Among the multitude of hitherto unsolved problems of astronomy we may enumerate the following: Why sun-spots travel faster around the sun when near his equator than when more distant from it. The physical causes of sun-spots, faculæ, and solar prominences. Why the number and size of sun-spots seem to affect terrestrial magnetism. The rational interpretation of the eleven-year and the long sun-spot cycles. The origin of the aurora borealis. The causes of the periodicity of regularly variable stars. How to explain, in accordance with the nebular hypothesis, why Algol and its companion, which are not greatly different in mass and volume, and both obviously gaseous, should so differ in character, one being a bright sun and the other a dark planet. Whether there are great, compact, but dark bodies, comparable to suns and planets in magnitude, and unconnected with any solar system, floating about in space. Why double and multiple stars are so frequently of contrasted or complementary colors. Why regularly variable stars are longer in decline than in growth of brilliancy, since such decline is no criterion of loss of heat, but rather the reverse. Why the sun and fixed stars have atmospheres largely composed of free hydrogen, and the planets have atmospheres of free oxygen and nitrogen. Why a small and sometimes even scarcely visible star occasionally is seen to suddenly blaze up, in a few hours, to hundreds of times its normal brilliancy, and then far more gradually fade, through months and years, back to its former state, in which thenceforth it continues to maintain its original lustre. Why comets, when they have tails, always project these appendages radially from the direction of the sun. How to account for the presence of cyanogen, and how for the absence of oxygen and the constant presence of hydrocarbon vapors around the nuclei of comets. Why some comets split up into separate comets and others sometimes show multiple tails. Why comets, when they pass around and behind the sun, in some cases reappear shorn of their splendor and in other cases with their splendor greatly enhanced. Whence comets are derived, where is their permanent abiding-place, and how did they originally reach those distant regions which they occupy before entering our system, if merely the débris left behind from contraction of the mass of plasma out of which our solar system is supposed to have been formed. Why so many of the irresolvable nebulæ present the appearance of divergent spirals of many different forms. How to account for the annular nebulæ with hollow centers and for those partially-completed planetary nebulæ, so called, which afterwards appear to retrograde into diffused gaseous nebulæ again or gradually disappear. What is the ultimate constitution of interstellar space? Have the fixed stars planetary systems like our own, or not? Must they have such, or merely may they have? What principle of conservation of energy is it possible to apply to the