A sector was used in the measurement of the meridian in France, by Cassini de Thury and La Cattle, which greatly resembled the sector of Picard, except that the are was of much greater extent, being 52r and framed with three radii. The telescope was fixed at the back of the instrument, so as to be at once more firmly fastened and out of the way of the plumb-line; and, lastly its micrometer-screw was applied to the wires of the telescope (sometimes called the inttrior micrometer), Instead of moving the whole sector. lu this mode of observing, the instrument is set approximately to the star, (and the nearest dot accurately bisected. When the star is in the centre of the field, it Its bisected by the micrometer-screw which carries a wire in the focus of the object-glass, and thus the excess or defect from the nearest dot is ascertained. This improvement in the application of the micrometer serew is due to the Chevalier Louville, and in this respect we prefer the French to the English construction. See La .516ridienne de l'Observatoire Royal de Paris veriflse,' par M. Cassini do Thury, Paris, 1740. The sector is figured at page 31, and described at page lxxi.
Bouguer and La Condamine, in their measure of the arc of Peru, were compelled to fabricate their own zenith sectors, and adopted a very elegant mode of graduation, the merit of which is given by La Condamiue to their colleague Godin. The telescope and arc being prepared, a star Is selected which has pretty nearly the 911M13 zenith distance at both extremities of the arc of the meridian. Now calculate approximately the value of the chord of the double zenith distance of the star, and find what fractionalpart it is of the radius. Suppose it is nearly t4 of the radius, then take a beam compass, mark two dots on the are, and step seventeen times with the same opening along the radius, and so fix the dot over which the plumb-line is to pass. The instrument is now graduated, and. is used as follows :—After being adjusted to the meridian, the plumb-lino is made to lass over the upper dot and one of the lower dots, after which the star is bisected by the interior or Louville'e micrometer. On a following day the instrument is reversed, amid the plumbline being brought over the upper dot and the other lower dot, the star is again bisected by the micrometer. It is plain that the double zenith distance of the star, corrected for refraction, aberration, &c., is measured by the are sub tended at the central dot by time two dots below + the sum or difference of the micrometer readings. But the are is,Vy construction, that the eine of which iswhich is found from the tables; and the value of the micrometer readings being also known, the zenith distance of the star is known. The operation may be repeated at the other end of the are with the same star, and using a different submultiple of the radius. Sec .Mcaure dee trois premiers degrea du mdridien,' par M.
de la Condamine, Paris, 1751, pp. 105 et ems ; Figura do la Terre,' par M. Bouguer, Paris, 1749, pp. 170 et seq.
We insert hero the method employed by Maupertuis, La Caille, and others to ascertain the value of the total arc of the sector. A line of considerable length 11;113 carefully measured from a well-defined spot and a signal erected ; then a perpendicular was measured from the signal, of such a length as very nearly subtended at the spot the arc to be verified, and here a second signal was placed. The sector was then laid horizontally on a bed prepared for it the centre being exactly over the defined spot, and the telescope pointed to the first signal ; when this was done satisfactorily, a fine line was stretched over the centre and the first dot of the divided arc. Now shifting the sector round, the second signal was bisected, and it was seen what division was lob sected by the lice which continued to pass over the centre. The true angle is evidently that marked an the ground, and is calcu lated from the given length of the perpendicular and the distance. The value of the are read off on the sector is compared with this, and the error of the total arc detected, which is afterwards used for correcting all the angles observed. At present the value of the total arc of a sector would be determined by 0 comparison with the mural circle.
In 1775 Bird erected a zenith sector at the Observatory of Oxford, which is in most respects similar to Graham'e, but it is fixed to 811 upright pillar which revolves freely, so that the instrument is rever sible. From some cause or other, though observations have been made with this instrument, they have not been considered satisfactory. It appears to us to be an excellent instrument, and one capable of doing good work, though one chief use of zenith sectors, namely, ascertaining the index error of the meridian declination instrument, has been sup plied to modern circles by observations by reflexion.
The zenith sector of Rameden, which was used in the trigonometrical survey of Great Britain, and In the Holstein arc, is described and figured in great detail In the ' Phil. Trans.' for 1803, and in the second volume of the ' Account of the Ordnance Trigonometrical Survey of England and Wales.' It was burned in the fire which consumed a considerable part of the Tower in 1841. As this instrument very fully detailed in the amount referred to, it is useless to enter into par ticulars here. Rameeden viewed the upper dot by a long microscope, which saved considerable trouble, as well as avoided the chance of deranging the bisection by mounting to rend it. The • Astronomical Observations with Rawsden's Zenith Sector,' reduced by Lieutenant Tolland, It.E., were published iu 1342 by order of the Board of Ordnance.