I have recently suggested that the Cepheid variables, whose unknown mechanism of light-variation renders such valuable service to the astronomer, are merely stars in the act of fission. Want of space prevents our entering here into the intricate question of how far they exhibit the peculiarities which mathematical analysis requires of stars in process of fission, but it is easily seen that they satisfy the three simple tests outlined above. They are certainly variable stars, and the light-variations of different stars are so similar as to suggest very strongly that they all arise from the same cause. The periods of a number of Cepheids are suspected of change, and Hertzsprung has estimated that the prototype star, δ Cephei, which has now been observed for 126 years, is decreasing its period of light-fluctuation at the rate of about a tenth of a second per annum; thus a million years would reduce its present period of 5⅓ days by over a day. Finally Dr Otto Struve has found that the sequence of Cepheids fits almost perfectly on to that of newly formed binaries. Thus the prospects for the “fission theory” of Cepheid variables seem hopeful, but the theory must be very thoroughly tested before it can be accepted, and it cannot be claimed that it has been so far either tested thoroughly or accepted extensively. An alternative view, first propounded by Plummer and Shapley, regards Cepheid variables as pulsating spheres of gas. The behaviour of such masses of gas has been investigated mathematically by Eddington and others, but it does not appear that it can be reconciled with the observed behaviour of Cepheid variables. THE DEVELOPMENT OF BINARY SYSTEMS Whatever the process of formation of binary systems may be, we experience fairly plain sailing in attempting to trace out the subsequent development of such systems. Three factors are simultaneously in operation. TIDAL FRICTION. The first of these three factors, which is only of brief duration, was designated “tidal friction” by Sir George Darwin, who first drew attention to it, and investigated the manner of its operation. When first a rotating mass breaks up and forms a binary system, the two components are so near that they necessarily raise tremendous tides on one another; Darwin shewed that these drive the two bodies apart, and equalise their rates of rotation in so doing. After these processes have been in operation for millions of years, the rates of rotation of the two bodies and their rate of revolution about one another must all become equal, so that each body perpetually turns the same face to its companion, and the two rotate about one another like the two masses of a dumb-bell joined by an invisible arm.