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

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 ad. vantage in practice; and the idea of this does not seem to have occurred to Morin. (See Lalande, ubi supra.)

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.

(134.) This is the principle of the mural circle, which is nothing more than such a circle as we have described in art. 129., firmly supported, in the plane of the meridian, on a long and powerful horizontal axis. This axis is let into a massive pier, or wall, of stone (whence the name of the instrument), and so secured by screws as to be capable of adjustment both in a vertical and horizontal direction; so that, like the axis of the transit, it can be maintained in the exact direction of the east and west points of the horizon, the plane of the circle being consequently truly meridional.

(135.) The meridian, being at right angles to all the diurnal circles described by the stars, its arc intercepted between any two of them will measure the least distance between these circles, and will be equal to the difference of the declinations, as also to the difference of the meridian altitudes of the objects—at least when corrected for refraction. These differences, then, are the angular intervals directly measured by the mural circle. But from these, supposing the law of refraction known, it is easy to conclude, not their differences only, but the quantities themselves, as we shall now explain.

(136.) The declination of a heavenly body is the complement of its distance from the pole. The pole, being a point in the meridian, might be directly observed on the limb of the circle, if any star stood exactly therein; and thence the polar distances, and, of course, the declinations of all the rest, might be at once determined. But this not being the case, a bright star as near the pole as can be found is selected, and observed in its upper and lower culminations; that is, when it passes the meridian above and below the pole. Now, as its distance from the pole remains the same, the difference of reading off the circle in the two cases is, of course (when corrected for refraction), equal to twice the polar distance of the star; the arc intercepted on the limb of the circle being, in this case, equal to the angular diameter of the star's diurnal circle. In the annexed diagram, H PO represents the celestial meridian, P the pole,

BR, AQ, C D the diurnal circles of stars which arrive on the meridian-at B A and C in their upper,

and at R Q D in their lower culminations, of which D happens above the horizon HO. P is the pole; and if we suppose po to be the mural circle, having S for its centre, ba cp d will be the points on its circumference corresponding to BAC PD in the heavens. Now, the arcs ba, bc, bd, and cd are given immediately by observation; and since C P=P D, we have also c p=p d, and each of them = c d, consequently the place of the polar point, as it is called, upon the limb of the circle becomes known, and the arcs p b, pa, pc, which represent on the circle the polar distances required, become also known.

(137.) The situation of the pole star, which is a very brilliant one, is eminently favourable for this purpose, being only about a degree and a half from the pole; it is, therefore, the star usually and almost solely chosen for this important purpose; the more especially because, both its culminations taking place at great and not very different altitudes, the refractions by which they are affected are of small amount, and differ but slightly from each other, so that their correction is easily and safely applied: The brightness of the pole star, too, allows it to be easily observed in the daytime. consequence of these peculiarities, this star is one of con

In