252 MICROMETEE [HELIOMETEE. 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 below). Ramsden (Phil. Trails., vol. xix. p. 419) has suggested the division of the small speculum of a Cassegrain telescope and the production of double image by micrometric rotation of the semi- specula in the plane passing through their axis. Brewster (Enctj. Brit., 8th ed., vol. xiv. p. 749) proposes 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 reflexion 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 reflexion, and a small telescope through which the rays must pass ; consequently there is great loss of light. Micrometers Depending on Double Refraction. Rochon s _ To the Abbe Rochon (Jour, dc Phys., liii., 1801, pp. 169-198) micro- is due the happy idea of applying the two images formed by double meter. 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 separa tion of the images increases as the prism is approached to the object- glass, and diminishes as it is approached towards the eye-piece. Arago (Comptes Rcndus, 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 incon veniently 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/ 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. 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 instalment (figs. 31, 32) a is the sphere, placed in half-holes on Fig. 31. j overcome by Dollond; and in the hands of Dawes (Mem. R. A. S., xxxv. p. 144 sq. ) 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. The Modern Heliometer. The Konigsberg heliometer is represented in fig. 33. No part of Konigs- the equatorial mounting is shown in the figure, as it resembles in berg every respect the usual Fraunhofer mounting. An adapter h is helio- fixed on a telescope- meter, tube, made of wood, in Fraunhofer s usual fashion. To this adapter is attached a flat circular flange h. The slides carrying the segments of the divided object-glass are mounted on a plate, which is fitted and ground to rotate smoothly on the flange h. Rotation is communicated by a pinion, turned by the handle c (concealed in the figure), which works in teeth cut on the edge of the flange h. The counterpoise w balances the head about its axis of rotation. The slides are moved by the screws a and b, the divided heads of which serve to measure the separation of the segments. These screws are turned from the eye-end by bevelled wheels and pinions, the latter connected with the handles a , b . The reading micrometers e, /also serve to measure, independently, the separation of the segments, by scales attached to the slides; such measurements can be employed as a check on those made by the screws. The measurement of position angles is provided for by a graduated circle attached to the head. There is also a position circle, attached at m to the eye-end, provided with a slide to move the eye-piece radially from the axis of the telescope, and with a micrometer to measure the distance of an object from that axis. The ring which carries the supports of the handles a , b , c is capable of a certain amount of rotation on the tube. The weight of the handles and their supports is balanced by the counterpoise z. This ring is necessary in order to allow the rods to follow the micrometer heads when the position angle is changed. Complete rotation of the head is obviously impossible because of the inter ference of the declination axis with the rods, and therefore, in some angles, objects cannot be measured in two positions of the circle. The object-glass has an aperture of 6J inches, and 102 inches focal length. There are three methods in which this heliometer can be used. First Method. One of the segments is fixed in the axis of the telescope, and the eye-piece is also placed in the axis. Measures are made with the moving segment displaced alternately on opposite sides of the fixed segment. Second Method. One segment is fixed, and the measures are made as in the first method, excepting that the eye-piece is placed symmetrically with respect to the images under measurement. For this purpose the position angle of the eye-piece micrometer is set to that of the head, and the eye-piece is displaced from the axis of the tube (in the direction of the movable segment) by an amount equal to half the angle under measurement. Third Method. The eye-piece is fixed in the axis, and the segments are symmetrically displaced from the axis each by an amount equal to half the angle measured. Of these methods Bessel generally employed the first because of its simplicity, notwithstanding that it involved a resetting of the right ascension and declination of the axis of the tube with each reversal of the segments. The chief objections to the method are that, as one star is in the axis of the telescope and the other dis placed from it, the images are not both in focus of the eye-piece, 2 and the rays from the two stars do not make the same angle with the optical axis of each segment. Thus the two images under measurement are not defined with equal sharpness and symmetry. The second method is free from the objection of non-coincidence in focus of the images, but is more troublesome in practice from the the axis bb, so that when its principal axis is parallel to the axis of j the telescope it gives only one image of the object. In a direction f 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 S,f e8 ?i*L for fr f l" ent ^adjustment of the position of the eye-piece, the graduated circle C. The angle between the objects measured Th< ? tlurd - me . thod 1S the most symmetrical of all, both in obser- is = rsin20, where r is a constant to be determined for each mag nifying power employed, 1 and 8 the angle through which the sphere has been turned from zero (i.e.. from coincidence of its prin cipal 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 consider able difficulties of construction, but these have been successfully vation and reduction ; but it was not employed by Bessel, on the ground that it involved the determination of the errors of two screws instead of one. On the other hand it is not necessary to reset the telescope after each reversal of the segments. 3
- The distances of the optical centres of the segments from the eye-piece are in
this method as 1 : secant of the angle under meiisuremcnt. In Hessel s heliometer ee of , Aij n th of an inch when an angle of 1* is t inch. IJessel confined his meiis i TViii/ nc. esse conne s meiis Dollond piovides for changing the power by sliding the lens d nearer to or In criticizing lU-scl s clu.i involved in each, it must be re of an e diffeience would amount to near res to distances considerably less than 1. c of method*, and considering the loss of time
ien;beied that Kraunhoter provided no means of
