[1] The circles by Reichenbach, then almost exclusively used in Germany, were read by verniers only.
[2] 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).
[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 measurement. In Bessel’s heliometer this would amount to a difference of 15⁄1000th of an inch when an angle of 1° is measured. For 2° the difference would amount to nearly 1⁄10th of an inch. Bessel confined his measures to distances considerably less than 1°.
[4] 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.
[5] 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.
[6] Bessel found, in course of time, that the original corrections for the errors of his screw were no longer applicable.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.
[7] The tube, being of wood, was probably liable to warp and twist in a very uncertain way.
[8] We have been unable to find any published drawing showing how the segments are fitted in their cells.
[9] 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.