Page images
PDF
EPUB

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

[graphic][subsumed][ocr errors]

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.

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

[merged small][ocr errors]

pound 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 formed in the focus of the object lens upon the very same principle with that explained, art. 157. for the pointing of the telescope, only that here the fiducial cross is made moveable; and by the turns and parts of a turn of the screw

H

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

(166.) The exactness of the result thus obtained must depend, 1st, on the precision with which the tube a b 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 performed. 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 a b be nothing more than 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, an eye-piece at a, and a fiducial cross in their common focus, as explained in art. 157.; and if the motion of the tube on the limb of the circle be arrested when the object is brought just into coincidence with the intersectional point of that cross, 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.

In the great Ertel circle at Pulkova, the probable amount of the accidental error of division is stated by M. Struve not to exceed 0" 264. Desc. de l'Obs. centrale de Pulkova, p. 147.

(167.) The simplest mode in which the measurement 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.

(168.) This is the principle of the mural circle, which is nothing more than such a circle as we have described in art. 163., 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.

(169.) 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 and amount of refraction known, it is easy to conclude, not their differences only, but the quantities themselves, as we shall now explain.

(170.) 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, B R, A Q, C D the diurnal circles of

P

A

с

B

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 and Q happen above the horizon HO. P is the pole; and if we suppose h po to be the mural circle, having S for its centre, ba cpd will be the points on its g circumference corresponding to B ACPD in the heavens.

Now

the arcs b a, b c, b d, and c d are given immediately by observation;

D

R

[ocr errors]

and since CP=P D, we have also cp=p d, and each of them cd, consequently the place of the polar point, as it is called, upon the limb of the circle becomes known, and the arcs pb, pa, pc, which represent on the circle the polar distances required, become also known.

(171.) The situation of the pole star, which is a very brilliant one, is eminently favourable for this purpose, being only about a degree and 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. In consequence of these peculiarities, this star is one of constant resort with astronomers for the adjustment and verification of instruments of almost every description. In the case of the transit, for instance, it furnishes an excellent object for the application of the method of testing the meridional situation of the instrument described in art. 162., in fact, the most advantageous of any for that purpose, owing to its being the most remote from the zenith, at its upper culmination, of all bright stars observable both above and below the pole.

(172.) The place of the polar point on the limb of the mural

Ο

« PreviousContinue »