In dividing, the points of the beam compass should never be brought nearer together than two or three inches, except near the ends of the arch or line to be divided ; and there spring-dividers, having round points, which may be put in and taken out occasionally, will best answer the purpose.
The next thing to be considered is, the method of mak ing the points. The prick-punch for this purpose must be extremely sharp and round, the• conical point to make a pretty acute angle ; and as the points herewith to be made should not exceed 0.001 of an inch, when linear divi sions are to be cut from them, a magnifying glass of 3 inch focal length should be used ; by the assistance of which, the impression or scratch, made by the points of the beam. compass, will be very conspicuous; and if the said im pression be not too faint, feeling, as well as seeing, will greatly contribute to make the points properly.
It is scarce necessary to say any thing about the arc of 96°. I shall only mention, that it contains 1536 divisions; is to be divided into three equal parts, in the same manner as the arc of 90°. Each third contains 512 divisions; which number is divisible continually by 2, and gives 16 in each 96th part of the whole arc.
This arc of 96, (so far as I know,) was first applied to the iron quadrant in the Royal Observatory, in the year 1725, by my late worthy friend, Mr George Graham. It was not only a severe check upon that great mechanic, but will be so to all others, who divide the two arcs upon one and the same instrument ; yet, if the above instructions be strictly followed, the agreement between the two will be surprising, and differ very little from the truth.
The next step is, to cut the linear divisions from the points. The best instrument for this purpose is the beam compass, having both its points conical, and very sharp. Draw a tangent to the arc b d, suppose at e, it will inter sect the arc x y in q ; this will be the distance between the points of the beam compass to cut the divisions (nearly at right angles to the arc b d.) Lodge that point of the beam compass next your right hand, in the point r; let the other fall freely into the arc, x y ; press gently with your finger upon the screw-head, which fastens the socket (this must be convex, and right over the point ;) and, with the poin, towards the right hand, cut the divisions.—In this manner you must pro
ceed with the rear.
Having finished the divisions of the limb, the nonius divisions arc next to be divided. Choose any part of the arch, where there is a coincidence of the 90 and 96 arches, which let be at e: Draw the faint arcs s t and i k, which may be continued to any length towards A, upon which the nonius divisions must be divided in points ; a tangent line, as before, intersecting this arc, gives the distance of the points in the beam compass. Now as the nonius divisions of the arc 90° subdivide the divisions of the limb of the mural arc at Greenwich to half a minute, 11 divisions of the limb being equal to 10 upon the nonius plate (a num ber which only 5 and 2 will divide) recourse must again be had to computation. Measure the radius of the arc, and compute the chord of 16, or rather 32, of the nonius divi sions ; the quantity of an arc equal thereto may be casiN had by the following proportion: 4• 10 din.: 55' (me number of minutes in I I divisions of the : 32 div. 2°, 56, the chord of which must be computed, and taken from the scale of equal parts : But as different subdivisions by the nonius may be required, let n = number of nonius divisions, m = number of minutes taken in by the 11071i118, 32, or 64, and x= arc sought ; then as n: b : x.
Lay off with the beam compass, having the length of the tangent between the points, the Mint q from e, and the chord of 32 from q towards the left hand, and divide by continual bisections, 10 of those divisions, counting front q to the left, will be the points required. As the number of nonius divisions for the 96 arch should always be 16, 32, &c. 1 need only mention, that the extremes may be laid off from the divisions of the limb, without computation.
Now the place tij)on the chamfered edge of the nonius plate, where the nonius is to begin, may be found in the following manner. Measure the distance of the quadrant centre, from the axis of the telescope ; this distance from the axis of the telescope at the eye-end, will be the place for the first division of the lionizes, where draw a faint line from the centre. The greater accuracy with which this is laid off, the nearer to the axis of the tube will be the intersec tion of the wires, in the common focus of the object and eye glasses.