Thus, for refined purposes, it cannot be assumed with any certainty that the instantaneous scale-value of the heliometer is known, or that it is a function of the temperature. Of course, for many purposes, mean conditions may be adopted and mean scale-values be found which are applicable with considerable precision to small angles or to comparatively crude observations of large distances; but the highest refinement is lost unless means are provided for determining the scale-value for each observer at each epoch of observation.
In determinations of stellar or solar parallax, comparison stars, symmetrically situated with respect to the object whose parallax is sought, should be employed, in which case the instantaneous scale-value may be regarded as an unknown quantity which can be derived in the process of the computation of the results. Examples of this mode of procedure will be found, in the case of stellar parallax in the Mem. R.A.S. vol. xlviii. pp. 1-194, and in the Annals of the Cape Observatory, vol. viii. parts 1 and 2; and in the case of planetary parallax in the Mem. R.A.S. vol. xlvi. pp. 1-171, and in the Annals of the Cape Observatory, vol. vi. In other operations, such as the triangulation of large groups of stars, it is necessary to select a pair of standard stars, if possible near the middle of the group, and to determine the scale-value by measures of this standard distance at frequent intervals during the night (see Annals of the Cape Observatory, vol. vi. pp. 3-224). In other cases, such as the measurement of the mutual distances and position angles of the satellites of Jupiter, for derivation of the elements of the orbits of the satellites and the mass of Jupiter, reference must also be made to measures of standard stars whose relative distance and position angle is accurately determined by independent methods (see Annals of the Cape Observatory, vol. xii. part 2).
| Fig. 17. |
Gill introduced a powerful auxiliary to the accuracy of heliometer measures in the shape of a reversing prism placed in front of the eye-piece, between the latter and the observer’s eye. If measures are made by placing the image of a star in the centre of the disk of a planet, the observer may have a tendency to do so systematically in error from some acquired habit or from natural astigmatism of the eye. But by rotating the prism 90° the image is presented entirely reversed to the eye, so that in the mean of measures made in two such positions personal error is eliminated. Similarly the prism may be used for the study and elimination of personal errors depending on the angle made by a double star with the vertical. The best plan of mounting such a prism has been found to be the following. l1, l2 (fig. 17) are the eye lens and field lens respectively of a Merz positive eye-piece. In this construction the lenses are much closer together and the diaphragm for the eye is much farther from the lenses than in Ramsden’s eye-piece. The prism p is fitted accurately into brass slides (care has to be taken in the construction to place the prism so that an object in the centre of the field will so remain when the eye-piece is rotated in its adapter). There is a collar, clamped by the screw at S, which is so adjusted that the eye-piece is in focus when pushed home, in its adapter, to this collar. The prism and eye-piece are then rotated together in the adapter.
The Double Image Micrometer.—Thomas Clausen in 1841 (Ast. Nach. No. 414) proposed a form of micrometer consisting of a divided plate of parallel glass placed within the cone of rays from the object-glass at right angles to the telescope axis. One-half of this plane remains fixed, the other half is movable. When the inclination of the movable half with respect to the axis of the telescope is changed by rotation about an axis at right angles to the plane of division, two images are produced. The amount of separation is very small, and depends on the thickness of the glass, the index of refraction and the focal length of the telescope. Angelo Secchi (Comptes rendus, xli., 1855, p. 906) gives an account of some experiments with a similar micrometer; and Ignarjio Porro (Comptes rendus, xli. p. 1058) claims the original invention and construction of such a micrometer in 1842. Clausen, however, has undoubted priority. Helmholtz in his “Ophthalmometer” has employed Clausen’s principle, but arranges the plates so that both move symmetrically in opposite directions with respect to the telescope axis. Should Clausen’s micrometer be employed as an astronomical instrument, it would be well to adopt the improvement of Helmholtz.
Double-Image Micrometers with Divided Lenses.—Various micrometers have been invented besides the heliometer for measuring by double image. Ramsden’s dioptric micrometer consists of a divided lens placed in the conjugate focus of the innermost lens of the erecting eye-tube of a terrestrial telescope. The inventor claimed that it would supersede the heliometer, but it has never done anything for astronomy. Dollond claims the independent invention and first construction of a similar instrument (Pearson’s Practical Astronomy, ii. 182). Of these and kindred instruments only two types have proved of practical value. G. B. Amici of Modena (Mem. Soc. Ital. xvii., 1815, pp. 344-359) describes a micrometer in which a negative lens is introduced between the eye-piece and the object-glass. This lens is divided and mounted like a heliometer object-glass; the separation of the lenses produces the required double image, and is measured by a screw. W. R. Dawes very successfully used this micrometer in conjunction with a filar micrometer, and found that the precision of the measures was in this way greatly increased (Monthly Notices, vol. xviii. p. 58, and Mem. R.A.S. vol. xxxv. p. 147).
In the improved form[19] of Airy’s divided eye-glass micrometer (Mem. R.A.S. vol. xv. pp. 199-209) the rays from the object-glass pass successively through lenses as follows:
| Lens. | Distance from next Lens. | Focal Length. |
| a. An equiconvex lens | p | arbitrary = p |
| b. ” ” | 2 | 5 |
| c. Plano-convex, convex towards b | 1¾ | 1 |
| d. Plano-convex, convex towards c | ” | 1 |
The lens b is divided, and one of the segments is moved by a micrometer screw. The magnifying power is varied by changing the lens a for another in which p has a different value. The magnifying power of the eye-piece is that of a single lens of focus = 4⁄5p.
In 1850 J. B. Valz pointed out that the other optical conditions could be equally satisfied if the divided lens were made concave instead of convex, with the advantage of giving a larger field of view (Monthly Notices, vol. x. p. 160).