ZENITH SECTOR. This instrument is, as its name implies, a portion of a divided circle, which is employed in measuring the zenith distances of stars. Picard, in his celebrated operation for determining the figure of the earth, first applied a short arc to a long telescope, thus obtaining at the same time great accuracy with portability. The instrument which he used for measuring the celestial arc between Nalvoisine, Sourdon, and Amiens, is figured and described in his tract entitled ' Mesure de la Terre ; ' • the following is a copy of his plate and description. The instrument is of ken, strengthened with edge bars, and covered with copper in the places required. The limb con tains only about the twentieth part of the circumference of a circle of ten feet radius, and is divided by transversal lines LVI:itxren] to thirds of a minute. The telescope is ten feet long, and the wires are illu minated either from the top or by an aperture on one side of the telescope. The plumb-line is enclosed in a tin tube to protect it from the wind, and the observations were always made in a close apartment through an aperture in the roof.
The figure shows all this sufficiently, and also the foot-screws for setting the axis vertical, which it is when, on turning the instrument round, the plumbline hangs before the same division of the limb. In making the observation, suppose the axis to be vertical and the limb to be towards the reader, as in jig. 1 (the limb should also be in the piano of the meridian), and the telescope directed to a star, at its transit. Now if we suppose a line to be drawn through the centre, parallel to the line of sight of the telescope. the angle between the line so drawn and the plumbline is the zenith distance of the star ; but as the point where the are is cut by the line supposed is not as yet defined, except by its parallelism to an optical and intangible line, there is as yet no measure. Bead off, however, the division on which the plumb-lino beats. Turn the instrument half round on its vertical axis, when the plumb-line remains on its former division, and the telescope points to the same zenith distance, but on the other aide of the zenith ; if, then, we would observe the same star as before, the sector must he turned on its horizontal axis through twice the zenith distance ; and as the plumbline always keeps parallel to its position, and passes through the centre, the division on which it now beats must be distant from the division first bisected by twice the angle moved through, that is, by twice tho star's zenith distance, and the division which bisects the two readings is the zero point, or reading which corresponds to the zenith. It, is not necessary that the star should be observed in both positions on the mine night, provided the centre and arc of the sector continue to have the same position with regard to the line of sight. In this
case, reversion on a following night will serve just as well for deter mining the division which corresponds to tho zenith direction of the telescope. If this reading is not that which was intended by the maker, the difference is called the error of collimation, and is applied as a correction, additive or subtractive, to all the observations, according as they are on one or the other side of the zenith.
Picard enters into no details with respect to his observations, but gives at each place a zenith distance, which is the mean of a considerable number. He only observed one star, and that to the north, namely, the Knee of Cassiopeia (s), giving as a reason. " that a star nearer to the zenith would have been more difficult to observe, and that if the star had been between the two zeniths, the error of the instrument (the division corresponding to the zenith, or error of collimation), which might have been imperfectly determined, would have been doubled in the apparent distance between the two zeniths, because then the sum of the two observations must have been taken ; whereas when a star is always observed on the same side of the zenith, there is only the difference to be taken, which must be correct, provided the instrument is well centred and well divided." In 1674 Hooke published • An Attempt to prove the Motion of the Earth from Observations.' in which he describes the instrument he contrived for observing the distance of -y Draconis from the zenith of Gresham College, and the apparatus for measuring the variations which might occur. This consisted of an object-glass of 35 feet focus length, fixed at the top of the house, and referred by two plumb-lines hanging from a bar in the object-cell and passing through apertures in the floors, to a system of wires below. Before each observation Hooke set certain marks in his wire-cell to the plumb-lines, then fixed the wire-cell, removed the plumb-lines, and bisected the star ; after the observation, he verified the position of the Wire-cell on replacing the plumb-lines. There is a great deal to admire in this simple and ingenious contrivance, but his mensurator for noting the small variations seems clumsy and inexact. " Inconvenient weather and great indisposition in his health" limited Hooke's observations to four in number. from which he erroneously concluded that there was an annual parallax of the earth's orbit, and therefore that Copernicus's theory was true. With very little alteration, such as a nicer reference of the plumb-lines to the cell of the eye-piece, and a screw micrometer for a mensurator, Hooke's apparatus would still be applicable; and if his idea of using a deep dry well for the telescope-tube were adopted, we conceive that most accurate determinations might now be made.