Chapter XVIII: Part 18

HELIODORUS, of Emesa in Syria, Greek writer of romance. According to his own statement his father's name was Theodosius, and he belonged to a family of priests of the sun. He was the author of the _Aethiopica_, the oldest and best of the Greek romances that have come down to us. It was first brought to light in modern times in a MS. from the library of Matthias Corvinus, found at the sack of Buda (Ofen) in 1526, and printed at Basel in 1534. Other codices have since been discovered. The title is taken from the fact that the action of the beginning and end of the story takes place in Aethiopia. The daughter of Persine, wife of Hydaspes, king of Aethiopia, was born white through the effect of the sight of a marble statue upon the queen during pregnancy. Fearing an accusation of adultery, the mother gives the babe to the care of Sisimithras, a gymnosophist, who carries her to Egypt and places her in charge of Charicles, a Pythian priest. The child is taken to Delphi, and made a priestess of Apollo under the name of Chariclea. Theagenes, a noble Thessalian, comes to Delphi and the two fall in love with each other. He carries off the priestess with the help of Calasiris, an Egyptian, employed by Persine to seek for her daughter. Then follow many perils from sea-rovers and others, but the chief personages ultimately meet at Meroe at the very moment when Chariclea is about to be sacrificed to the gods by her own father. Her birth is made known, and the lovers are happily married. The rapid succession of events, the variety of the characters, the graphic descriptions of manners and of natural scenery, the simplicity and elegance of the style, give the _Aethiopica_ great charm. As a whole it offends less against good taste and morality than others of the same class. Homer and Euripides were the favourite authors of Heliodorus, who in his turn was imitated by French, Italian and Spanish writers. The early life of Clorinda in Tasso's _Jerusalem Delivered_ (canto xii. 21 sqq.) is almost identical with that of Chariclea; Racine meditated a drama on the same subject; and it formed the model of the _Persiles y Sigismunda_ of Cervantes. According to the ecclesiastical historian Socrates (_Hist. eccles._ v. 22), the author of the _Aethiopica_ was a certain Heliodorus, bishop of Tricca in Thessaly. It is supposed that the work was written in his early years before he became a Christian, and that, when confronted with the alternative of disowning it or resigning his bishopric, he preferred resignation. But it is now generally agreed that the real author was a sophist of the 3rd century A.D.

The best editions are: A. Coraes (1804), G. A. Hirschig (1856); see
also M. Oeftering, _H. und seine Bedeutung fur die Literatur_, with
full bibliographies (1901); J. C. Dunlop, _History of Prose Fiction_
(1888); and especially E. Rohde, _Der griechische Roman_ (1900). There
are translations in almost all European languages: in English, in
Bohn's _Classical Library_ and the "Tudor" series (v., 1895,
containing the old translation by T. Underdowne, 1587, with
introduction by C. Whibley); in French by Amyot and Zevort.

HELIOGABALUS (ELAGABALUS), Roman emperor (A.D. 218-222), was born at Emesa about 205. His real name was Varius Avitus. On the murder of Caracalla (217), Julia Maesa, Varius's grandmother and Caracalla's aunt, left Rome and retired to Emesa, accompanied by her grandsons (Varius and Alexander Severus). Varius, though still only a boy, was appointed high priest of the Syrian sun-god Elagabalus, one of the chief seats of whose worship was Emesa (Homs). His beauty, and the splendid ceremonials at which he presided, made him a great favourite with the troops stationed in that part of Syria, and Maesa increased his popularity by spreading reports that he was in reality the illegitimate son of Caracalla. Macrinus, the successor and instigator of the murder of Caracalla, was very unpopular with the army; an insurrection was easily set on foot, and on the 16th of May 218 Varius was proclaimed emperor as Marcus Aurelius Antoninus. The troops sent to quell the revolt went over to him, and Macrinus was defeated near Antioch on the 8th of June. Heliogabalus was at once recognized by the senate as emperor. After spending the winter in Nicomedia, he proceeded in 219 to Rome, where he made it his business to exalt the deity whose priest he was and whose name he assumed. The Syrian god was proclaimed the chief deity in Rome, and all other gods his servants; splendid ceremonies in his honour were celebrated, at which Heliogabalus danced in public, and it was believed that secret rites accompanied by human sacrifice were performed in his honour. In addition to these affronts upon the state religion, he insulted the intelligence of the community by horseplay of the wildest description and by childish practical joking. The shameless profligacy of the emperor's life was such as to shock even a Roman public. His popularity with the army declined, and Maesa, perceiving that the soldiers were in favour of Alexander Severus, persuaded Heliogabalus to raise his cousin to the dignity of Caesar (221), a step of which he soon repented. An attempt to murder Alexander was frustrated by the watchful Maesa. Another attempt in 222 produced a mutiny among the praetorians, in which Heliogabalus and his mother Soemias (Soaemias) were slain (probably in the first half of March).

AUTHORITIES.--Life by Aelius Lampridius in _Scriptores historiae
Augustae_; Herodian v. 3-8; Dio Cassius lxxviii. 30 sqq., lxxix. 1-21;
monograph by G. Duviquet, _Heliogabale_ (1903), containing a
translation of the various accounts of Heliogabalus in Greek and Latin
authors, notes, bibliography and illustrations; O. F. Butler, _Studies
in the Life of Heliogabalus_ (New York, 1908); Gibbon, _Decline and
Fall_, ch. 6; H. Schiller, _Geschichte der romischen Kaiserzeit_, i.
pt. ii. (1883), p. 759 ff. On the Syrian god see F. Cumont in
Pauly-Wissowa's _Realencyclopadie_, v. pt. ii. (1905).

HELIOGRAPH (from Gr. [Greek: elios], sun, and [Greek: graphein] to write), an instrument for reflecting the rays of the sun (or the light obtained from any other source) over a considerable distance. Its main application is in military signalling (see SIGNAL). A similar instrument is the heliotrope, used principally for defining distant points in geodetic surveys, such as in the triangulation of India, and in the verification of the African arc of the meridian. It is necessary to distinguish the method of signalling termed heliography from the photographic process of the same name (see PHOTOGRAPHY).

HELIOMETER (from Gr. [Greek: helios], sun, and [Greek: metron], a measure), an instrument originally designed for measuring the variation of the sun's diameter at different seasons of the year, but applied now to the modern form of the instrument which is capable of much wider use. The present article also deals with other forms of double-image micrometer.

The discovery of the method of making measures by double images is
stated to have been first suggested by O. Roemer about 1768. But no
such suggestion occurs in the _Basis Astronomiae_ of Peter Horrebow
(Copenhagen, 1735), which contains the only works of Roemer that
remain to us. It would appear that to Servington Savary is due the
first invention of a micrometer for measurement by double image. His
heliometer (described in a paper communicated to the Royal Society in
1743, and printed, along with a letter from James Short, in _Phil.
Trans._, 1753, p. 156) was constructed by cutting from a complete lens
abcd the equal portions aghc and acfe (fig. 1). The segments gbh and
efd so formed were then attached to the end of a tube having an
internal diameter represented by the dotted circle (fig. 2). The width
of each of the portions aghc and acfe cut away from the lens was made
slightly greater than the focal length of lens X tangent of sun's
greatest diameter. Thus at the focus two images of the sun were formed
nearly in contact as in fig. 3. The small interval between the
adjacent limbs was then measured with a wire micrometer.

Savary also describes another form of heliometer, on the same
principle, in which the segments aghc and acfe are utilized by
cementing their edges gh and ef together (fig. 4), and covering all
except the portion indicated by the unshaded circle. Savary expresses
preference for this second plan, and makes the pertinent remark that
in both these models "the rays of red light in the two solar images
will be next to each other, which will render the sun's disk more easy
to be observed than the violet ones." This he mentions "because the
glasses in these two sorts are somewhat prismatical, but mostly those
of the first model, which could therefore bear no great charge
(magnifying power)."

A third model proposed by Savary consists of two complete lenses of
equal focal length, mounted in cylinders side by side, and attached to
a strong brass plate (fig. 5). Here, in order to fulfil the purposes
of the previous models, the distance of the centres of the lenses from
each other should only slightly exceed the tangent of sun's diameter X
focal length of lenses. Savary dwells on the difficulty both of
procuring lenses sufficiently equal in focus and of accurately
adjusting and centring them.

In the _Mem. Acad. de Paris_ (1748), Pierre Bouguer describes an
instrument which he calls a heliometer. Lalande in his _Astronomie_
(vol. ii. p. 639) mentions such a heliometer which had been in his
possession from the year 1753, and of which he gives a representation
on Plate XXVIII., fig. 186, of the same volume. Bouguer's heliometer
was in fact similar to that of Savary's third model, with the
important difference that, instead of both object-glasses being fixed,
one of them is movable by a screw provided with a divided head. No
auxiliary filar micrometer was required, as in Savary's heliometer, to
measure the interval between the limbs of two adjacent images of the
sun, it being only necessary to turn the screw with the divided head
to change the distance between the object-glasses till the two images
of the sun are in contact as in fig. 6. The differences of the
readings of the screw, when converted into arc, afford the means of
measuring the variations of the sun's apparent diameter.

On the 4th of April 1754 John Dollond communicated a paper to the
Royal Society of London (_Phil. Trans._, vol. xlviii. p. 551) in which
he shows that a micrometer can be much more easily constructed by
dividing a single object-glass through its axis than by the employment
of two object-glasses. He points out--(1) that a telescope with an
object-glass so divided still produces a single image of any object to
which it may be directed, provided that the optical centres of the
segments are in coincidence (i.e. provided the segments retain the
same relative positions to each other as before the glass was cut);
(2) that if the segments are separated in any direction two images of
the object viewed will be produced; (3) that the most convenient
direction of separation for micrometric purposes is to slide these
straight edges one along the other as the figure on the margin (fig.
7) represents them: "for thus they may be moved without suffering any
false light to come in between them; and by this way of removing them
the distance between their centres may be very conveniently measured,
viz. by having a vernier's division fixed to the brass work that holds
one segment, so as to slide along a scale on the plate to which the
other part of the glass is fitted."

Dollond then points out three different types in which a glass so
divided and mounted may be used as a micrometer:--

"1. It may be fixed at the end of a tube, of a suitable length to its
focal distance, as an object-glass,--the other end of the tube having
an eye-glass fitted as usual in astronomical telescopes.

"2. It may be applied to the end of a tube much shorter than its focal
distance, by having another convex glass within the tube, to shorten
the focal distance of that which is cut in two.

"3. It may be applied to the open end of a reflecting telescope,
either of the Newtonian or the Cassegrain construction."

Dollond adds his opinion that the third type is "much the best and
most convenient of the three"; yet it is the first type that has
survived the test of time and experience, and which is in fact the
modern heliometer. It must be remembered, however, that when Dollond
expressed preference for this third type he had not then invented the
achromatic object-glass.

Some excellent instruments of the second type were subsequently made
by Dollond's eldest son Peter, in which for the "convex glass within
the tube" was substituted an achromatic object-glass, and outside that
a divided negative achromatic combination of long focus. In the fine
example of this instrument at the Cape Observatory the movable
negative lenses consist of segments of the shape gach and acfe (fig.
1) cut from a complete negative achromatic combination of 8(1/4) in.
aperture and about 41 ft. focal length, composed of a double concave
flint lens and a double convex crown. This was applied to an excellent
achromatic telescope of 3(1/4) in. aperture and 42 in. focal length. In
this instrument a considerable linear relative movement of the divided
lens corresponds with a comparatively small separation of the double
image, so that simple verniers reading to 1/1000 in. are sufficient
for measurement.

With one of these instruments of somewhat smaller dimensions
(telescope 2(1/2) in. aperture and 3(1/2) ft. focus), Franz von Paula
Triesnecker made a series of measurements at the observatory of Vienna
which has been reduced by Dr Wilhelm Schur of Strasburg (_Nova Acta
der Ksl. Leop.-Carol. Deutschen Akademie der Natursforscher_, 1882,
xlv. No. 3). The angle between the stars [zeta] and g Ursae maj.
(708".55) was measured on four nights; the probable error of a measure
on one night was [+-]0".44. Jupiter was measured on eleven nights in
the months of June and July 1794; from these measures Schur derives
the values 35".39 and 37".94 for the polar and equatorial diameter
respectively, at mean distance, corresponding with a compression
1/14.44. These agree satisfactorily with the corresponding values
35".21, 37".60, 1/15.59 afterwards obtained by F. W. Bessel
(_Konigsberger Beobachtungen_, xix. 102). From a series of measures of
the angle between Jupiter's satellites and the planet, made in June
and July 1794 and in August and September 1795, Schur finds the mass
of Jupiter = 1/1048.55 [+-] 1.45, a result which accords well within
the limits of its probable error with the received value of the mass
derived from modern researches. The probable errors for the measures
of one night are [+-]0".577, [+-]0".889, [+-]0".542, [+-]1".096, for
Satellites I., II., III. and IV. respectively.

Considering the accuracy of these measures (an accuracy far surpassing
that of any other contemporary observations), it is somewhat
surprising that this form of micrometer was never systematically used
in any sustained or important astronomical researches, although a
number of instruments of the kind were made by Dollond. Probably the
last example of its employment is an observation of the transit of
Mercury (November 4, 1868) by Mann, at the Royal Observatory, Cape of
Good Hope (_Monthly Notices R.A.S._ vol. xxix. p. 197-209). The most
important part, however, which this type of instrument seems to have
played in the history of astronomy arises from the fact that one of
them was in the possession of Bessel at Konigsberg during the time
when his new observatory there was being built. In 1812 Bessel
measured with it the angle between the components of the double star
61 Cygni and observed the great comet of 1811. He also observed the
eclipse of the sun on May 4, 1818. In the discussion of these
observations (_Konigsberger Beobacht_, Abt. 5, p. iv.) he found that
the index error of the scale changed systematically in different
position angles by quantities which were independent of the direction
of gravity relative to the position angle under measurement, but which
depended solely on the direction of the measured position angle
relative to a fixed radius of the object-glass. Bessel attributed this
to non-homogeneity in the object-glass, and determined with great care
the necessary corrections. But he was so delighted with the general
performance of the instrument, with the sharpness of the images and
the possibilities which a kindred construction offered for the
measurement of 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 1/1000th 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 Konigsberg
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.

_The Modern Heliometer._

The Konigsberg 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 6(1/2) 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 Konigsberg 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 (_Konigsb. 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 by
Merz in 1839 on the model of Bessel's heliometer, submits the
following suggestions for its improvement:[12] (1) to give
automatically to the two segments simultaneous equal and opposite
movement;[13] and (2) to make the tube of metal instead of wood; to
attach the heliometer head firmly to this tube; to place the eye-piece
permanently in the axis of the telescope; and to fix a strong cradle
on the end of the declination axis, in which the tube, with the
attached head and eye-piece, could rotate on its axis.

Both suggestions are important. The first is originally the idea of
Dollond; its advantages were overlooked by his son, and it seems to
have been quite forgotten till resuggested by Struve. But the method
is not available if the separation is to be measured by screws; it is
found, in that case, that the direction of the final motion of turning
of the screw must always be such as to produce motion of the segment
against gravity, otherwise the "loss of time" is apt to be variable.
Thus the simple connexion of the two screws by cog-wheels to give them
automatic opposite motion is not an available method unless the
separation of the segments is independently measured by scales.

Struve's second suggestion has been adopted in nearly all succeeding
heliometers. It permits complete rotation of the tube and measurement
of all angles in reversed positions of the circle; the handles that
move the slides can be brought down to the eye-end, inside the tube,
and consequently made to rotate with it; and the position circle may
be placed at the end of the cradle next the eye-end where it is
convenient of access. Struve also points out that by attaching a fine
scale to the focusing slide of the eye-piece, and knowing the
coefficient of expansion of the metal tube, the means would be
provided for determining the absolute change of the focal length of
the object-glass at any time by the simple process of focusing on a
double star. This, with a knowledge of the temperature of the screw or
scale and its coefficient of expansion, would enable the change of
screw-value to be determined at any instant.

It is probable that the Bonn heliometer was in course of construction
before these suggestions of Struve were published or discussed, since
its construction resembles that of the Konigsberg and Pulkowa
instruments. Its dimensions are similar to those of the former
instrument. Bessel, having been consulted by the celebrated statesman,
Sir Robert Peel, on behalf of the Radcliffe trustees, as to what
instrument, added to the Radcliffe Observatory, would probably most
promote the advancement of astronomy, strongly advised the selection
of a heliometer. The order for the instrument was given to the
Repsolds in 1840, but "various circumstances, for which the makers are
not responsible, contributed to delay the completion of the
instrument, which was not delivered before the winter of 1848."[14]
The building to receive it was commenced in March 1849 and completed
in the end of the same year. This instrument has a superb object-glass
of 7(1/2) in. aperture and 126 in. focal length. The makers availed
themselves of Bessel's suggestion to make the segments move in
cylindrical slides, and of Struve's to have the head attached to a
brass tube; the eye-piece is set permanently in the axis, and the
whole rotates in a cradle attached to the declination axis. They
provided a splendid, rigidly mounted, equatorial stand, fitted with
every luxury in the way of slow motion, and scales for measuring the
displacement of the segments were read by powerful micrometers from
the eye-end.[15] It is somewhat curious that, though Struve's second
suggestion was adopted, his first was overlooked by the makers. But it
is still more curious that it was not afterwards carried out, for the
communication of automatic symmetrical motion to both segments only
involves a simple alteration previously described. But, as it came
from the hands of the makers in 1849, the Oxford heliometer was
incomparably the most powerful and perfect instrument in the world for
the highest order of micrometric research. It so remained, unrivalled
in every respect, till 1873.

As the transit of Venus of 1874 approached, preparations were set on
foot by the German Government in good time; a commission of the most
celebrated astronomers was appointed, and it was resolved that the
heliometer should be the instrument chiefly relied on. The four
long-neglected small heliometers made by Fraunhofer were brought into
requisition. Fundamental alterations were made upon them: their wooden
tubes were replaced by tubes of metal; means of measuring the focal
point were provided; symmetrical motion was given to the slides;
scales on each slide were provided instead of screws for measuring the
separation of the segments, and both scales were read by the same
micrometer microscope; a metallic thermometer was added to determine
the temperature of the scales. These small instruments have since done
admirable work in the hands of Schur, Hartwig, Kustner, Elkin, Auwers
and others.

The Russian Government ordered three new heliometers (each of 4 in.
aperture and 5 ft. focal length) from the Repsolds, and the design for
their construction was superintended by Struve, Auwers and Winnecke,
the last-named making the necessary experiments at Carlsruhe. Fig. 9
represents the resulting type of instrument which was finally designed
and constructed by Repsolds. The brass tube, strengthened at the
bearing points by strong truly turned collars, rotates in the cast
iron cradle q attached to the declination axis, a is the eye-piece
fixed in the optical axis, b the micrometer for reading both scales, c
and d are telescopes for reading the position circle p, e the handle
for quick motion in position angle, f the slow motion in position
angle, g the handle for changing the separation of the segments by
acting on the bevel-wheel g' (fig. 10). h is a milled head connected
by a rod with h' (fig. 10), for the purpose of interposing at pleasure
the prism [pi] in the axis of the reading micrometer; this enables the
observer to view the graduations on the face of the metallic
thermometer [tau tau] (composed of a rod of brass and a rod of zinc),
i is a milled head connected with the wheel i'i' (fig. 10), and
affords the means of placing the screen s (fig. 9), counterpoised by w
over either half of the object-glass. k clamps the telescope in
declination, n clamps it in right ascension, and the handles m and l
provide slow motion in declination and right ascension respectively.

The details of the interior mechanism of the "head" will be almost
evident from fig. 10 without description. The screw, turned by the
wheels at g', acts in a toothed arc, whence, as shown in the figure,
equal and opposite motion is communicated to the slides by the jointed
rods v, v. The slides are kept firmly down to their bearings by the
rollers r, r, r, r, attached to axes which are, in the middle, very
strong springs. Side-shake is prevented by the screws and pieces k, k,
k, k. The scales are at n, n; they are fastened only at the middle,
and are kept down by the brass pieces t, t.

A similar heliometer was made by the Repsolds to the order of Lord
Lindsay for his Mauritius expedition in 1874. It differed only from
the three Russian instruments in having a mounting by the Cookes in
which the declination circle reads from the eye-end.[16] This
instrument was afterwards most generously lent by Lord Lindsay to Gill
for his expedition to Ascension in 1877.[17]

These four Repsold heliometers proved to be excellent instruments,
easy and convenient in use, and yielding results of very high
accuracy in measuring distances. Their slow motion in position angle,
however, was not all that could be desired. When small movements were
communicated to the handle e (fig. 9) by the tangent screw f, acting
on a small toothed wheel clamped to the rod connected with the driving
pinion, there was apt to be a torsion of the rod rather than an
immediate action. Thus the slow motion would take place by jerks
instead of with the necessary smoothness and certainty. When the
heliometer-part of Lord Lindsay's heliometer was acquired by Gill in
1879, he changed the manner of imparting the motion in question. A
square toothed racked wheel was applied to the tube at r (fig. 9).
This wheel is acted on by a tangent screw whose bearings are attached
to the cradle; the screw is turned by means of a handle supported by
bearings attached to the cradle, and coming within convenient reach of
the observer's hand. The tube turns smoothly in the racked wheel, or
can be clamped to it at the will of the observer. This alteration and
the new equatorial mounting have been admirably made by Grubb; the
result is completely successful. The instrument so altered was in use
at the Cape Observatory from March 1881 till 1887 in determining the
parallax of some of the more interesting southern stars. The
instrument then passed, by purchase from Gill, to Lord McLaren, by
whom it was presented to the Royal Observatory, Edinburgh.

Still more recently the Repsolds have completed a new heliometer for
Yale College, New Haven, United States. The object-glass is of 6 in.
aperture and 98 in. focal length. The mounting, the tube,
objective-cell, slides, &c., are all of steel.[18] The instrument is
shown in fig. 11. The circles for position angle and declination are
read by micrometer-microscopes illuminated by the lamp L; the scales
are illuminated by the lamp l. T is part of the tube proper, and turns
with the head. The tube V, on the contrary, is attached to the cradle,
and merely forms a support for the finder Q, the handles at f and p,
and the moving ring P. The latter gives quick motion in position
angle; the handles at p clamp and give slow motion in position angle,
those at f clamp and give slow motion in right ascension and
declination. a is the eye-piece, b the handle for moving the segments,
c the micrometer microscope for reading the scales and scale
micrometer, d the micrometer readers of the position and declination
circles, e the handle for rotating the large wheel E which carries the
screens. The hour circle is also read by microscopes, and the
instrument can be used in both positions (tube preceding and
following) for elimination of the effect of flexure on the position
angles. Elkin found that the chief drawbacks to speed and convenience
in working this heliometer were: (1) The loss of time involved in
entering the corresponding readings of the micrometer pointings on two
scales. (2) That an additional motion intermediate between the quick
and slow motion in position angle was necessary, because, whilst the
slow motion provided by Repsolds was admirably adapted for adjusting
the pointings in position angle, it was too slow for causing the
images to "cross through" each other in the process of measuring
distances. To remedy drawback (1) Repsolds devised the form of
printing micrometer which is shown in figs. 12 and 13. This micrometer
is provided with two pairs of parallel webs. One fixed pair of webs is
attached to the micrometer-box, the other pair is moved by the screw
S. The whole micrometer-box is moved by the screw attached to the
heads. Accordingly, in reading the scales A and B (attached to the
slides which carry the two halves of the object-glass), it is only
necessary to turn the screws until the fixed double web is pointed
symmetrically on one of the divisions of scale A, then to move the
other double web by the screw S until it is symmetrically pointed on
the adjoining division of scale B. By turning the quick acting screw P
(fig. 13) to the right, the cushion C (which is faced with
india-rubber) presses the paper ribbon (shown in fig. 13) against the
index-edge and type-wheels, and thus the beautifully cut divisions of
the micrometer-head, the numbers marking the 1/100 parts of the head,
the index and the total number of revolutions are all sharply embossed
together upon the paper ribbon. Fig. 14 shows the record of several
successive paintings on the same scale as that given by the
micrometer. The reverse motion of P automatically moves the paper
ribbon forward, ready to receive the next impression. It must be
mentioned that the pressure of the cushion C on the type-wheels has no
influence whatever upon the micrometer-screw, because the type-wheels
are mounted on a hollow cylindrical axis, concentric with the axis of
the screw, but entirely disconnected from the screw itself. The only
connexion between the type-wheel and the screw-head S is by the pin p
(which is screwed into S), the cylindrical end of which acts in a slot
cut in the type-wheel. To remedy drawback (2) Repsolds provided for
the Yale heliometer an additional handle for motion in position angle,
intermediate in velocity between the original quick and slow motions.

FIG. 15.]

In the 7-in. heliometer, completed in 1887 for the Royal Observatory
at the Cape of Good Hope, Repsolds, on Gill's suggestion, introduced
the following improvements: (a) Four different speeds of motion in
position angle were provided. The quickest movement is given by the
hand-ring, 73 (fig. 15). This ring runs between friction wheels and is
provided with teeth on its inner periphery, and these teeth transmit
motion to a pinion on a spindle having at its other end another pinion
which, through an intermediate wheel, rotates the heliometer tube. The
transmission spindle, just mentioned, carries at its end a head, 74,
which, if turned directly, gives the second speed. The slowest speed
is given by means of a tangent screw which is carried by a
ball-bearing on the flange of the telescope-sleeve, whilst its nut is
double-jointed to a ring that encircles the flange of the
heliometer-tube. This ring is provided with a clamping screw, which,
through the intervention of bevel-gear and rods, is operated by means
of the hand-wheel 78. With similar bevel-gear and rods the tangent
screw is connected to the hand-wheel, 79, by which the observer
communicates the fourth or slowest motion in position angle. Finally
the hand-wheel 80 is connected by gearing to the rod carrying the
hand-wheel 79, and it can thus be used to give the latter a more rapid
motion than if used direct; this constitutes the third speed of
movement.

(b) In lieu of oil-lamps, small, conveniently placed incandescent
electric 6-volt lamps are employed; and these are fitted with suitable
switches and variable resistances. Thus the scales, the position- and
declination-circles, the field of view, the heads of all the
micrometer-microscopes, the focusing scale, &c., are read without the
aid of a hand-lamp and with an amount of illumination that can be
regulated at the observer's pleasure.

(c) A button in the centre of the position-angle handle (74) connects
with a chronograph which enables the observer to record the instant of
observation. Little card-holders (81) (also illuminated) enable the
astronomer to enter beforehand the R.A. and Dec. of the object to be
observed, the scale divisions to be pointed upon, and thus, in
measures of distance, with the aid of the chronograph and printing
micrometer, enable the observer to adjust the instrument for
observation and obtain a record of his observations without the aid of
a hand-lamp or the necessity to make any records in his notebook. In
observations of position angle one of the two tablets 81 can be used
to record the readings.

(d) The scales are made of iridio-platinum instead of silver, and the
magnifying power of the reading microscope is increased fourfold (viz.
to 100 diameters). A special microscope is introduced for determining
the division errors of the scales. It enables the observer to compare
any division-interval on one half of either scale with any
corresponding interval on the other scale. With this apparatus Gill
was enabled (_Annals Cape Obs._ vii. 29-42, and _Monthly Notices,
R.A.S._, xlix. 105-115) to determine the division error of every line
on both scales with a probable error corresponding to [+-]0".0092 arc.

(e) A position-micrometer is attached to the finder to enable the
observer to select comparison stars for observation with some
unexpected object. Thus a comet may be encountered in the morning dawn
or evening twilight, and without such an adjunct the astronomer may
lose the whole available opportunity for observation in the vain
endeavour to find a suitable comparison-star. But with such a
position-micrometer of large field he has no difficulty. Directing the
finder to the comet, he has at once in the field of view all available
comparison stars. Having selected the most suitable one he directs the
axis of the finder to the estimated middle point between the comet and
the star, turns the finder-micrometer in position angle until the
images of comet and star lie symmetrically between the parallel
position wires, and then turns the micrometer screw (which moves the
distance-wires symmetrically from the centre in opposite directions)
till one wire bisects the comet and the other the star. The reading of
the position-circle of the finder is then the reading to which the
position-circle of the heliometer should be set, and from the readings
of the micrometer-screw he finds, by a convenient table, the proper
settings of the heliometer scales in distance. When the scales and
position-circle of the heliometer have been set to these readings, the
comet and the selected comparison-star appear together in the field of
view.

Fig. 15 shows the very convenient arrangement of the eye-end of the
instrument. The disk, 30 with its small projecting handle enables the
2 segments of the divided object to be moved rapidly or with any
required delicacy relative to each other. The disk 32 operates the
wire gauze screens for equalizing the brightness of the two stars
under observation. The dial between 30 and 32 indicates the screen in
use. 18 clamps and 19 gives slow motion in declination; 20 clamps and
21 gives slow motion in right ascension. The two handles 82 serve for
manipulating the instrument. The microscopes adjoining 82 read the
position and declination circles; for, by an ingenious arrangement of
prisms and screens, the images of both circles can be read by each
single microscope as shown in fig. 16, thus avoiding the necessity for
the employment of two additional micrometers.

Experience has shown that there is little that can be advantageously
changed to improve this instrument either in convenience or precision
of working. A series of observations can be easily and more accurately
accomplished with the Cape heliometer in half an hour; with the Oxford
heliometer it would occupy 2 hours, and with the 4 in. Repsold
heliometer (fig. 9) 1 hour. Heliometers of 6 to 8 in. aperture have
subsequently been constructed by Repsolds on these plans for
Gottingen, Bamberg, Leipzig and the Kuffner Observatory (near Vienna),
and all of them have made important contributions to astronomy of
precision.

Heliometer observations of distance in their most refined sense cannot
be considered absolute measures of angles. Essentially the scale-value
of the instrument depends on the relation of the focal length of the
object-glass to the length of the unit of the scale. But _the eye is
tolerant of small changes in the focal adjustment which sensibly
affect the scale-value_. These changes may and do arise from the
following causes: (i.) The focal length of the object-glass and the
length of the tube are affected by temperature. (ii.) The focal length
is sensibly different for objects of different colour. (iii.) The
length of the scale is affected by temperature. (iv.) The state of
adaptation of the observer's eye is dependent on his state of health,
on a condition of greater or less fatigue, or on the inclination of
the head in consequence of the altitude of the object observed. (v.)
The temperature of the object-glass, of the scale and of the tube,
cannot be assumed to be identical.

FIG. 16.]

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).

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 deg. 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. l^1, l^2
(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 | Focal Length. |
| | next Lens. | |
+-----------------------------------+---------------+---------------+
| a. An equiconvex lens | p | arbitrary = p |
| b. " " | 2 | 5 |
| c. Plano-convex, convex towards b | 1(3/4) | 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).

The last improvement on this instrument is mentioned in the _Report_
of the R.A.S. council, February 1865. It consists in the introduction
by Simms of a fifth lens, but no satisfactory description has ever
appeared. There is only one practical published investigation of
Airy's micrometer that is worthy of mention, viz. that of F. Kaiser
(_Annalen der Sternwarte in Leiden_, iii. 111-274). The reader is
referred to that paper for an exhaustive history and discussion of the
instrument.[20] It is somewhat surprising that, after Kaiser's
investigations, observers should continue, as many have done, to
discuss their observations with this instrument as if the screw-value
were constant for all angles.

Steinheil (_Journal savant de Munich_, Feb. 28, 1843) describes a
"heliometre-oculaire" which he made for the great Pulkowa refractor,
the result of consultations between himself and the elder Struve. It
is essentially the same in principle as Amici's micrometer, except
that the divided lens is an achromatic positive instead of a negative
lens. Struve (_Description de l'Observatoire Central de Pulkowa_, pp.
196, 197) adds a few remarks to Steinheil's description, in which he
states that the images have not all desirable precision--a fault
perhaps inevitable in all micrometers with divided lenses, and which
is probably in this case aggravated by the fact that the rays falling
upon the divided lens have considerable convergence. He, however,
successfully employed the instrument in measuring double stars, so
close as 1" or 2", and using a power of 300 diameters, with results
that agreed satisfactorily amongst themselves and with those obtained
with the filar micrometer. If Struve had employed a properly
proportioned double 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
_ante_).