In 1874 the German Government established at Potsdam the Astrophysical Observatory, for the spectroscopic study of the Sun and stars. A position on the staff was given to Hermann Carl Vogel, whose researches in astronomical spectroscopy rank with those of Secchi and Huggins. Born in Leipzig in 1842, he was from 1865 to 1869 employed in the Leipzig Observatory. Called to Bothkamp as director in 1870, he resigned his post in 1874 to accept a position on the staff at Potsdam Observatory. In 1882 he became director of that Institution, which position he still retains.

In 1874 Vogel revised Secchi’s classification of stellar spectra, and in 1895 he further improved on it. His classification improves rather than supersedes the previous work of Secchi; nevertheless, he approached the question from a different standpoint. Vogel concluded in 1874 that a rational scheme of stellar classification “can only be arrived at by proceeding from the standpoint that the phrase of development of the particular body is, in general, mirrored in its spectrum.” Vogel divides Secchi’s first type into three classes. In the first type, designated Ia,—represented by Sirius and Vega,—the metallic lines are “very faint and fine,” and the hydrogen lines conspicuous. In Ib no hydrogen lines are visible, while in Ic the hydrogen lines are bright. This class includes the gaseous stars. In 1895, after the recognition of helium in the stars by his assistant, Scheiner, Vogel separated the stars of class Ib from the first type altogether. These stars are sometimes designated as “Type O,” and sometimes as helium stars and Orion stars, as the majority of the stars in Orion are of that type. The solar type is divided into two classes, IIa being represented by the Sun, Capella, and other well-known stars, while IIb includes the Wolf-Rayet stars. Secchi’s third and fourth types are both classified by Vogel as of the third type. These red stars were specially studied from 1878 to 1884 by DunÉr at Lund. His results were published in a descriptive catalogue which appeared at Stockholm in 1884. His researches related to the spectra of 352 stars, 297 of Secchi’s third type and 55 of his fourth. DunÉr is perhaps the greatest authority on stars with banded spectra.

Vogel’s classification of spectra is generally adopted by astronomers, although others have been proposed by Lockyer and by Edward Charles Pickering (born 1846), director of the Harvard Observatory. Lockyer’s classification was designed to fit in with his “meteoritic hypothesis,” discussed in the chapter on Celestial Evolution. The stars were divided by Lockyer into seven groups, according to his views of their temperature, rising through gaseous stars, red stars of Secchi’s third type, and a division of solar stars to the Sirian type, and falling through a second division of the solar type to red stars of Secchi’s fourth type.

The first spectroscopic star-catalogue was published in 1883 by Vogel, assisted by Gustav MÜller (born 1851), a son-in-law of SpÖrer. The catalogue contained details of 4051 stars to the seventh magnitude, and more than half of these proved to be of Secchi’s first type. Vogel’s work was completed in different latitudes by DunÉr at Upsala, and by Nicolaus Thege von Konkoly (born 1842) at O’Gyalla in Hungary.

The famous ‘Draper Catalogue’ ranks as the greatest catalogue of stellar spectra. It was undertaken at Harvard Observatory by E. C. Pickering, in the form of a memorial to Henry Draper, the successful spectroscopist. Commenced in 1886, and published in 1890, it contains photographs of the spectra of no fewer than 10,351 stars, down to the eighth magnitude. Pickering subdivided Secchi’s types into various classes, the first or Sirian into four classes, the second into eight, while the third and fourth types each constitute a separate class. Pickering designated his classes by the capital letters of the alphabet.

Much useful work has been done also in the analysis of the various spectra. Julius Scheiner, now “chief observer” at Potsdam Astrophysical Observatory, has, since 1890, done much valuable work in this direction. Special attention was devoted to the spectrum of Capella, 490 lines in the spectrum of which were measured by Scheiner. In his own words, “he believes a complete proof of the absolute agreement between its spectrum and that of the Sun to be thereby furnished.” Other stars of the Sirian and solar classes were exhaustively studied by Scheiner.

The study of the exact brilliance of the stars was a branch of research long neglected, yet it is of much importance in astronomy, for it is only through exact measurement of stellar brilliance that stellar variation can be detected. Herschel commenced the study, which was continued by his son at the Cape, but it is only within the last twenty years that stellar photometry has become a recognised branch of astronomy; and the credit of this is due to the energy and zeal of the great American observer, Edward Charles Pickering.

Born in Boston in 1846, Edward Charles Pickering was appointed in 1865 Instructor of mathematics in the Lawrence Scientific School at Harvard, after a distinguished university career. In 1876 he succeeded Winlock as director of the Harvard Observatory, and in the following year he commenced his photometric studies. He invented an instrument named the meridian photometer, with the aid of which he succeeded in determining, in the years 1879 to 1882, the exact brilliance of 4260 stars to the sixth magnitude between the north celestial pole and thirty degrees of south declination. At a later date he devised a larger photometer, with which he made over one million observations. Pickering next extended his survey to the southern hemisphere, erecting the photometer on the slope of the Andes, where the Harvard auxiliary station at Arequipa is now located, and where 8000 determinations of stellar brilliance were made. Meanwhile Pritchard, at Oxford, published in 1885 his ‘Uranometria Nova Oxoniensis,’ with photometric determinations of the brilliance of 2784 stars from the pole to ten degrees of south declination. Both of these catalogues were epoch-making works, and testify to the enthusiasm and perseverance of the astronomers who designed them.

The study of stellar photometry glides into that of stellar variation. At the beginning of the nineteenth century the number of known variable stars was very small, as a glance at the list given in Brewster’s edition of Ferguson’s Astronomy (1811) will show. Some remarkable investigations were due to the English astronomer, John Goodricke (1764-1786), who rediscovered the variability of the star Algol, and accurately determined its period in 1782. Goodricke suggested that the regular variations in the light of Algol were due to the partial eclipse of its light by a dark satellite, a hypothesis now fully confirmed. Two years later, in 1784, Goodricke discovered other two variables, d Cephei and LyrÆ. He died in 1786 at the age of twenty-one, and thus variable-star astronomy was deprived of its founder.

The foundation of variable-star astronomy as an exact branch of the science is due to Argelander. In the years 1837-1845, while residing at Bonn during the erection of the observatory, of which he had been made director, he erected a temporary observatory, and there he carefully determined the magnitudes of all stars visible in Central Europe. From this he was led to the discussion of stellar variation, to which subject he continued to give much attention. He was the first to describe a method of observing variable stars scientifically and accurately,—a method consisting in estimating in “steps” or “grades” the difference in brilliance between the variable, or suspected variable, and other stars which are selected for comparison, and which are of various degrees of brilliance, so that they may be available for comparison with the variable throughout its fluctuations. Argelander’s “steps” are tenths of a magnitude, and Gore describes the method of observation as follows: “If we call a and b the comparison stars, and v the variable, a being brighter than b, and if v is judged to be midway in brightness between a and b, we write a5v5b. If v is slightly nearer to b, we write a6v4b. We may also write a3v7b, or a7v3b, the sum of the steps being always ten.”

This method, described in 1844, led to many discoveries at Bonn in the following twenty years by Argelander and his assistants Schmidt and SchÖnfeld. At this time Eduard Heis (1806-1877), at MÜnster, who also ranks as one of the founders of meteoric astronomy, while engaged on the construction of his great atlas, attentively determined the change of magnitude of stars visible to the naked eye; and by means of the naked eye, the opera-glass, and a small telescope, he amassed a large number of observations. At the same time two English observers, Hind and Pogson, were making remarkable discoveries which greatly increased the number of known variables. Among Hind’s discoveries were S Cancri of the Algol type; while Schmidt discovered another of the same class, d LibrÆ, and also the famous ? Geminorum. While director of the Observatory of Mannheim, an institution equipped with very antiquated instruments, SchÖnfeld devoted himself to the study of variable stars, and increased the number of known variables considerably. In the southern hemisphere Gould, in South America, did for the observation of variable stars what Argelander did in the northern.

In 1874 a very important, although not so obvious, service to variable-star astronomy was rendered by the Danish observer, Hans Carl Fredrik Christian Schjellerup (1827-1887). He translated from Arabic into French the works of the Persian astronomer of a thousand years ago, Al-Sufi, and thus rendered his observations available to modern astronomers. Al-Sufi was a most accurate observer, and, by comparing his catalogue with those of modern observers, it can be found whether stars have changed in brilliance during the past thousand years.

The study of variable stars has been pursued in recent years by many astronomers, both by means of photography and by the visual method. The most important names in the visual discovery of variables are Gustav MÜller and Paul Friedrich Ferdinand Kempf (born 1856) of Potsdam; Alexander William Roberts of Lovedale, South Africa; Seth Carlo Chandler of Boston; Nils Christopher DunÉr at Upsala; and John Ellard Gore (born 1845) in Dublin.

The researches of J. E. Gore are a brilliant example of how much may be done for astronomy by means of very moderate instruments. Born in 1845 at Athlone, in Connaught, he went to India in 1868 as engineer on the Sirhind Canal in the Punjab. While in India he erected his small telescopes on brick pillars, and took observations, many of them of stellar brilliance. In 1879 he returned to Ireland, and since then has devoted himself to astronomy with zeal and enthusiasm. His discoveries and investigations of variables have been made by means of the binocular. On December 13, 1885, he discovered a remarkable star in Orion, which was at first considered to be temporary, and called “Nova Orionis,” but was afterwards found to be a long-period variable star.

Recently photography has come much to the front in the discovery of variable stars. Pickering at Harvard, and Wolf at Heidelberg, have particularly distinguished themselves in this branch, and the number of known variables is now very large, as every year brings fresh discoveries, mostly by aid of photography. Many of these newly-discovered variables are in star-clusters and nebulÆ.

Pickering proposed in 1880 the following classification of variable stars, which has been adopted all over the scientific world: Class I., temporary star; Class II., stars undergoing in several months large variations, such as Mira Ceti and U Orionis; Class III., irregular variables, such as Betelgeux and a Herculis; Class IV., short-period variables, such as d Cephei, ? Geminorum, and LyrÆ; Class V., “Algol variables,” which undergo variations lasting but a few hours. It is doubtful whether new stars should be included in a classification of variables, although in one case, at least, a new star was found to be a long-period variable. To these a sixth class may now be added. This class, the detection of which is mainly due to the profound investigations of Gore, is composed of what have been termed “secular variables,” which undergo slow fluctuations in periods of many years, and sometimes of centuries. This Class includes d UrsÆ Majoris, Al-Fard, ? Draconis, ? Serpentis, e Pegasi, 83 UrsÆ Majoris, ? Piscis Australis, Leonis, a Ophiuchi, ? Crateris, and others. The secular variations of some of these stars have been detected by Gore himself during the past thirty years, while in other cases he has detected them by comparison of the most important star-catalogues, from Hipparchus and Al-Sufi down to our own time. In some cases the star in question seems to be slowly gaining in brilliance, in others slowly diminishing.

Thanks to the application of the spectroscope, much is now known of the cause of the light changes in variable stars. Goodricke’s theory of the variations of Algol was theoretically confirmed by the researches of E. C. Pickering in 1880. In 1889 Vogel proved beyond a doubt that the variation in the light of Algol is due to the partial eclipse of its light by a dark satellite. It was obvious to Vogel that, as both Algol and its companion are in revolution round their common centre of gravity, the motion of Algol in the line of sight might be detected by the spectroscopic method of observation. Vogel found that before each eclipse Algol was retreating from our system, while on recovering it gave signs of rapid approach, proving conclusively that both the star and its dark satellite were in revolution round their centre of gravity,—Algol suffering partial eclipse only because the plane of the orbit lies in our line of sight. Algol, therefore, is not inherently a variable star, but merely a binary. Following up his researches, Vogel, assuming that the bright and dark stars are of equal density, arrived at the conclusion that Algol is a globe about one and a half million miles in diameter, the satellite equalling the size of the Sun, and the centres of the stars being separated by about 3,230,000 miles. Thus, variable stars of the Algol type are not variable in the true sense of the word. Even the most irregular of the Algol variables have been explained. Perhaps the most irregular was Y Cygni, discovered by Chandler in 1886. It was soon found, however, that the variations recurred with great irregularity: in less than two years the phases differed by as much as seven hours from the predicted times. At length the subject was taken up by DunÉr at Upsala. A series of observations made with the 14-inch refractor at Upsala in 1891 and 1892 convinced him in the latter year that two eclipses take place in the course of one revolution: one star occults the other. DunÉr showed that the intervals between minima were thus—1 day 9 hours; 1 day 15 hours; 1 day 9 hours, and so on. Thus, the first, third, fifth, and seventh sets of minima obeyed a different law from the second, fourth, sixth, and eighth. DunÉr proved that two stars revolve round their centre of gravity in less than three days, alternately occulting each other, while the ellipticity of the orbit explains the irregularity of the light changes. In April 1900 DunÉr gave his final conclusions as follows: “The variable star Y Cygni consists of two stars of equal size and equal brightness, which move about their common centre of gravity in an elliptical orbit, whose major axis is eight times the radius of the stars.” He also stated the exact period of revolution and the eccentricity of the orbit.

In the case of the short-period variables, such as LyrÆ, d Cephei, ? Geminorum, and ? AquilÆ, the variations do not seem to be due to eclipse. It was discovered by Professor Pickering that LyrÆ is a spectroscopic binary, but Vogel and Keeler showed that the supposed orbit is incompatible with the eclipse theory. Vogel says: “I am convinced that LyrÆ represents a binary or multiple system, the fundamental revolutions of which in 12 days 22 hours in some way control the light change.” The eclipse theory, however, is still maintained by BÉlopolsky, who has framed a hypothesis according to which the chief minimum of the star’s light corresponds with the obscuration of the lesser star, the lesser minimum with that of the primary, implying that the primary is much less luminous in proportion to its light than its satellite,—a state of affairs which Miss Clerke concludes to be improbable.

The variable stars, d Cephei and ? AquilÆ, were both found in 1894 by BÉlopolsky to be binaries; but as the times of minimum light do not correspond with those of eclipses in the hypothetical orbits, he concludes that the variations cannot be explained on the eclipsing satellite theory. Miss Clerke is inclined to the theory that the increase of luminosity in short-period variables is due to tidal action, so that while the revolutions of the stars control their variability, they are inherently unstable in light. A large number of these stars are known, and it is a remarkable fact that the majority of these variables lie on or near the Galaxy, so that their variations have probably something to do with their vicinity.

We now come to the long-period variables of which Mira Ceti, ? Cygni, and U Orionis are examples. Although varying in regular periods, generally of about a year, they are subject to remarkable irregularities, so that an exact period cannot be assigned even to Mira Ceti, of which the maxima are at times retarded and at others accelerated with no apparent law. The spectroscopic investigations of Campbell in 1898 have shown that Mira Ceti is a solitary star, while bright lines of hydrogen appear in its spectrum at maximum, showing that the variations are due to periodical conflagrations in its atmospheres. In many other long-period variables bright lines have been observed.

A remarkable fact regarding these stars is the amount of their light change. Mira Ceti, for instance, varies from the first to the ninth magnitude, and U Orionis from the sixth to the twelfth. As M. Flammarion says, “the longer the period the greater the variation.” Another remarkable fact is that their light curves show a curious resemblance to the curves of the solar spots, only on a vastly greater scale, which indicates that, relatively, these long-period variables are much older than our Sun, the small variations in the light of which are imperceptible. “Here, if anywhere,” says Miss Clerke, “will be found the secret of stellar variability.”

To the irregular variables no period can be assigned. Betelgeux, in Orion, the variation of which was noted by Sir John Herschel in 1840, is a typically irregular variable. But the most extraordinary of all variables is ? Argus, in the southern hemisphere, which is probably a connecting link between variable and temporary stars. The traveller Burchell, from 1811 to 1815, observed the star as of the second magnitude, but in 1827 he noted it to be of the first magnitude. In the following year it fell to the second magnitude. In 1834 Sir John Herschel noted the star to be between the first and second magnitude, and in 1838 it rose to the first, being equal to a Centauri. After a decline, it became in 1843 equal to Canopus, and not much inferior to Sirius. Then it began to fade, and in 1868 it was only of the sixth magnitude. In 1899 Innes estimated it as 7·71. Rudolf Wolf suggested a period of 46 years, and Loomis 67 years; but astronomers generally agree with SchÖnfeld that the star has no regular period.

The first temporary star of the nineteenth century was discovered by Hind, in London, April 28, 1848. It was of the fifth magnitude at maximum, and soon after began to fade, falling to the tenth magnitude. In 1860 a new star appeared in the cluster Messier 80 in Scorpio, and was discovered by Auwers at KÖnigsberg. It reached only the seventh magnitude.

On the night of May 12, 1866, a new star of the second magnitude blazed out in the constellation Corona Borealis. It was first observed at Tuam, in Ireland, by the Irish astronomer, John Birmingham. Four hours earlier Schmidt had been observing that part of the heavens, and it was not then visible. Birmingham at once communicated the discovery to Huggins, at Tulse Hill, who had commenced his spectroscopic observations. On May 16 Huggins observed its spectrum. In the words of Miss Clerke, “The star showed what was described as a double spectrum. To the dusky flutings of Secchi’s third type, four brilliant rays were added. The chief of these agreed in position with lines of hydrogen; so that the immediate cause of the outburst was plainly perceived to have been the eruption, or ignition, of vast masses of that subtle kind of matter.” Nine days after the appearance of the new star it was invisible to the naked eye, and afterwards fell to the tenth magnitude. In 1856 SchÖnfeld had observed it at Bonn as a telescopic star, so that it was not a “new star” in the true sense of the word.

The next temporary star observed was discovered by Schmidt, at Athens, November 24, 1876. It was of the third magnitude, situated in the constellation Cygnus. On December 2 its spectrum was examined at Paris by Alfred Cornu (1841-1902), and some days later at Potsdam by Vogel and Lohse. It was closely similar to that of the new star of 1866, bright lines of hydrogen and other elements standing out in front of an “absorption” spectrum. By the end of 1876 the star was of the seventh magnitude. On September 2, 1877, Nova Cygni was observed at Dunecht, and its spectrum was found to have been transformed into that of a planetary nebula. Three years later, however, the ordinary stellar spectrum reappeared.

A new star appeared in the centre of the great nebula in Andromeda in August 1885. The first announcement of the discovery was by Karl Ernst Albrecht Hartwig (born 1851), who observed the new star on August 31; but it had been previously seen by several other observers. On September 1 it was of the seventh magnitude, and by March of the following year had fallen to the sixteenth. Observed by Vogel, Young, and Hasselberg, the new star gave a continuous spectrum, but Huggins and Copeland succeeded in discerning bright lines. Hall, at Washington, undertook a series of measures to detect the parallax of Nova AndromedÆ, but his efforts were unsuccessful.

The discovery of the next temporary star was announced February 1, 1892, by the Rev. Thomas D. Anderson, a Scottish amateur astronomer, in a post-card to the Astronomer-Royal of Scotland. The star was situated in the constellation Auriga. An examination of photographs, taken at Harvard Observatory, showed that the new star had appeared December 10, 1891, and had risen to a maximum of the fourth magnitude ten days later. On a photograph taken by Max Wolf on December 8 the new star was not visible. After Anderson’s visual discovery, the spectrum of the new star was studied by Copeland, Huggins, Lockyer, Vogel, Campbell, and others. Bright hydrogen lines were visible in the spectrum, which appeared to be actually double, giving support to the theory that the outburst was the result of a collision between two dark bodies; and this was confirmed by the measurements of radial motion by the Potsdam astronomers.

After March 9, 1892, the new star steadily faded, falling to the sixteenth magnitude on April 26. But on August 17 Edward Singelton Holden (born 1846), director of the Lick Observatory, and his assistants, Schaeberle and Campbell, found it of the tenth magnitude. On August 19 Barnard found it transformed into a planetary nebula: while various spectroscopic observations of the revived Nova revealed the nebular lines. By the end of 1894 the new star had faded to the eleventh magnitude, and early in 1901 was observed as a minute nebula.

After 1892 several new stars appeared, and were detected on photographic plates by Mrs Fleming (born 1857), of Harvard Observatory. The first of these, in the southern constellation Norma, was discovered in 1893 by its peculiar spectrum on a Draper spectrographic plate taken at Harvard. But the new star rose only to the seventh magnitude. Other new stars were discovered in Carina (Argo) in 1895, in Centaurus in 1895, in Sagittarius in 1898, and in Aquila in 1900. Nova Sagittarii was, at its brightest, fully equal to Nova AurigÆ, and was plainly visible to the naked eye, but was never observed visually.

A temporary star, appropriately designated “the new star of the new century,” blazed out in Perseus on the night of February 21, 1901. It was discovered independently by several observers: on February 21, by Borisiak, a student at Kiev, in Russia; on the following morning, by Anderson in Edinburgh; and on the next evening, by Gore at Dublin, Nordvig in Denmark, Grimmler at Erlangen, and other observers. When first seen by Anderson, it was equal to Algol, of the second magnitude. A photograph by Williams at Brighton showed that it must have been fainter than the twelfth magnitude on February 20. On the evening of February 23 the star was brighter than Capella, and was then the brightest star in the northern hemisphere. On February 25 it fell to the first magnitude; on March 1 to the second, and on March 6 to the third. During the spring and summer the light fluctuated considerably, but in September and October faded to the 6·7 magnitude. In March 1902 it was of the eighth magnitude, and in July 1903 of the twelfth.

The spectrum of Nova Persei was found by Pickering to be of the Orion type on February 22 and 23. On February 24 the spectrum had become one of the bright and dark lines, and the hydrogen lines indicated a velocity of 700 to 1000 miles a second. Measures of the sodium and calcium lines, by Campbell and others, indicated a velocity of only three miles a second, so that the displacements of the hydrogen lines may have been due to an outburst of hydrogen in the star. The spectrum was carefully studied during the spring and summer by Pickering, Lockyer, Huggins, Vogel, and others. On June 25 Pickering reported that the spectrum was slowly changing into that of a gaseous nebula. In August and September 1901 the nebular spectrum became more apparent.

In August 1901 Wolf at Heidelberg discovered a faint trace of nebula near the nova. On September 20 this nebula was photographed by George Ritchey at the Yerkes Observatory, and was seen to be of a spiral form. This was confirmed by Perrine, who also found, from plates taken in November, that the nebula was moving at the rate of eleven minutes of arc a year. This extraordinary velocity was exceedingly puzzling to astronomers, and at length Kapteyn suggested that the nebula shone only by reflected light from the new star, and that the apparent motion was an illusion caused by the flare of the explosion travelling out from the nova.

On March 16, 1903, Herbert Hall Turner (born 1861), Professor of Astronomy at Oxford, discovered a new star of the seventh magnitude in the constellation Gemini, from an examination of photographic plates. Photographs taken at Harvard showed that on March 1 it must have been fainter than the twelfth magnitude, while five days later it was of the fifth. In August 1903 Pickering found its spectrum nebular. In August 1905 another small nova was found by Mrs Fleming on the Harvard photographs, situated in Aquila.

Many theories have been advanced to account for temporary stars. Flammarion has shown that a body surrounded by a hydrogen atmosphere, on grazing a dark body enveloped in oxygen, would produce a tremendous explosion. In 1892 Huggins suggested that the outburst of Nova AurigÆ was due to the near approach of two bodies with large velocities, disturbances of a tidal nature resulting and producing enormous outbursts. Vogel suggested that the new star was due to the encounter of a dark star with a worn-out system of planets; while Lockyer believes all new stars to be due to the collision of swarms of meteors. Perhaps the most probable theory is that of Seeliger, which attributes these outbursts to the movement of a dark body through nebulous matter, which is extensively diffused throughout space. This theory explains the changes in the spectra as well as the revivals of brightness which characterised Nova AurigÆ and the fluctuations of Nova Persei. In a paper read to the Royal Society of Edinburgh in November 1904, the German astronomer, Jacobus Halm, of the Royal Observatory, Edinburgh, extended and developed Seeliger’s theory, showing also that the necessary consequence of such an encounter as the theory assumes is the formation of an atmosphere of incandescent gases, followed by that of a revolving ring of nebulous matter. In the hands of Halm, therefore, Seeliger’s theory leads to the nebular hypothesis as advanced by Laplace and Herschel.