1892. | Repetition of Angles. 73 
The reduction of these observations by least squares gave the 
following corrections, which enter in three angle, and one side 
equations : 
(1) = —0°50 
(2) = +0°47 
(3) = 40°04 
(4) = +0°38 
(5) = —0 23 
(6) = —0°87 
(7) == +0°14 
(8) ——_ +0°24 
(9) == —1:04 
(10) = +014 
Only a few of the other angles of the triangulation were obtained 
by repetition in the manner finally adopted in the last portion of 
the work, and the other corrections are thus not generally comparable ; 
correction (3) derived from an adjoining block is also +0"-04, an. 
agreement which must however be largely due to fortuitous causes. 
The manner of observing was this :—The zero of the circle having’ 
been made to correspond nearly to one of the directions observed, 
the upper vertical axis was levelled vertical, by means of the 
level of the vernier plate, in two directions at right angles,- 
regardless of other positions. For the reversed series, the telescope’ 
was turned half round the horizontal axis without changing the 
pivots, so as to eliminate in the mean, both the collimation error and 
that due to the inclination of the horizontal axis relatively to the 
upper vertical axis. By turning the circle 180°, the first zero was 
again taken, and by relevelling the upper vertical axis with the 
level in the two directions opposite those adopted in the first series,. 
the residual level error was neutralised, as well as the error intro- 
duced by the inclination between the vertical axes. It may be 
noticed incidentally that this mode of elimination of uncorrected level 
error is also applicable to ordinary work by reiteration, provided: | 
the vertical axis is sufficiently true. To obviate so much as possible 
the play of the footscrews, a source of error which proved one of the 
most troublesome to avoid, both the circle and the vernier plate were 
uniformly turned in one direction until the direct series was completed; 
they were then uniformly turned in the contrary direction during the 
reversed series, but the angles measured, in both cases, with the 
