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CHAP. II.

cent.

MEASUREMENT OF ANGLES.

83

pendicular to the pivot; and also the two arms, mn, at right angles to it, and forming one piece with the tube and the axis; so that the motion of the axis on the centre shall carry the tube and arms smoothly round the circle, to be arrested and fixed at any point we please, by a contrivance called a clamp. Suppose, now, we would measure the angular interval between two fixed objects, ST. The plane of the circle must first be adjusted so as to pass through them both. This done, let the axis ab of the tube be directed to one of them, S, and clamped. Then will a mark on the arm m point either exactly to some one of the divisions on the limb, or between two of them adjaIn the former case, the division must be noted, as the reading of the arm m. In the latter, the fractional part of one whole interval between the consecutive divisions by which the mark on m surpasses the last inferior division must be estimated or measured by some mechanical or optical means. (See art. 130.) The division and fractional part thus noted, and reduced into degrees, minutes, and seconds, is to be set down as the reading of the limb corresponding to that position of the tube ab, where it points to the object S. The same must then be done for the object T; the tube pointed to it, and the limb " read off." It is manifest, then, that, if the lesser of these readings be subtracted from the greater, their difference will be the angular interval between S and T, as seen from the centre of the circle, at whatever point of the limb the commencement of the graduations on the point 0° be situated.

(129.) The very same result will be obtained, if, instead of making the tube moveable upon the circle, we connect it invariably with the latter, and make both revolve together on an axis concentric with the circle, and forming one piece with it, working in a hollow formed to receive and fit it in some fixed support. Such a combination is represented in section in the annexed sketch. T is the tube or sight, fastened, at pp, on the circle AB, whose axis, D, works in the solid

metallic centring E, from which originates an arm, F, carrying at its extremity an index,or other proper mark,

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to point out and read off the exact division of the circle at B, the point close to it. It is evident that, as the telescope and circle revolve through any angle, the part of the limb of the latter, which by such revolution is carried past the index F, will measure the angle described. This is the most usual mode of applying divided circles in astronomy.

(130.) The index F may either be a simple pointer, like a clock hand (fig. a); or a vernier (fig. b); or,

a

lastly, a compound microscope (fig. c), represented in section (in fig. d), and furnished with a cross in the common focus of its object and eye-glass, moveable by a fine-threaded screw, by which the intersection of the cross may be brought to exact coincidence with the image of the nearest of the divisions of the circle; and by the turns and parts of a turn of the screw required for this purpose the distance of that division from the original or zero point of the microscope may be estimated. This simple but delicate contrivance gives to the reading off of a circle a degree of accuracy only limited by the power of the microscope, and the perfection with which a screw can be executed, and places

CHAP. II.

APPLICATION OF THE TELESCOPE.

85

the subdivision of angles on the same footing of optical certainty which is introduced into their measurement by the use of the telescope.

(131.) The exactness of the result thus obtained must depend, 1st, on the precision with which the tube ab can be pointed to the objects; 2dly, on the accuracy of graduation of the limb; 3dly, on the accuracy with which the subdivision of the intervals between any two consecutive graduations can be accomplished. The mode of accomplishing the latter object with any required exactness has been explained in the last article. With regard to the graduation of the limb, being merely of a mechanical nature, we shall pass it without remark, further than this, that, in the present state of instrument-making, the amount of error from this source of inaccuracy is reduced within very narrow limits indeed. With regard to the first, it must be obvious that, if the sights ab be nothing more than what they are represented in the figure (art. 128.) simple crosses or pin-holes at the ends of a hollow tube, or an eye-hole at one end, and a cross at the other, no greater nicety in pointing can be expected than what simple vision with the naked eye can command. But if, in place of these simple but coarse contrivances, the tube itself be converted into a telescope, having an object-glass at b, and an eye-piece at a; and if the motion of the tube on the limb of the circle be arrested when the object is brought just into the centre of the field of view, it is evident that a greater degree of exactness may be attained in the pointing of the tube than by the `unassisted eye, in proportion to the magnifying power and distinctness of the telescope used. The last attainable degree of exactness is secured by stretching in the common focus of the object and eye-glasses two delicate fibres, such as fine hairs or spider-lines, intersecting each other at right angles in the centre of the field of view. Their points of intersection afford a permanent mark with which the image of the object can be brought to exact

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coincidence by a proper degree of caution (aided by mechanical contrivances), in bringing the telescope to its final situation on the limb of the circle, and retaining it there till the "reading off" is finished.

(132.) This application of the telescope may be considered as completely annihilating that part of the error of observation which might otherwise arise from erroneous estimation of the direction in which an object lies from the observer's eye, or from the centre of the instrument. It is, in fact, the grand source of all the precision of modern astronomy, without which all other refinements in instrumental workmanship would be thrown away; the errors capable of being committed in pointing to an object, without such assistance, being far greater than what could arise from any but the very coarsest graduation.* In fact, the telescope thus applied becomes, with respect to angular, what the microscope is with respect to linear dimension. By concentrating attention on its smallest points, and magnifying into palpable intervals the minutest differences, it enables us not only to scrutinize the form and structure of the objects to which it is pointed, but to refer their apparent places, with all but geometrical precision, to the parts of any scale with which we propose to compare them.

(133.) The simplest mode in which the measure

The honour of this capital improvement has been successfully vindicated by Derham (Phil. Trans. xxx. 603.) to our young, talented, and unfortunate countryman Gascoigne, from his correspondence with Crabtree and Horrockes, in his (Derham's) possession. The passages cited by Derham from these letters leave no doubt that, so early as 1640, Gascoigne had applied telescopes to his quadrants and sextants, with threads in the common focus of the glasses; and had even carried the invention so far as to illuminate the field of view by artificial light, which he found " very helpful when the moon appeareth not, or it is not otherwise light enough. These inventions were freely communicated by him to Crabtree, and through him to his friend Horrockes, the pride and boast of British astronomy; both of whom expressed their unbounded admiration of this and many other of his delicate and admirable improvements in the art of observation. Gascoigne, however, perished, at the age of twenty-three, at the battle of Marston Moor; and the premature and sudden death of Horrockes, at a yet earlier age, will account for the temporary oblivion of the invention. It was revived, or re-invented, in 1667, by Picard and Auzout (Lalande, Astron. 2310.), after which its use became universal. Morin, even earlier than Gascoigne (in 1635), had proposed to substitute the telescope for plain sights; but it is the thread or wire stretched in the focus with which the image of a star can be brought to exact coincidence, which gives the telescope its advantage in practice; and the idea of this does not seem to have occurred to Morin. (See Lalande, ubi supra.)

CHAP. II. INTERVALS IN DECLINATION MEASURED. 87

ment of an angular interval can be executed, is what we have just described; but, in strictness, this mode is applicable only to terrestrial angles, such as those occupied on the sensible horizon by the objects which surround our station,-because these only remain stationary during the interval while the telescope is shifted on the limb from one object to the other. But the diurnal motion of the heavens, by destroying this essential condition, renders the direct measurement of angular distance from object to object by this means impossible. The same objection, however, does not apply if we seek only to determine the interval between the diurnal circles described by any two celestial objects. Suppose every star, in its diurnal revolution, were to leave behind it a visible trace in the heavens, —a fine line of light, for instance, then a telescope once pointed to a star, so as to have its image brought to coincidence with the intersection of the wires, would constantly remain pointed to some portion or other of this line, which would therefore continue to appear in its field as a luminous line, permanently intersecting the same point, till the star came round again. From one such line to another the telescope might be shifted, at leisure, without error; and then the angular interval between the two diurnal circles, in the plane of the telescope's rotation, might be measured. Now, though we cannot see the path of a star in the heavens, we can wait till the star itself crosses the field of view, and seize the moment of its passage to place the intersection of its wires so that the star shall traverse it; by which, when the telescope is well clamped, we equally well secure the position of its diurnal circle as if we continued to see it ever so long. The reading off of the limb may then be performed at leisure; and when another star comes round into the plane of the circle, we may unclamp the telescope, and a similar observation will enable us to assign the place of its diurnal circle on the limb: and the observations may be repeated alternately, every day, as the stars pass, till we are satisfied with their result.

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