Part 43

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_).

Ramsden (_Phil. Trans._ vol. xix. p. 419) suggested the division of the small speculum of a Cassegrain telescope and the production of double image by micrometric rotation of the semispecula in the plane passing through their axis. Brewster (_Ency. Brit._ 8th ed. vol. xiv. p. 749) proposed a plan on a like principle, by dividing the plane mirror of a Newtonian telescope. Again, in an ocular heliometer by Steinheil double image is similarly produced by a divided prism of total reflection placed in parallel rays. But practically these last three methods are failures. In the last the field is full of false light, and it is not possible to give sufficiently minute and steady separation to the images; and there are of necessity a collimator, two prisms of total reflection, and a small telescope through which the rays must pass; consequently there is great loss of light.

_Micrometers Depending on Double Refraction._--To the Abbe Rochon (_Jour. de phys._ liii., 1801, pp. 169-198) is due the happy idea of applying the two images formed by double refraction to the construction of a micrometer. He fell upon a most ingenious plan of doubling the amount of double refraction of a prism by using two prisms of rock-crystal, so cut out of the solid as to give each the same quantity of double refraction, and yet to double the quantity in the effect produced. The combination so formed is known as Rochon's prism. Such a prism he placed between the object-glass and eye-piece of a telescope. The separation of the images increases as the prism is approached to the object-glass, and diminishes as it is approached towards the eye-piece.

D. F. J. Arago (_Comptes rendus_, xxiv., 1847, pp. 400-402) found that in Rochon's micrometer, when the prism was approached close to the eye-piece for the measurement of very small angles, the smallest imperfections in the crystal or its surfaces were inconveniently magnified. He therefore selected for any particular measurement such a Rochon prism as when fixed between the eye and the eye-piece (i.e. where a sunshade is usually placed) would, combined with the normal eye-piece employed, bring the images about to be measured nearly in contact. He then altered the magnifying power by sliding the field lens of the eye-piece (which was fitted with a slipping tube for the purpose) along the eye-tube, till the images were brought into contact. By a scale attached to the sliding tube the magnifying power of the eye-piece was deduced, and this combined with the angle of the prism employed gave the angle measured. If p" is the refracting angle of the prism, and n the magnifying power of the eye-piece, then p"/n will be the distance observed. Arago made many measures of the diameters of the planets with such a micrometer.

[Illustration: FIG. 18.]

[Illustration: FIG. 19.]

Dollond (_Phil. Trans._, 1821, pp. 101-103) describes a double-image micrometer of his own invention, in which a sphere of rock-crystal is substituted for the eye-lens of an ordinary eye-piece. In this instrument (figs. 18, 19) a is the sphere, placed in half-holes on the axis bb, so that when its principal axis is parallel to the axis of the telescope it gives only one image of the object. In a direction perpendicular to that axis it must be so placed that when it is moved by rotation of the axis bb the separation of the images shall be parallel to that motion. The angle of rotation is measured on the graduated circle C. The angle between the objects measured is = r sin 2[theta], where r is a constant to be determined for each magnifying power employed,[21] and [theta] the angle through which the sphere has been turned from zero (i.e. from coincidence of its principal axis with that of the telescope). The maximum separation is consequently at 45 deg. from zero. The measures can be made on both sides of zero for eliminating index error. There are considerable difficulties of construction, but these have been successfully overcome by Dollond; and in the hands of Dawes (_Mem. R.A.S._ xxxv. p. 144 seq.) such instruments have done valuable service. They are liable to the objection that their employment is limited to the measurement of very small angles, viz. 13" or 14" when the magnifying power is 100, and varying inversely as the power. Yet the beautiful images which these micrometers give permit the measurement of very difficult objects as a check on measures with the parallel-wire micrometer.

On the theory of the heliometer and its use consult Bessel, _Astronomische Untersuchungen_, vol. i.; Hansen, _Ausfuhrliche Methode mit dem Fraunhoferschen Heliometer anzustellen_ (Gotha, 1827); Chauvenet, _Spherical and Practical Astronomy_, vol. ii. (Philadelphia and London, 1876); Seeliger, _Theorie des Heliometers_ (Leipzig, 1877); Lindsay and Gill, _Dunecht Publications_, vol. ii. (Dunecht, for private circulation, 1877); Gill, _Mem. R.A.S._ vol. xlvi. pp. 1-172, and references mentioned in the text. (D. Gi.)

FOOTNOTES:

[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.

See Strabo xvii. cap. 1. 27-28; Baedeker's _Egypt_. (F. Ll. G.)

HELIOSTAT (from Gr. [Greek: helios], the sun, [Greek: statos], fixed, set up), an instrument which will reflect the rays of the sun in a fixed direction notwithstanding the motion of the sun. The optical apparatus generally consists of a mirror mounted on an axis parallel to the axis of the earth, and rotated with the same angular velocity as the sun. This construction assumes that the sun describes daily a small circle about the pole of the celestial sphere, and ignores any diurnal variation in the declination. This variation is, however, so small that it can be neglected for most purposes.

[Illustration: FIG. 1.]

[Illustration: FIG. 2.]

[Illustration: From Jamin and Bouty, _Cours de physique_, Gauthier-Villars.

FIG. 3.--Silbermann's Heliostat.]

Many forms of heliostats have been devised, the earliest having been described by Wilhelm Jacob s' Gravesande in the 3rd edition of his _Physices elementa_ (1742). One of the simplest consists of a plane mirror rigidly connected with a revolving axis so that the angle between the normal to the mirror and the axis of the instrument equals half the sun's polar distance, the mirror being adjusted so that the normal has the same right ascension as the sun. It is easily seen that if the mirror be rotated at the same angular velocity as the sun the right ascensions will remain equal throughout the day, and therefore this device reflects the rays in the direction of the earth's axis; a second fixed mirror reflects them in any other fixed direction. Foucault's heliostat reflects the rays horizontally in any required direction. The principle of the apparatus may be explained by reference to fig. 1. The axis of rotation AB bears a rigidly attached rod DBC inclined to it at an angle equal to the sun's polar distance. By adjusting the right ascension of the plane ABC and rotating the axis with the angular velocity of the sun, it follows that BC will be the direction of the solar rays throughout the day. X is the mirror rotating about the point E, and placed so that (if EB is the horizontal direction in which the rays are to be reflected) (1) the normal CE to the mirror is jointed to BC at C and is equal in length to BE, (2) the rod DBC passes through a slot in a rod ED fixed to, and in the plane of, the mirror. Since CE equals BE these directions are equally inclined to, and coplanar with, the normal to the mirror. Hence light incident along the direction BC will be reflected along CE. Silbermann's heliostat reflects the rays in any direction. The principle may be explained by means of fig. 2. AB is the axis of rotation, BC an adjustable rod as in Foucault's construction, and BD is another rod which can be set to the direction in which the rays are to be reflected. The rods BC and DB carry two small rods EF, GF jointed at F; at this joint there is a pin which slides in a slot on the rod BH, which is normal to the mirror X. The rods EF, GF are such that BEFG is a rhombus. It is easy to show that rays falling on the mirror in the direction BC will be reflected along BD. One construction of the instrument, described in Jamin's _Cours de physique_, is shown in fig. 3. The mirror mm is attached to the framework _pafe_, the members of which are parallel to the incident and reflected rays SO, OR, and the diagonal pf is perpendicular to the mirror. The framework is attached to two independent circular arcs Cs and rr' having their centres at O and provided with clamps D and A on the axis F of the instrument. The arc Cs is graduated, and is set so that the angle COD equals the complement of the sun's declination. This can be effected (after setting the axis) by rotating Cs until a needle indicates true time on the hour dial B. The arc rr' is set so as to reflect the rays in the required direction. The axis F of the instrument is set at an angle equal to the latitude of the place of observation and in the meridian by means of the screw K, and rotated by clockwork contained in the barrel H. The setting in the meridian is effected by turning the instrument after setting for latitude until a pin-hole aperture s and a small screen P, placed so that Ps is parallel to CO, are in a line with the sun.

Many other forms of heliostats have been designed, the chief difference consisting in the mechanical devices for maintaining the constant direction of the reflecting ray. One of the most important applications of the heliostat is as an adjunct to the newer forms of horizontal telescopes (q.v.) and in conjunction with spectroscopic telescopes in observations of eclipses.

HELIOTROPE, or TURNSOLE, _Heliotropium_ (Gr. [Greek: heliotropion], i.e. a plant which follows the sun with its flowers or leaves, or, according to Theophrastus (_Hist, plant_, vii. 15), which flowers at the summer solstice), a genus of usually more or less hairy herbs or undershrubs of the tribe _Heliotropieae_ of the natural order Boraginaceae, having alternate, rarely almost opposite leaves; small white, lilac or blue flowers, in terminal or lateral one-sided simple or once or twice forked spikes, with a calyx of five deeply divided segments, a salver-shaped, hypogynous, 5-lobed corolla, and entire 4-celled ovary; fruit 2- to 4-sulcate or lobed, at length separable into four 1-seeded nutlets or into two hard 2-celled carpels. The genus contains 220 species indigenous in the temperate and warmer parts of both hemispheres. A few species are natives of Europe, as _H. europaeum_, which is also a naturalized species in the southern parts of North America.

[Illustration: _Heliotropium suaveolens._]

The common heliotrope of English hothouses, _H. peruvianum_, popularly known as "cherry-pie," is on account of the delicious odour of its flowers a great favourite with florists. It was introduced into Europe by the younger Jussieu, who sent seed of it from Peru to the royal garden at Paris. About the year 1757 it was grown in England by Philip Miller from seed obtained from St Germains. _H. corymbosum_ (also a native of Peru), which was grown in Hammersmith nurseries as early as 1812, has larger but less fragant flowers than _H. peruvianum_. The species commonly grown in Russian gardens is _H. suaveolens_, which has white, highly fragrant flowers.

Heliotropes may be propagated either from seed, or, as commonly, by means of cuttings of young growths taken an inch or two in length. Cuttings when sufficiently ripened, are struck in spring or during the summer months; when rooted they should be potted singly into small pots, using as a compost fibry loam, sandy peat and well-decomposed stable manure from an old hotbed. The plants soon require to be shifted into a pot a size larger. To secure early-flowering plants, cuttings should be struck in August, potted off before winter sets in, and kept in a warm greenhouse. In the spring larger pots should be given, and the plants shortened back to make them bushy. They require frequent shiftings during the summer, to induce them to bloom freely.