ference of each step from itself, and by
repeating the numbers already found in symmetrical positions with
their signs changed, since the excess of any step, say 6 over 3, is
evidently equal to that of 3 over 6 with the sign changed. The errors
of each step having been found by adding the columns, and dividing by
10, the corrections at each point of the calibration are deduced as
before.

TABLE II.--_Complete Calibration of Interval of 10 deg. in 10 Steps._

+--------------------------------+------+------+------+------+------+------+------+------+------+
| Lengths of Threads. |1 deg.|2 deg.|3 deg.|4 deg.|5 deg.|6 deg.|7 deg.|8 deg.|9 deg.|
+--------------------------------+------+------+------+------+------+------+------+------+------+
|Observed excess-lengths 0 deg. | -28 | -32 | -47 | -62 | -11 | -15 | -48 | - 2 | - 8 |
| of threads, in various 1 deg. | -33 | -21 | -47 | -28 | +14 | - 8 | -22 | +21 | +24 |
| positions, the 2 deg. | -17 | + 2 | - 8 | + 1 | +26 | +23 | + 6 | +58 | |
| beginning of the 3 deg. | - 9 | +26 | + 5 | - 3 | +41 | +36 | +28 | | |
| thread being set 4 deg. | + 6 | +31 | - 7 | + 4 | +45 | +49 | | | |
| near the points. 5 deg. | - 3 | + 5 | -15 | - 6 | +43 | | | | |
| 6 deg. | -20 | + 7 | -16 | + 2 | | | | | |
| 7 deg. | - 1 | +23 | +10 | | | | | | |
| 8 deg. | - 4 | +29 | | | | | | | |
| 9 deg. | + 5 | | | | | | | | |
+--------------------------------+------+------+------+------+------+------+------+------+------+

TABLE III.--_Solution of Complete Calibration._

+------------+------+------+------+------+------+------+------+------+------+------+
| Step No. | 1 | 2 | 3 | 4 | 5 | 6 | 7 | 8 | 9 | 10 |
+------------+------+------+------+------+------+------+------+------+------+------+
| 1 | 0 | - 5 | +11 | +20 | +34 | +25 | + 7 | +26 | +23 | +32 |
| 2 | + 5 | 0 | +16 | +23 | +39 | +29 | +12 | +31 | +28 | +37 |
| 3 | -11 | -16 | 0 | + 8 | +24 | +13