Spectacular as they are to the layman, novÆ, or temporary stars, are to the astronomers simply a class among many thousands of stars which they call variables, or variable stars. There are a few objects classified as irregular variables, one of which is very remarkable. We refer to Eta Argus, an erratic variable in the southern constellation Argo and surrounded by a well-known nebula. There is a pretty complete record of this star. Halley in 1677 when observing at Saint Helena recorded Eta Argus as of the fourth magnitude. During the 18th century, it fluctuated between the fourth magnitude and the second. Early in the 19th it rapidly waxed in brightness, fluctuating between the first and second magnitudes from 1822 to 1836. But two years later its light tripled, rivaling all the fixed stars except Canopus and Sirius. In 1843 it was even brighter for a few months, but since then it has declined fairly steadily, reaching a minimum at magnitude seven and a half in 1886, with a slight increase in brightness more recently. A period of half a century has been suggested, but it is very doubtful if Eta Argus has any regular period of variation.

Another very interesting class of variables is known as the Omicron Ceti type. Nearly all the time they are very faint, but quite suddenly they brighten through several magnitudes, and then fade away, more or less slowly, to their normal condition of faintness. But the extraordinary thing is that most of these variables go through their fluctuations in regular periods: from six months to two years in length. The type star, Omicron Ceti, or Mira, is the oldest known variable, having been discovered by Fabricius in 1596. Most of the time it is a relatively faint star of the 12th magnitude; but once in rather less than a year its brightness runs up to the fourth, third and sometimes even the second magnitude, where it remains for a week or ten days, and afterward it recedes more slowly to its usual faintness, the entire rise and decline in brightness usually requiring about 100 days. The spectrum of Omicron Ceti contains many very bright lines, and a large proportion of the variable stars are of this type.

Another class of variables is designated as the Beta LyrÆ type. Their periods are quite regular, but there are two or more maxima and minima of light in each period, as if the variation were caused by superposed relations in some way. Their spectra show a complexity of helium and hydrogen bands. No wholly satisfactory explanation has yet been offered. Probably they are double stars revolving in very small orbits compared with their dimensions, their plane of motion passing nearly through the earth.

But the most interesting of all the variables are those of the Algol type, their light curves being just the reverse of the Omicron Ceti type; that is, they are at their maximum brightness most of the time, and then suffer a partial eclipse for a relatively brief interval. Algol goes through its variations so frequently that its period is very accurately known; it is 2d. 20h. 48m. 55.4s. For most of this period Algol is an easy second magnitude star; then in about four and a half hours it loses nearly five-sixths of its light, receding to the fourth magnitude. Here at minimum it remains for fifteen or twenty minutes, and then in the next three and a half hours it regains its full normal brilliancy of the second magnitude. During these fluctuations the star's spectrum undergoes no marked changes. The spectra of all the Algol variables are of the first or Sirian type.

To explain the variation of the Algol type of variables is easy: a dark, eclipsing body, somewhat smaller than the primary is supposed to be traveling round it in an orbit lying nearly edgewise to our line of sight. The gravitation of this dark companion displaces Algol itself alternately toward and from the earth, because the two bodies revolve round their common center of gravity. With the spectroscope this alternate motion of Algol, now advancing and now receding at the rate of 26 miles per second, has been demonstrated; and the period of this motion synchronizes exactly with the period of the star's variability.

Russell and Shapley have made extended studies of the eclipsing binaries, and developed the formulÆ by which the investigations of their orbits are conducted. Heretofore, visual binaries and spectroscopic binaries afforded the only means of deriving data regarding double systems, but it is now possible to obtain from the orbits of eclipsing variables fully as much information relating to binary systems in general and their bearing on stellar evolution. After an orbit has been determined from the photometric data of the light curve, the addition of spectroscopic data often permits the calculation of the masses, dimensions and densities in terms of the sun. Shapley's original investigation included the orbits of ninety eclipsing variables, and with the aid of hypothetical parallaxes, he computed the approximate position of each system in space. The relation to the Milky Way is interesting, the condensation into the Galactic plane being very marked; only thirteen of the ninety systems being found at Galactic latitudes exceeding 30 degrees.

If we can suppose the variable stars covered with vast areas of spots, perhaps similar to the spots on the sun, and then combine the variation of these spot areas with rotation of the star on its axis, there is a possibility of explanation of many of the observed phenomena, especially where the range of variation is small. But for the Omicron Ceti type, no better explanation offers than that afforded by Sir Norman Lockyer's collision theory. First he assumes that these stars are not condensed bodies, but still in the condition of meteoric swarms, and the revolution of lesser swarms around larger aggregations, in elliptic orbits of greater or less eccentricity, must produce vast multitudes of collisions; and these collisions, taking place at pretty regular periods, produce the variable maximum light by raising hosts of meteoric particles to a state of incandescence simultaneously.

The catalogues of variable stars now contain many thousands of these objects. They are often designated by the letters R, S, T, and so on, followed by the genitive form of the name of the constellation wherein they are found. Most of the recently found variables have a range of less than one magnitude. They are so distributed as to be most numerous in a zone inclined about 18 degrees to the celestial equator, and split in two near where the cleft in the Galaxy is located. Nearly all the temporary stars are in this duplex region. Bailey of Harvard a quarter century ago began the investigation of variables in close star clusters, where they are very abundant, with marked changes of magnitude within only a few hours.

Many amateur astronomers afford very great assistance to the professional investigator of variable stars by their cooperation in observing these interesting bodies, in particular the American Association of Observers of Variable Stars, organized and directed by William Tyler Olcott.

For a high degree of accuracy in determining stellar magnitudes the photo-electric cell is unsurpassed. Stebbins of Urbana has been very successful in its application and he discovered the secondary minimum of Algol with the selenium cell. His most recent work was done with a potassium cell with walls of fused quartz, perfected after many trial attempts. The stars he has recently investigated are Lambda Tauri, and Pi Five Orionis. Combining results with those reached by the spectroscope, the masses of the two component stars of the former are 2.5 and 1.0 that of the sun, and the radii are 4.8 and 3.6 times the sun's.

Russell of Princeton thinks it probable that similar causes are at work in all these variables. In the case of the typical NovÆ there is evidence that when the outburst takes place a shell of incandescent gas is actually ejected by the star at a very high velocity. What may be the forces that cause such an explosion can only be guessed. Repeated outbursts have not, in the case of T Pyxidis, destroyed the star, because it has gone through this process three times in the past thirty years. Russell inclines to regard it as a standard process occurring somewhere in the stellar universe probably as often as once a year.

NovÆ, then, cannot be due to collisions between two stars, for even if we suppose the stars to be a thousand millions in number, no two should collide except at average intervals of many million years. The idea is gaining ground that the stars are vast storehouses of energy which they are gradually transforming into heat and radiating into space. "Under ordinary circumstances, it is probable that the rate of generation of heat is automatically regulated to balance the loss by radiation. But it is quite conceivable that some sudden disturbance in the substance of the star, near the surface, might cause an abrupt liberation of a great amount of energy, sufficient to heat the surface excessively, and drive the hot material off into infinite space, in much the form of a shell of gas, as seems to have been observed in the case of Nova AquilÆ…. With the rapid advance of our knowledge of the properties of the stars on one hand, and of the very nuclei of atoms on the other, we may, perhaps before many years have passed, find ourselves nearer a solution of the problem."

The Cepheid variables increase very rapidly in brightness from their least light to their maximum, and then fade out much more slowly, with certain irregularities or roughnesses of their light-curves when declining. Their spectral lines also shift in period with their variations of light. In the case of these variables, whose regular fluctuation of light cannot be due to eclipse, and is as a rule embraced within a few days, there is a fluctuation in color also between maximum and minimum, as if there were a periodic change in the star's physical condition. Eddington and Shapley advocate the theory of a mechanical pulsation of the star as most plausible. Knowledge of the internal conditions of the stars make it possible to predict the period of pulsation within narrow limits; and for Delta Cephei this theoretical period is between four and ten days. Its observed period is five and one-third days, and corresponding agreement is found in all the Cepheids so far tested.

Shapley of Mount Wilson finds that the Cepheid variables with periods exceeding a day in length all lie close to the Galactic lane. So greatly have the studies of these objects progressed that, as before remarked, when we know the star's period, we can get its absolute magnitude, and from this the star's distance. On all sides of the sun, the distances of the Cepheids range up to 4,000 parsecs. So they indicate the existence of a Galactic system far greater in extent than any previously dealt with.