[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 deg. is measured. For 2
deg. the difference would amount to nearly 1/10th of an inch. Bessel
confined his measures to distances considerably less than 1 deg.
[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 deg., 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for the errors of his screw were no longer applicable.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 Konigsberg heliometer in 1840, and they were
renewed in 1848 and 1850.
[10] 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.
[11] 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.
[12] _Description de l'observatoire central de Pulkowa_, p. 208.
[13] Steinheil applied such motion to a double-image micrometer made
for Struve. This instrument suggested to Struve the above-mentioned
idea of employing a similar motion for the heliometer.
[14] Manuel Johnson, M.A., Radcliffe observer, _Astronomical
Observations made at the Radcliffe Observatory, Oxford, in the Year
1850_, Introduction, p. iii.
[15] The illumination of these scales is interesting as being the
first application of electricity to the illumination of astronomical
instruments. Thin platinum wire was rendered incandescent by a
voltaic current; a small incandescent electric lamp would now be
found more satisfactory.
[16] For a detailed description of this instrument see _Dunecht
Publications_, vol. ii.
[17] _Mem. Royal Astronomical Society_, xlvi., 1-172.
[18] The primary object was to have the object-glass mounted in steel
cells, which more nearly correspond in expansion with glass. It
became then desirable to make the head of steel for sake of
uniformity of material, and the advantages of steel in lightness and
rigidity for the tube then became evident.
[19] For description of the earliest form see _Cambridge Phil.
Trans._ vol. ii., and _Greenwich Observations_ (1840).
[20] Dawes (_Monthly Notices_, January 1858, and _Mem. R.A.S._ vol.
xxxv. p. 150) suggested and used a valuable improvement for producing
round images, instead of the elongated images which are otherwise
inevitable when the rays pass through a divided lens of which the
optical centres are not in coincidence, viz. "the introduction of a
diaphragm having two circular apertures touching each other in a
point coinciding with the line of collimation of the telescope, and
the diameter of each aperture _exactly equal_ to the semidiameter of
the cone of rays at the distance of the diaphragm from the local
point of the object-glass." Practically the difficulty of making
these diaphragms for the different powers of the _exact_ required
equality is insuperable; but, if the observer is content to lose a
certain amount of light, we see no reason why they may not readily be
made slightly less. Dawes found the best method for the purpose in
question was to limit the aperture of the object-glass by a diaphragm
having a double circular aperture, placing the line joining the
centres of the circles approximately in the position angle under
measurement. Dawes successfully employed the double circular aperture
also with Amici's micrometer. The present writer has successfully
used a similar plan in measuring position angles of a Centauri with
the heliometer, viz. by placing circular diaphragms on the two
segments of the object-glass.
[21] Dollond provides for changing the power by sliding the lens d
nearer to or farther from a.
HELIOPOLIS, one of the most ancient cities of Egypt, met with in the
Bible under its native name On. It stood 5 m. E. of the Nile at the apex
of the Delta. It was the principal seat of sun-worship, and in historic
times its importance was entirely religious. There appear to have been
two forms of the sun-god at Heliopolis in the New Kingdom--namely,
Ra-Harakht, or Re'-Harmakhis, falcon-headed, and Etom, human-headed; the
former was the sun in his mid-day strength, the latter the evening sun.
A sacred bull was worshipped here under the name Mnevis (Eg. _Mreu_),
and was especially connected with Etom. The sun-god Re' (see EGYPT:
_Religion_) was especially the royal god, the ancestor of all the
Pharaohs, who therefore held the temple of Heliopolis in great honour.
Each dynasty might give the first place to the god of its
residence--Ptah of Memphis, Ammon of Thebes, Neith of Sais, Bubastis of
Bubastis, but all alike honoured Re'. His temple became in a special
degree a depository for royal records, and Herodotus states that the
priests of Heliopolis were the best informed in matters of history of
all the Egyptians. The schools of philosophy and astronomy are said to
have been frequented by Plato and other Greek philosophers; Strabo,
however, found them deserted, and the town itself almost uninhabited,
although priests were still there, and cicerones for the curious
traveller. The Ptolemies probably took little interest in their "father"
Re', and Alexandria had eclipsed the learning of Heliopolis; thus with
the withdrawal of royal favour Heliopolis quickly dwindled, and the
students of native lore deserted it for other temples supported by a
wealthy population of pious citizens. In Roman times obelisks were taken
from its temples to adorn the northern cities of the Delta, and even
across the Mediterranean to Rome. Finally the growth of Fostat and
Cairo, only 6 m. to the S.W., caused the ruins to be ransacked for
building materials. The site was known to the Arabs as _'Ayin esh
shems_, "the fountain of the sun," more recently as Tel Hisn. It has now
been brought for the most part under cultivation, but the ancient city
walls of crude brick are to be seen in the fields on all sides, and the
position of the great temple is marked by an obelisk still standing (the
earliest known, being one of a pair set up by Senwosri I., the second
king of the Twelfth Dynasty) and a few granite blocks bearing the name
of Rameses II.