considerable angles with micrometric accuracy, that he resolved, when he should have the choice of a new telescope for the observatory, to secure some form of heliometer.
Nor is it difficult to imagine the probable course of reasoning which led Bessel to select the model of his new heliometer. Why, he might ask, should he not select the simple form of Dollond’s first type? Given the achromatic object-glass, why should not it be divided? This construction would give all the advantage of the younger Dollond’s object-glass micrometer, and more than its sharpness of definition, without liability to the systematic errors which may be due to want of homogeneity of the object-glass; for the lenses will not be turned with respect to each other, but, in measurement, will always have the same relation in position angle to the line joining the objects under observation. It is true that the scale will require to be capable of being read with much greater accuracy than 11000th of an inch—for that, even in a telescope of 10 ft. focus, would correspond with 2″ of arc. But, after all, this is no practical difficulty, for screws can be used to separate the lenses, and, by these screws, as in a Gascoigne micrometer, the separation of the lenses can be measured; or we can have scales for this purpose, read by microscopes, like the Troughton[1] circles of Piazzi or Pond, or those of the Carey circle, with almost any required accuracy.
Whether Bessel communicated such a course of reasoning to Fraunhofer, or whether that great artist arrived independently at like conclusions, we have been unable to ascertain with certainty. The fact remains that before 1820[2] Fraunhofer had completed one or more of the five heliometers (3 in. aperture and 39 in. focus) which have since become historical instruments. In 1824 the great Königsberg heliometer was commenced, and it was completed in 1829.
To sum up briefly the history of the development of the heliometer. The first application of the divided object-glass and the employment of double images in astronomical measures is due to Savary in 1743. To Bouguer in 1748 is due the true conception of measurement by double image without the auxiliary aid of a filar micrometer, viz. by changing the distance between two object-glasses of equal focus. To Dollond in 1754 we owe the combination of Savary’s idea of the divided object-glass with Bouguer’s method of measurement, and the construction of the first really practical heliometers. To Fraunhofer, some time not long previous to 1820, is due, so far as we can ascertain, the construction of the first heliometer with an achromatic divided object-glass, i.e. the first heliometer of the modern type.
 |
| Fig. 8. |
The Königsberg heliometer is represented in fig. 8. No part of the equatorial mounting is shown in the figure, as it resembles in every respect the usual Fraunhofer mounting. An adapter h is fixed on a telescope-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, f 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 c, which carries the supports of the handles a′, b′, 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 interference 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 612 in. and 102 in. 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 displaced from it, the images are not both in focus of the eye-piece,[3] 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 necessity for frequent readjustment of the position of the eye-piece. The third method is the most symmetrical of all, both in observation 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.[4]
When Bessel ordered the Königsberg heliometer, he was anxious to have the segments made to move in cylindrical slides, of which the radius should be equal to the focal length of the object-glass. Fraunhofer, however, did not execute this wish, on the ground that the mechanical difficulties were too great.
M. L. G. Wichmann states (Königsb. Beobach. xxx. 4) that Bessel had indicated, by notes in his handbooks, the following points which should be kept in mind in the construction of future heliometers: (1) The segments should move in cylindrical slides;[5] (2) the screw should be protected from dust;[6] (3) the zero of the position circle should not be so liable to change;[7] (4) the distance of the optical centres of the segments should not change in different position angles or otherwise;[8] (5) the points of the micrometer screws should rest on ivory plates;[9] (6) there should be an apparatus for changing the screen.[10]
Wilhelm Struve, in describing the Pulkowa heliometer,[11] made
- ↑ The circles by Reichenbach, then almost exclusively used in Germany, were read by verniers only.
- ↑ The diameter of Venus was measured with one of these heliometers at the observatory of Breslau by Brandes in 1820 (Berlin Jahrbuch, 1824, p. 164).
- ↑ The distances of the optical centres of the segments from the eye-piece are in this method as 1; secant of the angle under measurement. In Bessel’s heliometer this would amount to a difference of 151000th of an inch when an angle of 1° is measured. For 2° the difference would amount to nearly 110th of an inch. Bessel confined his measures to distances considerably less than 1°.
- ↑ In criticizing Bessel’s choice of methods, and considering the loss of time involved in each, it must be remembered that Fraunhofer provided no means of reading the screws or even the heads from the eye-end. Bessel’s practice was to unclamp in declination, lower and read off the head, and then restore the telescope to its former declination reading, the clockwork meanwhile following the stars in right ascension. The setting of both lenses symmetrically would, under such circumstances, be very tedious.
- ↑ This most important improvement would permit any two stars under measurement each to be viewed in the optical axis of each segment. The optical centres of the segments would also remain at the same distance from the eye-piece at all angles of separation. Thus, in measuring the largest as well as the smallest angles, the images of both stars would be equally symmetrical and equally well in focus. Modern heliometers made with cylindrical slides measure angles over 2°, the images remaining as sharp and perfect as when the smallest angles are measured.
- ↑ Bessel found, in course of time, that the original corrections for the errors of his screw were no longer applicable. He considered that the changes were due to wear, which would be much lessened if the screws were protected from dust.
- ↑ The tube, being of wood, was probably liable to warp and twist in a very uncertain way.
- ↑ We have been unable to find any published drawing showing how the segments are fitted in their cells.
- ↑ We have been unable to ascertain the reasons which led Bessel to choose ivory planes for the end-bearings of his screws. He actually introduced them in the Königsberg heliometer in 1840, and they were renewed in 1848 and 1850.
- ↑ A screen of wire gauze, placed in front of the segment through which the fainter star is viewed, was employed by Bessel to equalize the brilliancy of the images under observation. An arrangement, afterwards described, has been fitted in modern heliometers for placing the screen in front of either segment by a handle at the eye-end.
- ↑ This heliometer resembles Bessel’s, except that its foot is a solid block of granite instead of the ill-conceived wooden structure that supported his instrument. The object-glass is of 7.4 in. aperture and 123 in. focus.
