The last improvement on this instrument is mentioned in the Report of the R.A.S. council, February 1865. It consists in the introduction by Simms of a fifth lens, but no satisfactory description has ever appeared. There is only one practical published investigation of Airy’s micrometer that is worthy of mention, viz. that of F. Kaiser (Annalen der Sternwarte in Leiden, iii. 111-274). The reader is referred to that paper for an exhaustive history and discussion of the instrument.[20] It is somewhat surprising that, after Kaiser’s investigations, observers should continue, as many have done, to discuss their observations with this instrument as if the screw-value were constant for all angles.

Steinheil (Journal savant de Munich, Feb. 28, 1843) describes a “heliomètre-oculaire” which he made for the great Pulkowa refractor, the result of consultations between himself and the elder Struve. It is essentially the same in principle as Amici’s micrometer, except that the divided lens is an achromatic positive instead of a negative lens. Struve (Description de l’Observatoire Central de Pulkowa, pp. 196, 197) adds a few remarks to Steinheil’s description, in which he states that the images have not all desirable precision—a fault perhaps inevitable in all micrometers with divided lenses, and which is probably in this case aggravated by the fact that the rays falling upon the divided lens have considerable convergence. He, however, successfully employed the instrument in measuring double stars, so close as 1″ or 2″, and using a power of 300 diameters, with results that agreed satisfactorily amongst themselves and with those obtained with the filar micrometer. If Struve had employed a properly proportioned double circular diaphragm, fixed symmetrically with the axis of the telescope in front of the divided lens and turning with the micrometer, it is probable that his report on the instrument would have been still more favourable. This particular instrument has historical interest, having led Struve to some of those criticisms of the Pulkowa heliometer which ultimately bore such valuable fruit (see ante).

Ramsden (Phil. Trans. vol. xix. p. 419) suggested the division of the small speculum of a Cassegrain telescope and the production of double image by micrometric rotation of the semispecula in the plane passing through their axis. Brewster (Ency. Brit. 8th ed. vol. xiv. p. 749) proposed a plan on a like principle, by dividing the plane mirror of a Newtonian telescope. Again, in an ocular heliometer by Steinheil double image is similarly produced by a divided prism of total reflection placed in parallel rays. But practically these last three methods are failures. In the last the field is full of false light, and it is not possible to give sufficiently minute and steady separation to the images; and there are of necessity a collimator, two prisms of total reflection, and a small telescope through which the rays must pass; consequently there is great loss of light.

Micrometers Depending on Double Refraction.—To the Abbé Rochon (Jour. de phys. liii., 1801, pp. 169-198) is due the happy idea of applying the two images formed by double refraction to the construction of a micrometer. He fell upon a most ingenious plan of doubling the amount of double refraction of a prism by using two prisms of rock-crystal, so cut out of the solid as to give each the same quantity of double refraction, and yet to double the quantity in the effect produced. The combination so formed is known as Rochon’s prism. Such a prism he placed between the object-glass and eye-piece of a telescope. The separation of the images increases as the prism is approached to the object-glass, and diminishes as it is approached towards the eye-piece.

D. F. J. Arago (Comptes rendus, xxiv., 1847, pp. 400-402) found that in Rochon’s micrometer, when the prism was approached close to the eye-piece for the measurement of very small angles, the smallest imperfections in the crystal or its surfaces were inconveniently magnified. He therefore selected for any particular measurement such a Rochon prism as when fixed between the eye and the eye-piece (i.e. where a sunshade is usually placed) would, combined with the normal eye-piece employed, bring the images about to be measured nearly in contact. He then altered the magnifying power by sliding the field lens of the eye-piece (which was fitted with a slipping tube for the purpose) along the eye-tube, till the images were brought into contact. By a scale attached to the sliding tube the magnifying power of the eye-piece was deduced, and this combined with the angle of the prism employed gave the angle measured. If p″ is the refracting angle of the prism, and n the magnifying power of the eye-piece, then p″/n will be the distance observed. Arago made many measures of the diameters of the planets with such a micrometer.

Fig. 18.Fig. 19.

Dollond (Phil. Trans., 1821, pp. 101-103) describes a double-image micrometer of his own invention, in which a sphere of rock-crystal is substituted for the eye-lens of an ordinary eye-piece. In this instrument (figs. 18, 19) a is the sphere, placed in half-holes on the axis bb, so that when its principal axis is parallel to the axis of the telescope it gives only one image of the object. In a direction perpendicular to that axis it must be so placed that when it is moved by rotation of the axis bb the separation of the images shall be parallel to that motion. The angle of rotation is measured on the graduated circle C. The angle between the objects measured is = r sin 2θ, where r is a constant to be determined for each magnifying power employed,[21] and θ the angle through which the sphere has been turned from zero (i.e. from coincidence of its principal axis with that of the telescope). The maximum separation is consequently at 45° from zero. The measures can be made on both sides of zero for eliminating index error. There are considerable difficulties of construction, but these have been successfully overcome by Dollond; and in the hands of Dawes (Mem. R.A.S. xxxv. p. 144 seq.) such instruments have done valuable service. They are liable to the objection that their employment is limited to the measurement of very small angles, viz. 13″ or 14″ when the magnifying power is 100, and varying inversely as the power. Yet the beautiful images which these micrometers give permit the measurement of very difficult objects as a check on measures with the parallel-wire micrometer.

On the theory of the heliometer and its use consult Bessel, Astronomische Untersuchungen, vol. i.; Hansen, Ausführliche Methode mit dem Fraunhoferschen Heliometer anzustellen (Gotha, 1827); Chauvenet, Spherical and Practical Astronomy, vol. ii. (Philadelphia and London, 1876); Seeliger, Theorie des Heliometers (Leipzig, 1877); Lindsay and Gill, Dunecht Publications, vol. ii. (Dunecht, for private circulation, 1877); Gill, Mem. R.A.S. vol. xlvi. pp. 1-172, and references mentioned in the text.

(D. Gi.)