We have first to distinguish the two great classes of irregular and periodic stars. The irregular ones increase and diminish in so fitful a way that no law of their change can be laid down. To this class belong the so-called ‘new stars’, which, at various periods in history, have blazed out in the heavens, and then in a few weeks or months have again faded away. It is a remarkable fact that no star of the latter class has ever been known to blaze out more than once. This fact distinguishes new stars from other irregularly variable ones. 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 63 Stars. Between 50 and 100 days 6 ” ” 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.