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A complex mechanical system may be capable of motion in several distinct modes or types； and the motions corresponding to each such type may be arranged as before in families。 For the sake of simplicity I will suppose that only two types are possible； so that there will only be two families； and the rotational momentum is to be constant。 The two types of motion will have certain features in common which we denote in a sort of shorthand by the letter A。 Similarly the two types may be described as A ＋ a and A ＋ b； so that a and b denote the specific differences which discriminate the families from one another。 Now following in imagination the family of the type A ＋ a； let us begin with the case where the specific difference a is well marked。 As we cast our eyes along the series forming the family； we find the difference a becoming less conspicuous。 It gradually dwindles until it disappears； beyond this point it either becomes reversed； or else the type has ceased to be a possible one。 In our shorthand we have started with A ＋ a； and have watched the characteristic a dwindling to zero。 When it vanishes we have reached a type which may be specified as A； beyond this point the type would be A … a or would be impossible。
Following the A ＋ b type in the same way； b is at first well marked； it dwindles to zero； and finally may become negative。 Hence in shorthand this second family may be described as A ＋ b；。。。A；。。。A … b。
In each family there is one single member which is indistinguishable from a member of the other family； it is called by Poincare a form of bifurcation。 It is this conception of a form of bifurcation which forms the important consideration in problems dealing with the forms of liquid or gaseous bodies in rotation。
But to return to the general question；thus far the stability of these families has not been considered； and it is the stability which renders this way of looking at the matter so valuable。 It may be proved that if before the point of bifurcation the type A ＋ a was stable； then A ＋ b must have been unstable。 Further as a and b each diminish A ＋ a becomes less pronouncedly stable； and A ＋ b less unstable。 On reaching the point of bifurcation A ＋ a has just ceased to be stable； or what amounts to the same thing is just becoming unstable； and the converse is true of the A ＋ b family。 After passing the point of bifurcation A ＋ a has become definitely unstable and A ＋ b has become stable。 Hence the point of bifurcation is also a point of 〃exchange of stabilities between the two types。〃 （In order not to complicate unnecessarily this explanation of a general principle I have not stated fully all the cases that may occur。 Thus： firstly； after bifurcation A ＋ a may be an impossible type and A ＋ a will then stop at this point； or secondly； A ＋ b may have been an impossible type before bifurcation； and will only begin to be a real one after it； or thirdly； both A ＋ a and A ＋ b may be impossible after the point of bifurcation； in which case they coalesce and disappear。 This last case shows that types arise and disappear in pairs； and that on appearance or before disappearance one must be stable and the other unstable。）
In nature it is of course only the stable types of motion which can persist for more than a short time。 Thus the task of the physical evolutionist is to determine the forms of bifurcation； at which he must； as it were； change carriages in the evolutionary journey so as always to follow the stable route。 He must besides be able to indicate some natural process which shall correspond in effect to the ideal arrangement of the several types of motion in families with gradually changing specific differences。 Although； as we shall see hereafter； it may frequently or even generally be impossible to specify with exactness the forms of bifurcation in the process of evolution； yet the conception is one of fundamental importance。
The ideas involved in this sketch are no doubt somewhat recondite； but I hope to render them clearer to the non…mathematical reader by homologous considerations in other fields of thought （I considered this subject in my Presidential address to the British Association in 1905； 〃Report of the 75th Meeting of the British Assoc。〃 （S。 Africa； 1905）； London； 1906； page 3。 Some reviewers treated my speculations as fanciful； but as I believe that this was due generally to misapprehension； and as I hold that homologous considerations as to stability and instability are really applicable to evolution of all sorts； I have thought it well to return to the subject in the present paper。）； and I shall pass on thence to illustrations which will teach us something of the evolution of stellar systems。
States or governments are organised schemes of action amongst groups of men； and they belong to various types to which generic names； such as autocracy； aristocracy or democracy； are somewhat loosely applied。 A definite type of government corresponds to one of our types of motion； and while retaining its type it undergoes a slow change as the civilisation and character of the people change； and as the relationship of the nation to other nations changes。 In the language used before； the government belongs to a family； and as time advances we proceed through the successive members of the family。 A government possesses a certain degree of stability hardly measurable in numbers howeverto resist disintegrating influences such as may arise from wars； famines； and internal dissensions。 This stability gradually rises to a maximum and gradually declines。 The degree of stability at any epoch will depend on the fitness of some leading feature of the government to suit the slowly altering circumstances； and that feature corresponds to the characteristic denoted by a in the physical problem。 A time at length arrives when the stability vanishes； and the slightest shock will overturn the government。 At this stage we have reached the crisis of a point of bifurcation； and there will then be some circumstance； apparently quite insignificant and almost unnoticed； which is such as to prevent the occurrence of anarchy。 This circumstance or condition is what we typified as b。 Insignificant although it may seem； it has started the government on a new career of stability by imparting to it a new type。 It grows in importance； the form of government becomes obviously different； and its stability increases。 Then in its turn this newly acquired stability declines； and we pass on to a new crisis or revolution。 There is thus a series of 〃points of bifurcation〃 in history at which the continuity of political history is maintained by means of changes in the type of government。 These ideas seem； to me at least； to give a true account of the history of states； and I contend that it is no mere fanciful analogy but a true homology； when in both realms of thought the physical and the politicalwe perceive the existence of forms of bifurcation and of exchanges of stability。
Further than this； I would ask whether the same train of ideas does not also apply to the evolution of animals？ A species is well adapted to its environment when the individual can withstand the shocks of famine or the attacks and competition of other animals； it then possesses a high degree of stability。 Most of the casual variations of individuals are indifferent； for they do not tell much either for or against success in life； they are small oscillations which leave the type unchanged。 As circumstances change； the stability of the species may gradually dwindle through the insufficiency of some definite quality； on which in earlier times no such insistent demands were made。 The individual animals will then tend to fail in the struggle for life； the numbers will dwindle and extinction may ensue。 But it may be that some new variation； at first of insignificant importance； may just serve to turn the scale。 A new type may be formed in which the variation in question is preserved and augmented； its stability may increase and in time a new species may be produced。
At the risk of condemnation as a wanderer beyond my province into the region of biological evolution； I would say that this view accords with what I understand to be the views of some naturalists； who recognise the existence of critical periods in biological history at which extinction occurs or which form the starting…point for the formation of new species。 Ought we not then to expect that long periods will elapse during which a type of animal will remain almost constant； followed by other periods； enormously long no doubt as measured in the life of man； of acute struggle for existence when the type will change more rapidly？ This at least is the view suggested by the theory of stability in the physical universe。 （I make no claim to extensive reading on this subject； but refer the reader for example to a paper by Professor A。A。W。 Hubrecht on 〃De Vries's theory of Mutations〃； 〃Popular Science Monthly〃； July 1904； especially to page 213。）
And now I propose to apply these ideas of stability to the theory of stellar evolution； and finally to illustrate them by certain recent observations of a very remarkable character。
Stars and planets are formed of materials whic