general climatic conditions of the past, however, Shapley points out that the hypothesis has the objection of being vague, and that nebulosity should not be regarded as more than "a possible factor." One of the chief difficulties seems to be the enormously wide distribution of as yet undiscovered nebulous matter which must be assumed if any large share of the earth's repeated climatic changes is to be ascribed to such matter. If such matter is actually abundant in space, it is hard to see how any but the nearest stars would be visible. Another objection is that there is no known nebulosity near at hand with which to connect the climatic vicissitudes of the last glacial period. Moreover, the known nebulæ are so much less numerous than stars that the chances that the sun will encounter one of them are extremely slight. This, however, is not an objection, for Shapley points out that during geological times the sun can never have varied as much as do the novæ, or even as most of the friction variables. Thus the hypothesis stands as one that is worth investigating, but that cannot be finally rejected or accepted until it is made more definite and until more information is available.
Another suggested cause of solar variations is the relatively sudden contraction of the sun such as that which sometimes occurs on the earth when continents are uplifted and mountains upheaved. It seems improbable that this could have occurred in a gaseous body like the sun. Lacking, as it does, any solid crust which resists a change of form, the sun probably shrinks steadily. Hence any climatic effects thus produced must be extremely gradual and must tend steadily in one direction for millions of years.
Still another suggestion is that the tidal action of the stars and other bodies which may chance to approach
the sun's path may cause disturbances of the solar atmosphere. The vast kaleidoscope of space is never quiet. The sun, the stars, and all the other heavenly bodies are moving, often with enormous speed. Hence the effect of gravitation upon the sun must vary constantly and irregularly, as befits the geological requirements. In the case of the planets, however, the tidal effect does not seem competent to produce the movements of the solar atmosphere which appear to be concerned in the inception of sunspots. Moreover, there is only the most remote probability that a star and the sun will approach near enough to one another to produce a pronounced gravitational disturbance in the solar atmosphere. For instance, if it be assumed that changes in Jupiter's tidal effect on the sun are the main factor in regulating the present difference between sunspot maxima and sunspot minima, the chances that a star or some non-luminous body of similar mass will approach near enough to stimulate solar activity and thereby bring on glaciation are only one in twelve billion years, as will be explained below. This seems to make a gravitational hypothesis impossible.
Another possible cause of solar disturbances is that the stars in their flight through space may exert an electrical influence which upsets the equilibrium of the solar atmosphere. At first thought this seems even more impossible than a gravitational effect. Electrostatic effects, however, differ greatly from those of tides. They vary as the diameter of a body instead of as its mass; their differentials also vary inversely as the square of the distance instead of as the cube. Electrostatic effects also increase as the fourth power of the temperature or at least would do so if they followed the law of black bodies; they are stimulated by the approach of one body
to another; and they are cumulative, for if ions arrive from space they must accumulate until the body to which they have come begins to discharge them. Hence, on the basis of assumptions such as those used in the preceding paragraph, the chances of an electrical disturbance of the solar atmosphere sufficient to cause glaciation on the earth may be as high as one in twenty or thirty million years. This seems to put an electrical hypothesis within the bounds of possibility. Further than that we cannot now go. There may be other hypotheses which fit the facts much better, but none seems yet to have been suggested.
In the rest of this chapter the tidal and electrical hypotheses of stellar action on the sun will be taken up in detail. The tidal hypothesis is considered because in discussions of the effect of the planets it has hitherto held almost the entire field. The electrical hypothesis will be considered because it appears to be the best yet suggested, although it still seems doubtful whether electrical effects can be of appreciable importance over such vast distances as are inevitably involved. The discussion of both hypotheses will necessarily be somewhat technical, and will appeal to the astronomer more than to the layman. It does not form a necessary part of this book, for it has no bearing on our main thesis of the effect of the sun on the earth. It is given here because ultimately the question of changes in solar activity during geological times must be faced.
In the astronomical portion of the following discussion we shall follow Jeans[117] in his admirable attempt at a mathematical analysis of the motions of the universe. Jeans divides the heavenly bodies into five main types. (1) Spiral nebulæ, which are thought by some astronomers
to be systems like our own in the making, and by others to be independent universes lying at vast distances beyond the limits of our Galactic universe, as it is called from the Galaxy or Milky Way. (2) Nebulæ of a smaller type, called planetary. These lie within the Galactic portion of the universe and seem to be early stages of what may some day be stars or solar systems. (3) Binary or multiple stars, which are extraordinarily numerous. In some parts of the heavens they form 50 or even 60 per cent of the stars and in the galaxy as a whole they seem to form "fully one third." (4) Star clusters. These consist of about a hundred groups of stars in each of which the stars move together in the same direction with approximately the same velocity. These, like the spiral nebulæ, are thought by some astronomers to lie outside the limits of the galaxy, but this is far from certain. (5) The solar system. According to Jeans this seems to be unique. It does not fit into the general mathematical theory by which he explains spiral nebulæ, planetary nebulæ, binary stars, and star clusters. It seems to demand a special explanation, such as is furnished by tidal disruption due to the passage of the sun close to another star.
The part of Jeans' work which specially concerns us is his study of the probability that some other star will approach the sun closely enough to have an appreciable gravitative or electrical effect, and thus cause disturbances in the solar atmosphere. Of course both the star and the sun are moving, but to avoid circumlocution we shall speak of such mutual approaches simply as approaches of the sun. For our present purpose the most fundamental fact may be summed up in a quotation from Jeans in which he says that most stars "show evidence of having experienced considerable disturbance by other systems; there is no reason why our solar system should