For the verifying of this position, or bringing it strict ly to the truth, two methods may next be recommended : the one by the meridian observation of any circumpolar star above and below the pole ; the other by the obser vation of two well-known stars over the meridian which differ considerably from each other in elevation, and ob serving how far the times of their passage differ respec tively from the exact time of each by strict calculation." We shall have occasion to consider these methods more at length under TRANSIT INSTRUMENT.
On the Repeating Circle.
THE principle to which the repeating circle owes its existence, was discovered by Professor Mayer of Got tingen. That learned and laborious astronomer, in the year 1753, communicated his invention to the Royal So ciety of that city, in a memoir upon an instrument which he calls a goniometer, the principles of which he had mentioned to other astronomers eight years before. The goniometer was intended for observing angular distances between terrestrial objects in land surveying ; and, al though far front being well contrived for the purpose, it was capable of performing this much better than any in strument known at that time.
It consisted of two bars of about a foot in length ; the lower one was attached to a stand and socket like a com mon theodolite, and capable of being turned round, or set fast at pleasure. The upper bar was connected by centre work to the lower, upon which it turned all round, and carried along with it a telescope, with cross wires for observation. The instrument had no divided limb, in stead of which, upon the end of each ruler, was made a fine clot, and the angle by IS hich the bars opened was measured, by taking off the distance between the dots in a pair of compasses, the angular value of which was as certained on a line of chords of a proper radius, diagon ally _divided to the exactness of 2'. As the two bars were required to be moved quite round upon each other, the two clots could not lie precisely in the same plane, and of course their exact coincidence could not be determin ed. This error, therefore, as well as that of the collima tion of the telescope, required some kind of artifice to remove. 'This was neatly done, by throwing these errors hack into an angle on the outside of the real point of com mencement, as will appear in the following example of the use of the instrument.
Bisect with the wire of the telescope the object to the left, having the lower bar pointed a little more to that hand, and made last to the stand. Non carry Inr•ards
the telescope, by opening the angle between the bars, and bisect the object to the right. The opening between the bars must now be taken in the compasses, and its va lue ascertained by the scale, which suppose to be 45°. With this distance unaltered, carry the back ward round the socket of the stand, until it again bisect the object on the left, and again by opening the bars, make the telescope bisect the object on the right. The angular opening of the bars must now again be ascer tained as before, which suppose to be 75°. It is obvious, that this last quantity is twice the distance of the objects and the exterior angle, and that the former was the an gular distance and exterior ancrle • therefore their differ ence is the approximate angle between the objects, and this angle taken front the first measured quantity leaves the exterior angle 15°. This last quantity enables us. to ascertain the point of commencement besides, and we have proceeded two steps in the business of repeti tion. The observations must now be continued, by turn ing the instrument backwards round the socket to bisect the object to the left, and the telescope alone must be carried forward to bisect the object on the right, and so on alternately until a great number of observations have been made ; but care must be taken, that however often the bars are carried round, the operations may finish, when they arc in a position thartheir angle may be mea sured with the compasses. Suppose we leave off when the instrument has gone through nearly a revolution, and that the opening of the bars is found to measure 44° 50', this quantity, as well as 15n, the value of the exterior an gle, taken front S60°, leaves for the whole amount of 10 repetitions 300° 1(4 and this divided by the number gives 30° 1' for the true angle. Some knowledge of the ap proximate angle is useful, to prevent the division being made by a wrong number, in cases where the repetition has been long continued. The intermediate sights, pro vided they are well taken, do not at all affect the result, and no error of the instrument is charged upon the total angle but those of the commencing and ending points ; and whatever the errors of these may be, by long conti nued observation they may be almost annihilated. With this instrument, therefore, and indeed the same may be said of all the repeaters, the patient perseverance of the observer becomes the measure of the accuracy of results obtained by them.