V.3 No 1

23

Chapter 1. Hypotheses of the Earth origin

Plateau [23] has partially answered this question by his surprisingly simple and original experiment with rotating spheres. J.G. Darwin describes it so: "The alcohol and water are mixed in such proportion that the mixture is as dense as the olive oil. If the densities were equalised quite accurate, the oil will float in liquid as a spherical aggregate and will tend neither up nor down. Thus the oil is actually free of the gravity force. The straight wire bearing a small round disk fitted to it perpendicularly is inserted from above of the vessel. When the disk reaches the oil aggregate, oil will crowd together near the disk, taking the spherical form symmetrical as to the wire. The disk encounters a slow and even rotation, it leads the oil, retaining the surrounding mixture at rest. The oil aggregate takes a shape oblate from the top and bottom, alike an orange; as the rotation accelerates, the hollows appear near the wire, and, finally, the oil separates from the disk and takes the form of actual ring. This last shape is only transitional, because the oil either aggregates again near the very disk or sometimes, at negligibly changed manipulations, the ring breaks into the parts that revolve around the centre, each spinning" [16, p. 218]. In this way we apparently see the process described by the nebular hypotheses; and though it does not corroborate that in case of celestial bodies the formation occurred just so, the Plateau experiment served a proper experimental corroboration for the Kant and Laplace hypotheses and spurred the development of new theoretical models.

Darwin [16] follows the spinning body shape variation in the Plateau experiment with the circular velocity variation. By Darwin's consideration, the sphere corresponds to the state of rest as the most stable shape of liquid body under affection of only its own gravity force. At the slow rotation, the centrifugal force is weak, and sphere some oblates near the poles; when accelerating, the body takes the shape of cheese head (MacLoren's spheroids) having as the limit a plane disk-like spin system, just as we observe the planet and galaxy systems (see Fig. 1.5) but at other parameters of spin there can also form a cigar-like shape (Jacobi spheroid).

Fig. 1.5. The spherical liquid body evolution in rotation, by Plateau, MacLoren, Darwin, Poincare [16, p. 223, Fig. 38].

"When rotations are alike and their speed grows evenly, we find the 'planet' more plane, 'cheese' constricts in diameter, 'cigar' shortens and thickens. … With the further growing of rotation speed, the length and width of 'cigar' equalise, but its rotation axis always remains the shortest of three… The upper oval in Fig. 1.5 gives a section view of both the 'planet' and 'cigar', when they appear equal - the first due to its flatting, and the second - to its shortening. Another upper shape shows the result of variation of cheese-like MacLoren figure; we can note some its similarity with the new 'planet' and 'cigar'. If the spin speed grows, the Jacoby figure already will not exist, and there will remain only two MacLoren spheroids. However it has an important consequence: both these shapes are unstable… Both these shapes, spinning with the more and more speed, … finally will appear the same. This limit of MacLoren spheroids is shown in the lower part of Fig. 1.5 … Its equilibrium will be unstable… A. Poincare has proved, if we follow a series of figures and reveal that they transit from stability to instability, we will find also another series of figures similar to this first. We already saw an example of this law: the MacLoren figures transit from stability to instability at the moment of their identity with the Jacoby figures. … Now let us imagine that the 'cigar' rotates with the speed consistent to this moment, and follow the sequence of changes, making it rotating lower and lower in our mind. We know, the 'cigar' will lengthen and become unstable, but Poincare not only proved the existence of parallel series but also derived that the shape of these figures is something like a pear. … How this shape develops with the further deceleration, we do not know, but almost undoubtedly the 'pear' will constrict in 'waist', and then recalls already a sand-glass. Further the neck of this sand-glass thins, and finally the entire figure divides in two" [16, p. 220- 224]. (Darwin supposed, the Moon separated from the Earth in such way). Poincare devoted to this problem his works [24]- [30].