The top of the column finishes in a square bar, to which the upper works and circle are firmly @crowed. We shall first describe the motions which are required for astronomical purposes, and point out the rest when the geodcsical properties of this instrument are con sidered. The azimuthal circle Is scarcely to be considered a part of the instrument.
The front telescope, its verniers, and clamp, are seen distinctly in front. (Fig. 1.) This moves very freely on a spindle within the axis of the circle. There is a level behind, a projecting end of which is seen in the figure. This and its accompanying back telescope are— one a little above and the other a little below the axis of the circle, and revolve 011 a collar which works on the outside of that axis. These can he fixed in any position by a clamp (also seen in the figure) which embraces the hack edge of the circle : the back telescope is for mea suring terrestrial angles. Finally, the axis of the circle Itself passes through a fitting, on which it also tunin freely, carrying tcleacopen, level, &e., without altering their position in respect to itself. There in a clamp to restrain this motion and fix the circle, the head of which is seen at a, jig. 2, and a tangent screw for slow motion at a. This is the weakest and most Inconvenient part of the instrument, for the be the zenith distance of the star, and the errors of division or of reading off will also be divided by twenty. If the number of repeti tions which can be taken at one culmination are not thought euthicient to destroy these errors, the series may be prolonged on the following and subsequent nights, starting from the preceding reading without disturbing the verniers, until any number whatever aro taken, the only essential condition being that, in reversing, the level is undisturbed both in its attachment to the circle and in its own zero ; and that in bringing the telescope on the star by turning the whole on its hori zontal axis, the connection between the telescope and circle is perma nent. The hour, minute, and second at which each bisection is mad c are to be noted.
We have said that it is better to read off the level than to attempt to bring the ends of the bubble exactly to the same division, which is really an impossible condition with one observer, and scarcely practic able even with two. The differences should be as small as they can be
made with moderate care and in a moderato time; but a well-ground level will measure small arcs better than any graduated limb or even than any small telescope can do, and it is therefore as safe to correct for an error of level as to adjust. The level readings should be regis tered as towards the object end and eye end, or — and +, along with the times, and the correction may be made to the final arc. It is clear that if the level were always brought.to the same divisions, there would be no level error. The effect of a derangement of the vertical axis, which is shown by the level, is calculated as follows :—Let the reading of the level end towards the object be 10° larger than the reading towards the eye. To correct this, the footscrew towards the observer should be raised 5", when the two readings will agree; but now the telescope points 5" below its former position, in which it bisected the star correctly. The telescope therefore must be raised, that is, the zenith distance must be diminished 5" ; hence if 5" be sub tracted from the multiplied zenith distance on account of that observa tion, the error would be corrected, and so on with every other instance.
• The rule is, add together all the level readings towards the object end, prefix — ; do the same with those towards the eye end, and prefix +*; take their algebraic -.divide by twice the number of observations, and the result is the correction to be applied with its sign to the mean zenith distance. This will generally be a very small quantity. As the great difficulty in observing out of a regular obser vatory is in the reading off, the division of the level might be to every 2", but numbered as single seconds. These would be better seen, and the divisor of the difference would be the number of observations. When the instrument is very small, and the probable circumstances under which the observer may be placed promise few facilities, the scale may be cut to 10" only, with bold lines. A mistake of one or two tenths in guessing the subdivisions would be very rare, and scarcely cause a sensible error in the final result.