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19。 I have dwelt on the fundamental ideas of Lamprecht； because they are not yet widely known in England； and because his system is the ablest product of the sociological school of historians。 It carries the more weight as its author himself is a historical specialist； and his historical syntheses deserve the most careful consideration。 But there is much in the process of development which on such assumptions is not explained； especially the initiative of individuals。 Historical development does not proceed in a right line； without the choice of diverging。 Again and again； several roads are open to it； of which it chooses onewhy？ On Lamprecht's method； we may be able to assign the conditions which limit the psychical activity of men at a particular stage of evolution； but within those limits the individual has so many options； such a wide room for moving； that the definition of those conditions； the 〃psychical diapasons；〃 is only part of the explanation of the particular development。 The heel of Achilles in all historical speculations of this class has been the role of the individual。
The increasing prominence of economic history has tended to encourage the view that history can be explained in terms of general concepts or types。 Marx and his school based their theory of human development on the conditions of production； by which； according to them； all social movements and historical changes are entirely controlled。 The leading part which economic factors play in Lamprecht's system is significant； illustrating the fact that economic changes admit most readily this kind of treatment； because they have been less subject to direction or interference by individual pioneers。
Perhaps it may be thought that the conception of SOCIAL ENVIRONMENT （essentially psychical）； on which Lamprecht's 〃psychical diapasons〃 depend； is the most valuable and fertile conception that the historian owes to the suggestion of the science of biologythe conception of all particular historical actions and movements as （1） related to and conditioned by the social environment； and （2） gradually bringing about a transformation of that environment。 But no given transformation can be proved to be necessary （pre…determined）。 And types of development do not represent laws； their meaning and value lie in the help they may give to the historian； in investigating a certain period of civilisation； to enable him to discover the interrelations among the diverse features which it presents。 They are； as some one has said； an instrument of heuretic method。
20。 The men engaged in special historical researcheswhich have been pursued unremittingly for a century past； according to scientific methods of investigating evidence （initiated by Wolf； Niebuhr； Ranke）have for the most part worked on the assumptions of genetic history or at least followed in the footsteps of those who fully grasped the genetic point of view。 But their aim has been to collect and sift evidence； and determine particular facts； comparatively few have given serious thought to the lines of research and the speculations which have been considered in this paper。 They have been reasonably shy of compromising their work by applying theories which are still much debated and immature。 But historiography cannot permanently evade the questions raised by these theories。 One may venture to say that no historical change or transformation will be fully understood until it is explained how social environment acted on the individual components of the society （both immediately and by heredity）； and how the individuals reacted upon their environment。 The problem is psychical； but it is analogous to the main problem of the biologist。
XXVIII。 THE GENESIS OF DOUBLE STARS。
By SIR GEORGE DARWIN； K。C。B。； F。R。S。 Plumian Professor of Astronomy and Experimental Philosophy in the University of Cambridge。
In ordinary speech a system of any sort is said to be stable when it cannot be upset easily； but the meaning attached to the word is usually somewhat vague。 It is hardly surprising that this should be the case； when it is only within the last thirty years； and principally through the investigations of M。 Poincare； that the conception of stability has； even for physicists； assumed a definiteness and clearness in which it was previously lacking。 The laws which govern stability hold good in regions of the greatest diversity； they apply to the motion of planets round the sun； to the internal arrangement of those minute corpuscles of which each chemical atom is constructed； and to the forms of celestial bodies。 In the present essay I shall attempt to consider the laws of stability as relating to the last case； and shall discuss the succession of shapes which may be assumed by celestial bodies in the course of their evolution。 I believe further that homologous conceptions are applicable in the consideration of the transmutations of the various forms of animal and of vegetable life and in other regions of thought。 Even if some of my readers should think that what I shall say on this head is fanciful； yet at least the exposition will serve to illustrate the meaning to be attached to the laws of stability in the physical universe。
I propose； therefore； to begin this essay by a sketch of the principles of stability as they are now formulated by physicists。
I。
If a slight impulse be imparted to a system in equilibrium one of two consequences must ensue； either small oscillations of the system will be started； or the disturbance will increase without limit and the arrangement of the system will be completely changed。 Thus a stick may be in equilibrium either when it hangs from a peg or when it is balanced on its point。 If in the first case the stick is touched it will swing to and fro； but in the second case it will topple over。 The first position is a stable one； the second is unstable。 But this case is too simple to illustrate all that is implied by stability； and we must consider cases of stable and of unstable motion。 Imagine a satellite and its planet； and consider each of them to be of indefinitely small size； in fact particles； then the satellite revolves round its planet in an ellipse。 A small disturbance imparted to the satellite will only change the ellipse to a small amount； and so the motion is said to be stable。 If； on the other hand； the disturbance were to make the satellite depart from its initial elliptic orbit in ever widening circuits； the motion would be unstable。 This case affords an example of stable motion； but I have adduced it principally with the object of illustrating another point not immediately connected with stability； but important to a proper comprehension of the theory of stability。
The motion of a satellite about its planet is one of revolution or rotation。 When the satellite moves in an ellipse of any given degree of eccentricity； there is a certain amount of rotation in the system； technically called rotational momentum； and it is always the same at every part of the orbit。 （Moment of momentum or rotational momentum is measured by the momentum of the satellite multiplied by the perpendicular from the planet on to the direction of the path of the satellite at any instant。）
Now if we consider all the possible elliptic orbits of a satellite about its planet which have the same amount of 〃rotational momentum；〃 we find that the major axis of the ellipse described will be different according to the amount of flattening （or the eccentricity） of the ellipse described。 A figure titled 〃A 'family' of elliptic orbits with constant rotational momentum〃 （Fig。 1） illustrates for a given planet and satellite all such orbits with constant rotational momentum； and with all the major axes in the same direction。 It will be observed that there is a continuous transformation from one orbit to the next； and that the whole forms a consecutive group； called by mathematicians 〃a family〃 of orbits。 In this case the rotational momentum is constant and the position of any orbit in the family is determined by the length of the major axis of the ellipse； the classification is according to the major axis； but it might have been made according to anything else which would cause the orbit to be exactly determinate。
I shall come later to the classification of all possible forms of ideal liquid stars； which have the same amount of rotational momentum； and the classification will then be made according to their densities； but the idea of orderly arrangement in a 〃family〃 is just the same。
We thus arrive at the conception of a definite type of motion； with a constant amount of rotational momentum； and a classification of all members of the family； formed by all possible motions of that type； according to the value of some measurable quantity （this will hereafter be density） which determines the motion exactly。 In the particular case of the elliptic motion used for illustration the motion was stable； but other cases of motion might be adduced in which the motion would be unstable； and it would be found that classification in a family and specification by some measurable quantity would be equally applicable。
A complex mechanical system may be capable of motion in several dis