Part 41

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.

[Illustration: FIG. 1.]

[Illustration: FIG. 2.]

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.

[Illustration: FIG. 3.]

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)."

[Illustration: FIG. 4.]

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.

[Illustration: FIG. 5.]

[Illustration: FIG. 6.]

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."

[Illustration: FIG. 7.]

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._

[Illustration: FIG. 8.]

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.