ASTRONOMICAL Sector — 2nd ed. (1778

ASTRONOMICAL Sector, a very useful mathematical instrument, made by the late ingenious Mr Graham.

It is allowed that a micrometer is the most accurate and convenient instrument for observing the place of a planet or comet, when it happens to be near enough to any known star, by taking the differences of its right ascension and declination from those of the star: but this being frequently impracticable, by reason that many large places in the heavens are void of stars whose places are known, it is necessary to have recourse to moveable quadrants, or sextants, furnished with telescopic sights, for taking larger distances. But besides the difficulty and charge of procuring good instruments of this kind, the great trouble and uncertainties in observing with them are very notorious, arising chiefly from the difficulty the observers find in making their observations and each telescope correspond together at the same instant while the instrument is following the diurnal motion of the heavens. The lovers of astronomy are therefore much obliged to the late ingenious Mr George Graham, F. R. S. not only for many useful improvements in the mechanism of several astronomical instruments, but also for contriving a very commodious and accurate one for the purpose aforesaid; that is, for taking such differences of right ascension and declination as are too large to be observed through a fixed telescope; and yet with equal facility and exactness too in proportion to the radius of the instrument.

Let $AB$ represent an arch of a circle, containing ten or twelve degrees well divided, having a strong plate $CD$ for its radius, fixed to the middle of the arch at $D$ : let this radius be applied to the side of an axis $HI$ , and be moveable about a joint fixed to it

at $F$ , so that the plane of the sector may be always parallel to the axis $HI$ ; which being parallel to the axis of the earth, the plane of the sector will always be parallel to the plane of some hour-circle. Let a telescope $CE$ be moveable about the centre $C$ of the arch $AB$ , from one end of it to the other, by turning a screw at $G$ ; and let the line of sight be parallel to the plane of the sector. Now, by turning the whole instrument about the axis $HI$ , till the plane of it be successively directed, first to one of the stars, and then to another, it is easy to move the sector about the joint $F$ , into such a position, that the arch $AB$ , when fixed, shall take in both the stars in their passage, by the plane of it, provided the difference of their declinations does not exceed the arch $AB$ . Then, having fixed the plane of the sector a little to the westward of both the stars, move the telescope $CE$ by the screw $G$ ; and observe by a clock the time of each transit over the cross-hairs, and also the degrees and minutes upon the arch $AB$ , cut by the index at each transit; then, in the difference of the arches, the difference of the declinations, and by the difference of the times, we have the difference of the right ascensions of the stars.

The dimensions of this instrument are these: the length of the telescope, or the radius of the sector, is $2\frac{1}{2}$ feet; the breadth of the radius, near the end $C$ , is $1\frac{1}{2}$ inch; and at the end $D$ two inches. The breadth of the limb $AB$ is $1\frac{1}{2}$ inch; and its length six inches, containing ten degrees divided into quarters, and numbered from either end to the other. The telescope carries a nonius or subdividing plate, whose length, being equal to sixteen quarters of a degree, is divided into fifteen equal parts; which, in effect, divides the limb into minutes, and, by estimation, into smaller parts. The length of the square axis $HI$ is eighteen inches, and of the part $HI$ twelve inches; and its thickness is about a quarter of an inch: the diameters of the circles are each five inches: the thickness of the plates, and the other measures, may be taken at the direction of a workman.

This instrument may be rectified, for making observations, in this manner: By placing the intersection of the cross-hairs at the same distance from the plane of the sector, as the centre of the object-glass, the plane described by the line of sight, during the circular motion of the telescope upon the limb, will be sufficiently true, or free from conical curvity; which may be examined by suspending a long plumb-line at a convenient distance from the instrument; and by fixing the plane of the sector in a vertical position, and then by observing, while the telescope is moved by the screw along the limb, whether the cross hairs appear to move along the plumb-line.

The axis $bfo$ may be elevated nearly parallel to the axis of the earth, by means of a small common quadrant; and its error may be corrected, by making the line of sight follow the circular motion of any of the circumpolar stars, while the whole instrument is moved about its axis $bfo$ , the telescope being fixed to the limb: for this purpose, let the telescope $k$ be directed to the star $a$ , when it passes over the highest point of its diurnal circle, and let the division cut by the nonius be then noted: then, after twelve hours, when the star comes to the lowest point of its circle, having turned the instrument half round its axis, to bring the telescope

telescope into the position $mn$ ; if the cross hairs cover the same star supposed at $b$ , the elevation of the axis $bfo$ is exactly right; but if it be necessary to move the telescope into the position $uv$ , in order to point to this star at $c$ , the arch $mu$ , which measures the angle $mfu$ or $bfc$ , will be known; and then the axis $bfo$ must be depressed half the quantity of this given angle if the star passed below $b$ , or must be raised so much higher if above it; and then the trial must be repeated till the true elevation of the axis be obtained. By making the like observations upon the same star on each side the pole, in the fix-o'clock-hour-circle, the

error of the axis, toward the east or west, may also be found and corrected, till the cross-hairs follow the star quite round the pole: for supposing $aopbc$ to be an arch of the meridian (or in the second practice of the fix-o'clock hour-circle), make the angle $asp$ equal to half the angle $afc$ , and the line $sp$ will point to the pole; and the angle $osp$ , which is the error of the axis, will be equal to half the angle $bfc$ or $mfu$ , found by the observation; because the difference of the two angles $asb$ , $afc$ , is double the difference of their halves $asf$ and $asp$ . Unless the star be very near the pole, allowance must be made for refractions.

END OF THE FIRST VOLUME.

	Plate I.	To face	Page		26	Plate XXIV. (a)	To face	Page
1	I.	-	40	27	XXV.	-	-	526
2	II.	-	55	28	XXV. (A)	-	-	527
3	III.	-	66	29	XXV. (B)	}	-	608
4	IV.	-	144	30	XXVI.	}	-	608
5	V.	-	158	31	XXVII.	}	-	609
6	VI.	-	170	32	XXVIII.	}	-	609
7	VII.	}	185	33	XXIX.	}	-	611
8	VIII.	}	185	34	XXX.	}	-	611
9	IX.	-	204	35	XXXI.	}	-	615
10	X.	-	271	36	XXXII.	}	-	615
11	XI.	-	318	37	XXXIII.	}	-	616
12	XII.	-	335	38	XXXIV.	}	-	616
13	XIII.	-	358	39	XXXV.	}	-	618
14	XIV.	-	359	40	XXXVI.	}	-	618
15	XV.	-	365	41	XXXVII.	}	-	619
16	XVI.	-	366	42	XXXVIII.	}	-	619
17	XVII.	}	389	43	1^st XXXIX.	}	-	622
18	XIX.	}	389	44	2^d XXXIX.	}	-	622
19	XX.	-	390	45	3^d XXXIX.	}	-	627
20	XVIII.	-	394	46	4^th XXXIX.	}	-	627
21	XXI.	-	400	47	5^th XXXIX.	}	-	631
22	XXII.	-	420	48	XL.	}	-	631
23	XXIII.	-	440	49	XLI.	}	-	690
24	XXIV.	-	446	50	XLII.	}	-	690
25	XXIV. (a)	-	451					743

N. B. ERRATA, OMISSIONS, &c. noticed and supplied in the APPENDIX at the end of the Work.