The micrometer microscope, for reading off the divisions of graduated circles, depends upon the same principle as the wire micrometer. An enlarged image of the divisions of the limb of the circle is formed, and this image is measured by the revolutions and parts of a screw. [C3 RCLE.] 2. The diridecl of ject-glass micrometer and heliometer. If an object glue be cut across so as to form two semicircles, and the semilenses be separated by sliding one beyond the other, each portion will form its proper image, and these will retreat from each other as the semilenses are moved. The semilenses are mounted on slides, and the quantity of separation is read off upon a scale. In Bessel's heliometer, a very fine and perfect instrument of this class, the focal length of the object-glass is eight French feet, and the aperture nearly six French inches. A description and plate will be found in the ' Adronomische Nachrichten,' No, 189. The only objection which can be made to this species of micrometer, besides the extreme difficulty of constructing it, is, that stars are not seen so round and well defined as in an entire object glass. Bessel's measures of double stars are, however, so far as we can judge, the most accurate that have yet been made. Suppose a double star is to he measured with the heliometer : the whole of the object end is turned round, until four stars appear in a right line, and the scrailenses are separated until the stars appear to be exactly at the same distance from each other, when the scale is read off. The semilenses are then shifted in a contrary direction, sliding the two images over each other, until they again appear to be at equal dis tances, and the scale is a;ain read off. The separation of the scale is four times the angular distance between the stars. There is a position circle, on which the direction of tho stars is read of£ In measuring the diameters of the sun, planets, &c., the two images are made to touch on opposite sides; nod in observations of Halley's comet it was made to coincide with the neighbouring stars. The divided object. glass micrometer is on the same principle as the heliometer ; a cap containing the divided lenses is placed over the object-glass of the telescope. A similar micrometer may be obtained by dividing one of the lenses of an eyepiece; and it seems probable that, with large telescopes, this micrometer may be of considerable use in measuring small angles. There is a good deal of colour in the images, but not at the point of contact. Micrometers of this class require no illumi nation.
3. Reticle and circular micrometer. The micrometers hitherto de. scribed are applied to the accurate measures of small angles ; the present class, though very useful in certain cases, are of much lower pretensions. The reticle, or diaphragm, as it is sometimes called, is any fixed arrangement of wires or bars which can be applied to a telescope for the purpose of measurement. They are chiefly used when an object will not admit of illumination, or where the astronomer has no accurately divided instrument at his disposal, or, as in the case of La Caille at the Cape of Good Hope, when the object is to fix approxi mately a greater number of stars than could be done in the same time with ordinary instruments. Suppose a cross like an X or V to be cut out of brass-plate and inserted in the prinoipal focus of a telescope with the axis of the letter in a meridian. A star in passing through the field is occulted at its passage behind each of the bars, and the time noted. The interval will show, by an easy calculation, how far it passes from the vertex ; and the mean of the times, the moment when it passes the axis of the diaphragm. If the true position of any one
star so passing is known from any other source, all the other stars can be thus determined differentially with respect to it. The method is not very accurate, but may often be applied advantageously and with very small instrumental means. If a fine wire be drawn perpendicular to the axis, and a bright star, observed with illumination, be made to run along the wire, the axis of the diaphragm can be set in a meridian, and that is the only verification necessary. The computation in declination will be least if the angle between the bars is such that the base of the triangle is equal to its altitude. This reticle is very convenient for mapping, if placed in the meridian, or for cometary observation, if tho telescope is mounted as an equatorial, however rudely.
The circular micrometer was introduced, we believe, by Olbers, and perfected by Frauenhofer (` Aaron. Nachricht.' iv. 22 ). A metal ring is set in the centre of a perforated glass plate, and the outer and inner edge of the ring is turned true. The plate is fixed in the focus of a telescope, and the appearance is that of a ring suspended in the heavens. The telescope is pointed, and the observer notes the time when a star disappears at the outer ring, re-appears on the inner ring, disappears again, and finally re-appears. If two stars be thus observed, it is clear that when a mean is taken of the disappearances and re-appearances of each, that the difference between the two means will be the difference of right ascension between tile two stars, and therefore that if one be known, the other is determined. Again, if the diameter of the ring has been determined, and the declination of the stars nearly known, the time of describing the chord of the ring will give, by an easy com putation, the distance of the chord from the centre, and that the more accurately the smaller the chord described. The sum or difference of these two distances is the difference of the stars in declination. The computation of the second star with its approximate declination may be repeated if the stars are near the pole. It will be seen that nothing is required for the circular micrometer but the power of fixing the telescope for a few minutes until a known star passes the field, and that no illumination is required. It is especially the apparatus for determining the place of a faint comet or planet, and in the hands of Olbers, Harding, and many other German astronomers, has been of infinite use in cometary astronomy, and in the discovery and observa tion of the small planets. When the comet has a large motion, or when the position of the star is so low as to require attention to the difference of refraction, the computation is a little more complicated, but generally scarcely any computation is required, and the results, in right ascension at least, are good. The observations at the inner edge of the ring are to be preferred. When however the object will bear illumination, and the astronomer possesses a telescope so mounted that he can apply a wire micrometer to it, the results from this are incom parably more accurate, and the reticle above mentioned is certainly better for determining declination. Fraucnhofer afterwards (` Astronem. Nach.' iv. 43) proposed another ring and reticle micrometer. He cut a series of rings or lines upon a piece of plane glass which he placed in the principal focus of the object-glass, and then by a side lamp ilitimi nated the rings, leaving the rest of the field dark. It is evident that for certain observations this micrometer would have great advantages.