instrument is so contrived as to measure double the dip
angle twice over, so that we obtain four times the required
dip, and one quarter of this angle is what must be applied
to vertical angles, measured from that part of the horizon
which has been observed.
Figure I. is thé instrument seen in perspective, and
Fig. II. is a plan of it with the telescope removed. In
order to explain its use, let A and B (Fig. II.) represent the
two reflecting glasses a t right angles to the plane of the
instrument, and also nearly a t right angles to each other.
I t is clear that when the plane of the instrument is held
vertically, an eye situated at E, and looking through the
unsilvered part of the glass A at a distant point C, will at
the same time see by joint reflection from both glasses,
another distant point D at 180° from C ; and D will appear
to correspond with C, if a suitable motion be given to the
index glass B by the tangent screw F.
The instrument may now be supposed to measure the
arc CZD. If the points C and D be each three minutes
farther from the zenith than 90°, the entire angle will then
exceed 180° by double that quantity. The relative position
of the glasses then corresponds to 180° 6', and the six
minutes of excess would be shewn on the arc a t F if there
were no index error. But, by reason of the index error*
the real quantity will not be known till a similar observation
has been made with the instrument in an opposite
direction.
I f the instrument be now inverted, so that the unsilvered
glass is uppermost, the arc intended to be measured
is CND, or the sum of the distances of the points C.and D
from the Nadir instead of the Zenith, which of course falls
short of 180° by as much as the former arc exceeded that
qUaThey difference of the two arcs is consequently twelve
minutes, and if the index be now moved till the objecfe
C and S appear to correspond, the amount of this double
difference will be shewn by the change of position of the
vernier. . ,
Hence it is evidently unnecessary that the index erroi
should be previously known, and even preferable that its
amount should be such as to avoid the needless introduction
of negative quantities by positions on different sides of
55er°in the preceding description, it is supposed that the eye
I looking directly through the unsilvered glass a t the
horizon, and tha t it also perceives the opposite horizon
after two reflections 9 but an inspection of the figure will
shew that the observer's head would necessarily intercept
the rays from the horizon behind him. To obviate this,
both the direct and the reflected rays are received in coming
from the unsilvered glass, (and after passing through the
field-glass of the telescope) on a mirror placed at an angle ot
45% which reflects them to the eye. By this ingenious contrivance,
the obstruction is removed, and the opposite points
of the horizon may be both seen a t one moment.
In practice, it is most convenient to direct the telescope
to the same part of the horizon in both cases. Thus, if the
east and west parts of the horizon be observed, and that the
index glass be uppermost, and telescope pointing to the
west, the observer is on the south side, and his face must