The measures of this micrometer arc not confined to double stars only, but may be applied to any other ob jects that require the utmost accuracy, such as the dia meters of the planets or their satellites, the mountains of the moon, the diameters of the fixed stars, Ste. For instance, Oct. 22, 1781, Sir William Herschel measured the apparent diameter of a Lyra;; and judging it of the greatest importance to increase his scale as much as con venient, he placed the micrometer at the greatest conve nient distance and (with some trouble, for want of longer handles, which might easily be added) took the diameter of this star, by removing the two lucid points to such a distance as just to inclose the apparent diameter. \Vhen he measured his radius, it was found to be 22 feet 6 inches. The distance of the two lucid points was about three inches ; for extreme nicety could not be ob tained in this observation, on account of the very great power he used, which was 6450. From these measures we have the magnified angle 38' 10": this divided by the power gives 0".355 for the apparent diameter of a Lyr2e. The scale of the micrometer, on this occasion, was no less than 8.443 inches to a second, as will be found by multiplying the natural tangent of a second with the power and radius in inches. In Nov. 1781, he measured the diameter of the new star ; but the air was not very favourable, for this singular star was not so distinct with 227 that evening as it generally is with 460 : therefore, without laying much stress on the ex actness of the observation, he only reports it, to ex emplify the use of his micrometer. His radius was 35 feet 11 inches. The diameter of the star, by the distance of the lucid points, was 2.4 inches, and the power he used 227 : hence the magnified angle is found 19', and the real diameter of the star 5".022. The scale of this measure is .474 millesimals of an inch, or almost half an inch to a second." A lucid disc micrometer was also used by M. Schroe ter of Lilienthal, in his observations on the new pla nets, but we are not acquainted with the principles of its construction.
A luminous image micrometer, in which the angle, subtended by two lucid points, is measured by expand ing them into circular discs, and marking the instant of contact, has been described by Dr. Brewster in his Treatise on New Philosophical Instruments, p. 40.
On Doubly Refracting illicrometers.
The first person who proposed to employ the sepa ration of two images, formed by double refraction, as the principle of a micrometer, was the late inge nious Abhe Rochon. On the 5th March 1777, Messrs. Leroi, Lemonnier, and Condorcet, gave a favourable report of this new invention, which was brought to a considerable degree of perfection by successive im provements, with which M. Rochon was constantly occu pied till the time of his death, which took place in1817.
If we suppose ABC, (Plate CCCLXXVI. Fig. 19.) a prism of rock crystal, so cut out of the hexacclral prism in which this substance is generally formed, that AC is the axis of the prism, and BCD another prism, so cut out of the same crystal, that BC is the axis of the prism, then a ray of light RR incident pet- pendicularly at R, will go on to R' without being di vided into two pencil'-, as the doubly refracting force vanishes in the direction of the axis; but when it reaches R' it will be divided into two pencils R' R", R' c, one of which, R R", the ordinary pencil, will go on in the direction R' E without any deviation, as it is in no way affected with the doubly refracting force of the second prism BCD, while the extraordinary pencil R' c will deviate from the line R' E, in virtue of the doubly refracting force of the second prism BCD.
An eye placed at E will obviously not receive the two rays R' E and R' e, but if we draw E r", r" r', r' r re spectively parallel to a g, g R', r" R' R, a ray r r incident perpendicularly at r, will give an extraordinary ray r" E, which will reach the eye E at the same time with the ordinary ray R' E, and the ohserver will see two distinct images of the object from which these rays proceed.
In order to apply this compound prism to the pur poses of a micrometer, M. Rochon introduces it be tween the object-glass and the eyeglass of an astrono mical telescope, as shown in Plate CCCLXXVI. Fig. 20; and by moving it along the axis of the telescope, the angular separation of the two images of the object s s' is made to vary in a manner similar to what has been already described in the prismatic micrometer of Dr. Alaskelyne.
In the year 1812, M. Rochon proposed another form of his micrometer, from which he expected great ad vantages. lie took a parallelopiped of rock crystal, formed of two prisms, cut with angles of about 30°, and so as to make the images of the sun overlap one another about five minutes. When joined together by mastic, it was ground into a convex lens, and was united with a concave lens of glass, so as to form an achromatic object-glass. The object-glass, which had a focal length of about three decimeters, separated the centres of the images of the sun about 28 minutes. He then adapted to this object-glass a common mi crometer, which measured angles of. 10 minutes, and he had thus three decimetres or 10 minutes to com plete the measure of the diameters of the sun or moon.
Ingenious as these micrometers are, we conceive them to be liable to an objection of a very serious nature. Dr. Brewster has shown, from numerous experiments, that rock crystal is very imperfectly crystallized in the direction of its axis, and that it exhibits great devia tions from a homogeneous texture, both in its action upon common and polarised light. Distinct images therefore cannot be formed through prisms or lenses whose refracting surfaces are perpendicular, or neatly so, to the axis of the liexaedral prism. If astronomy therefore is to derive any advantage from doubly re fracting micrometers, we must have recourse to the refraction of other substances than rock crystal.
On Micrometers for illicroscopcs.