandth of a degree. The error of any
one of these readings probably does not exceed half a thousandth, but
they are given to the nearest thousandth only. The excess length of
the thread in each position over the corresponding degree is obtained
by subtracting the second reading from the first. Taking the average
of the numbers in this line, the mean excess-length is -10.4
thousandths. The error of each step is found by subtracting this mean
from each of the numbers in the previous line. Finally, the
corrections at each degree are obtained by adding up the errors of the
steps and changing the sign. The errors and corrections are given in
thousandths of 1 deg.

_Complete Calibration._--The simple method of Gay Lussac does very
well for short intervals when the number of steps is not excessive,
but it would not be satisfactory for a large range owing to the
accumulation of small errors of estimation, and the variation of the
personal equation. The observer might, for instance, consistently
over-estimate the length of the thread in one half of the tube, and
under-estimate it in the other. The errors near the middle of the
range would probably be large. It is evident that the correction at
the middle