Periodic stars are those which go through a regular cycle of changes in a definite interval of time, so that, after a certain number of days, sometimes of hours, the star returns to the same brightness. But even in the case of periodic stars, it is found that the period is more or less variable, and, in special cases, the amount of the variation is such that it cannot always be said whether we should call a star periodic or irregular.

The periodic stars show wide differences, both in the length of the period and in the character of the changes they undergo. In most cases they rapidly increase in brightness during a few days or weeks, and then slowly fade away, to go through the same changes again at the end of the period. In other cases they blaze up or fade out, from time to time, like the revolving light of a lighthouse. Some stars are distinguished more especially by their maximum, or period of greatest brightness, while others are more sharply marked by minima, or periods of least brightness. In some cases there are two unequal minima in the course of a period.

Chandler’s third catalogue of variable stars gives the periods of 280 of these objects, which seem to have been fairly well made out. A classification of these periods, as to their length, will be interesting. There are, of periods:

Less than 50 days 63Stars.
Between50and100days6”
”100”150”9”
”150”200”18”
”200”250”29”
”250”300”40”
”300”350”44”
”350”400”44”
”400”450”18”
”450”500”6”
”500”550”1”
”550”600”1”
”600”650”1”

It will be seen from this that, leaving out the cases of very short period, the greater number of the periods fall between 300 and 400 days. From this value the number falls off in both directions. Only three periods exceed 500 days, and of these the longest is 610 days. We infer from this that there is something in the constitution of these stars, or in the causes on which their variation depends, which limits the period. This limitation establishes a well-marked distinction between the periodic stars and the irregular variables to be hereafter described.

Returning to the upper end of the scale, the contrast between the great number of stars less than fifty days, and the small number between fifty and one hundred, seems to show that we have here a sharp line of distinction between stars of long and those of short period. But, when we examine the matter in detail, the statistics of the periods do not enable us to draw any such line. About eight periods are less than one day, and the number of this class known to us is continually increasing. About forty are between one and ten days, and from this point upwards they are scattered with a fair approach to equality up to a period of one hundred days. There is, however, a possible distinction, which we shall develop presently.

Fig. 1. The Law of Change in a Variable Star.

The law of change in a variable star is represented to the eye by a curve in the following way. We draw a straight horizontal line A X to represent the time. A series of equidistant points, a, b, c, d, etc., on this will represent moments of time. One of the spaces, a, b, c, etc., may represent an hour, a day, or a month, according to the rapidity of change. We take a to represent the initial moment, and erect an ordinate aa’, of such length as to represent the brightness of the star on some convenient scale at this moment. At the second moment, b, which may be an hour or a day later, we erect another ordinate bb’, representing the brightness at this moment. We continue this process as long as may be required. Then we draw a curve, represented by the dotted line, through the ends of all the ordinates. In the case of a periodic star it is only necessary to draw the curve through a single period, since its continuation will be a repetition of its form for any one period.

We readily see that if a star does not vary, all the ordinates will be of equal length, and the curve will be a horizontal straight line. Moreover, the curve will take this form through any portion of time during which the light of the star is constant.