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Rh former functions. An organ, when rendered useless, may well be variable, for its variations cannot be checked by natural selection. At whatever period of life disuse or selection reduces an organ, and this will generally be when the being has come to maturity and to its full powers of action, the principle of inheritance at corresponding ages will reproduce the organ in its reduced state at the same age, and consequently will seldom affect or reduce it in the embryo. Thus we can understand the greater relative size of rudimentary organs in the embryo, and their lesser relative size in the adult. But if each step of the process of reduction were to be inherited, not at the corresponding age, but at an extremely early period of life (as we have good reason to believe to be possible) the rudimentary part would tend to be wholly lost, and we should have a case of complete abortion. The principle, also, of economy, explained in a former chapter, by which the materials forming any part or structure, if not useful to the possessor, will be saved as far as is possible, will probably often come into play; and this will tend to cause the entire obliteration of a rudimentary organ.

As the presence of rudimentary organs is thus due to the tendency in every part of the organisation, which has long existed, to be inherited—we can understand, on the genealogical view of classification, how it is that systematists have found rudimentary parts as useful as, or even sometimes more useful than, parts of high physiological importance. Rudimentary organs may be compared with the letters in a word, still retained in the spelling, but become useless in the pronunciation, but which serve as a clue in seeking for its derivation. On the view of descent with modification, we may conclude that the existence of organs in a rudimentary, imperfect, and useless condition, or quite aborted, far


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456 from presenting a strange difficulty, as they assuredly do on the ordinary doctrine of creation, might even have been anticipated, and can be accounted for by the laws of inheritance.

Summary.—In this chapter I have attempted to show, that the subordination of group to group in all organisms throughout all time; that the nature of the relationship, by which all living and extinct beings are united by complex, radiating, and circuitous lines of affinities into one grand system; the rules followed and the difficulties encountered by naturalists in their classifications; the value set upon characters, if constant and prevalent, whether of high vital importance, or of the most trifling importance, or, as in rudimentary organs, of no importance; the wide opposition in value between analogical or adaptive characters, and characters of true affinity; and other such rules;—all naturally follow on the view of the common parentage of those forms which are considered by naturalists as allied, together with their modification through natural selection, with its contingencies of extinction and divergence of character. In considering this view of classification, it should be borne in mind that the element of descent has been universally used in ranking together the sexes, ages, and acknowledged varieties of the same species, however different they may be in structure. If we extend the use of this element of descent,—the only certainly known cause of similarity in organic beings,—we shall understand what is meant by the natural system: it is genealogical in its attempted arrangement, with the grades of acquired difference marked by the terms varieties, species, genera, families, orders, and classes.

On this same view of descent with modification, all the great facts in Morphology become intelligible,—

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Rh whether we look to the same pattern displayed in the homologous organs, to whatever purpose applied, of the different species of a class; or to the homologous parts constructed on the same pattern in each individual animal and plant.

On the principle of successive slight variations, not necessarily or generally supervening at a very early period of life, and being inherited at a corresponding period, we can understand the great leading facts in Embryology; namely, the resemblance in an individual embryo of the homologous parts, which when matured will become widely different from each other in structure and function; and the resemblance in different species of a class of the homologous parts or organs, though fitted in the adult members for purposes as different as possible. Larvæ are active embryos, which have become specially modified in relation to their habits of life, through the principle of modifications being inherited at corresponding ages. On this same principle—and bearing in mind, that when organs are reduced in size, either from disuse or selection, it will generally be at that period of life when the being has to provide for its own wants, and bearing in mind how strong is the principle of inheritance—the occurrence of rudimentary organs and their final abortion, present to us no inexplicable difficulties; on the contrary, their presence might have been even anticipated. The importance of embryological characters and of rudimentary organs in classification is intelligible, on the view that an arrangement is only so far natural as it is genealogical.

Finally, the several classes of facts which have been considered in this chapter, seem to me to proclaim so plainly, that the innumerable species, genera, and families of organic beings, with which this world is


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458 peopled, have all descended, each within its own class or group, from common parents, and have all been modified in the course of descent, that I should without hesitation adopt this view, even if it were unsupported by other facts or arguments.


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this whole volume is one long argument, it may be convenient to the reader to have the leading facts and inferences briefly recapitulated.

That many and grave objections may be advanced against the theory of descent with modification through natural selection, I do not deny. I have endeavoured to give to them their full force. Nothing at first can appear more difficult to believe than that the more complex organs and instincts should have been perfected, not by means superior to, though analogous with, human reason, but by the accumulation of innumerable slight variations, each good for the individual possessor. Nevertheless, this difficulty, though appearing to our imagination insuperably great, cannot be considered real if we admit the following propositions, namely,—that gradations in the perfection of any organ or instinct, which we may consider, either do now exist or could have existed, each good of its kind,—that all organs and instincts are, in ever so slight a degree, variable,—and, lastly, that there is a struggle for existence leading to the preservation of each profitable deviation of structure or instinct. The truth of these propositions cannot, I think, be disputed.


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 It is, no doubt, extremely difficult even to conjecture by what gradations many structures have been perfected, more especially amongst broken and failing groups of organic beings; but we see so many strange gradations in nature, as is proclaimed by the canon, "Natura non facit saltum," that we ought to be extremely cautious in saying that any organ or instinct, or any whole being, could not have arrived at its present state by many graduated steps. There are, it must be admitted, cases of special difficulty on the theory of natural selection; and one of the most curious of these is the existence of two or three defined castes of workers or sterile females in the same community of ants; but I have attempted to show how this difficulty can be mastered.

With respect to the almost universal sterility of species when first crossed, which forms so remarkable a contrast with the almost universal fertility of varieties when crossed, I must refer the reader to the recapitulation of the facts given at the end of the eighth chapter, which seem to me conclusively to show that this sterility is no more a special endowment than is the incapacity of two trees to be grafted together, but that it is incidental on constitutional differences in the reproductive systems of the intercrossed species. We see the truth of this conclusion in the vast difference in the result, when the same two species are crossed reciprocally; that is, when one species is first used as the father and then as the mother.

The fertility of varieties when intercrossed and of their mongrel offspring cannot be considered as universal; nor is their very general fertility surprising when we remember that it is not likely that either their constitutions or their reproductive systems should have been profoundly modified. Moreover, most of the


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 varieties which have been experimentised on have been produced under domestication; and as domestication apparently tends to eliminate sterility, we ought not to expect it also to produce sterility.

The sterility of hybrids is a very different case from that of first crosses, for their reproductive organs are more or less functionally impotent; whereas in first crosses the organs on both sides are in a perfect condition. As we continually see that organisms of all kinds are rendered in some degree sterile from their constitutions having been disturbed by slightly different and new conditions of life, we need not feel surprise at hybrids being in some degree sterile, for their constitutions can hardly fail to have been disturbed from being compounded of two distinct organisations. This parallelism is supported by another parallel, but directly opposite, class of facts; namely, that the vigour and fertility of all organic beings are increased by slight changes in their conditions of life, and that the offspring of slightly modified forms or varieties acquire from being crossed increased vigour and fertility. So that, on the one hand, considerable changes in the conditions of life and crosses between greatly modified forms, lessen fertility; and on the other hand, lesser changes in the conditions of life and crosses between less modified forms, increase fertility.

Turning to geographical distribution, the difficulties encountered on the theory of descent with modification are grave enough. All the individuals of the same species, and all the species of the same genus, or even higher group, must have descended from common parents; and therefore, in however distant and isolated parts of the world they are now found, they must in the course of successive generations have passed from some one part to the others. We are often wholly unable


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 even to conjecture how this could have been effected. Yet, as we have reason to believe that some species have retained the same specific form for very long periods, enormously long as measured by years, too much stress ought not to be laid on the occasional wide diffusion of the same species; for during very long periods of time there will always be a good chance for wide migration by many means. A broken or interrupted range may often be accounted for by the extinction of the species in the intermediate regions. It cannot be denied that we are as yet very ignorant of the full extent of the various climatal and geographical changes which have affected the earth during modern periods; and such changes will obviously have greatly facilitated migration. As an example, I have attempted to show how potent has been the influence of the Glacial period on the distribution both of the same and of representative species throughout the world. We are as yet profoundly ignorant of the many occasional means of transport. With respect to distinct species of the same genus inhabiting very distant and isolated regions, as the process of modification has necessarily been slow, all the means of migration will have been possible during a very long period; and consequently the difficulty of the wide diffusion of species of the same genus is in some degree lessened.

As on the theory of natural selection an interminable number of intermediate forms must have existed, linking together all the species in each group by gradations as fine as our present varieties, it may be asked, Why do we not see these linking forms all around us? Why are not all organic beings blended together in an inextricable chaos? With respect to existing forms, we should remember that we have no right to expect (excepting in rare cases) to discover directly connecting


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 links between them, but only between each and some extinct and supplanted form. Even on a wide area, which has during a long period remained continuous, and of which the climate and other conditions of life change insensibly in going from a district occupied by one species into another district occupied by a closely allied species, we have no just right to expect often to find intermediate varieties in the intermediate zone. For we have reason to believe that only a few species are undergoing change at any one period; and all changes are slowly effected. I have also shown that the intermediate varieties which will at first probably exist in the intermediate zones, will be liable to be supplanted by the allied forms on either hand; and the latter, from existing in greater numbers, will generally be modified and improved at a quicker rate than the intermediate varieties, which exist in lesser numbers; so that the intermediate varieties will, in the long run, be supplanted and exterminated.

On this doctrine of the extermination of an infinitude of connecting links, between the living and extinct inhabitants of the world, and at each successive period between the extinct and still older species, why is not every geological formation charged with such links? Why does not every collection of fossil remains afford plain evidence of the gradation and mutation of the forms of life? We meet with no such evidence, and this is the most obvious and forcible of the many objections which may be urged against my theory. Why, again, do whole groups of allied species appear, though certainly they often falsely appear, to have come in suddenly on the several geological stages? Why do we not find great piles of strata beneath the Silurian system, stored with the remains of the progenitors of the Silurian groups of fossils? For certainly on my theory such


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 strata must somewhere have been deposited at these ancient and utterly unknown epochs in the world's history.

I can answer these questions and grave objections only on the supposition that the geological record is far more imperfect than most geologists believe. It cannot be objected that there has not been time sufficient for any amount of organic change; for the lapse of time has been so great as to be utterly inappreciable by the human intellect. The number of specimens in all our museums is absolutely as nothing compared with the countless generations of countless species which certainly have existed. We should not be able to recognise a species as the parent of any one or more species if we were to examine them ever so closely, unless we likewise possessed many of the intermediate links between their past or parent and present states; and these many links we could hardly ever expect to discover, owing to the imperfection of the geological record. Numerous existing doubtful forms could be named which are probably varieties; but who will pretend that in future ages so many fossil links will be discovered, that naturalists will be able to decide, on the common view, whether or not these doubtful forms are varieties? As long as most of the links between any two species are unknown, if any one link or intermediate variety be discovered, it will simply be classed as another and distinct species. Only a small portion of the world has been geologically explored. Only organic beings of certain classes can be preserved in a fossil condition, at least in any great number. Widely ranging species vary most, and varieties are often at first local,—both causes rendering the discovery of intermediate links less likely. Local varieties will not spread into other and distant regions until they are considerably modified and


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 ; and when they do spread, if discovered in a geological formation, they will appear as if suddenly created there, and will be simply classed as new species. Most formations have been intermittent in their accumulation; and their duration, I am inclined to believe, has been shorter than the average duration of specific forms. Successive formations are separated from each other by enormous blank intervals of time; for fossiliferous formations, thick enough to resist future degradation, can be accumulated only where much sediment is deposited on the subsiding bed of the sea. During the alternate periods of elevation and of stationary level the record will be blank. During these latter periods there will probably be more variability in the forms of life; during periods of subsidence, more extinction.

With respect to the absence of fossiliferous formations beneath the lowest Silurian strata, I can only recur to the hypothesis given in the ninth chapter. That the geological record is imperfect all will admit; but that it is imperfect to the degree which I require, few will be inclined to admit. If we look to long enough intervals of time, geology plainly declares that all species have changed; and they have changed in the manner which my theory requires, for they have changed slowly and in a graduated manner. We clearly see this in the fossil remains from consecutive formations invariably being much more closely related to each other, than are the fossils from formations distant from each other in time.

Such is the sum of the several chief objections and difficulties which may justly be urged against my theory; and I have now briefly recapitulated the answers and explanations which can be given to them. I have felt these difficulties far too heavily during many years to


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 doubt their weight. But it deserves especial notice that the more important objections relate to questions on which we are confessedly ignorant; nor do we know how ignorant we are. We do not know all the possible transitional gradations between the simplest and the most perfect organs; it cannot be pretended that we know all the varied means of Distribution during the long lapse of years, or that we know how imperfect the Geological Record is. Grave as these several difficulties are, in my judgment they do not overthrow the theory of descent with modification.

Now let us turn to the other side of the argument. Under domestication we see much variability. This seems to be mainly due to the reproductive system being eminently susceptible to changes in the conditions of life; so that this system, when not rendered impotent, fails to reproduce offspring exactly like the parent-form. Variability is governed by many complex laws,—by correlation of growth, by use and disuse, and by the direct action of the physical conditions of life. There is much difficulty in ascertaining how much modification our domestic productions have undergone; but we may safely infer that the amount has been large, and that modifications can be inherited for long periods. As long as the conditions of life remain the same, we have reason to believe that a modification, which has already been inherited for many generations, may continue to be inherited for an almost infinite number of generations. On the other hand we have evidence that variability, when it has once come into play, does not wholly cease; for new varieties are still occasionally produced by our most anciently domesticated productions.

Man does not actually produce variability; he only


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 unintentionally exposes organic beings to new conditions of life, and then nature acts on the organisation, and causes variability. But man can and does select the variations given to him by nature, and thus accumulate them in any desired manner. He thus adapts animals and plants for his own benefit or pleasure. He may do this methodically, or he may do it unconsciously by preserving the individuals most useful to him at the time, without any thought of altering the breed. It is certain that he can largely influence the character of a breed by selecting, in each successive generation, individual differences so slight as to be quite inappreciable by an uneducated eye. This process of selection has been the great agency in the production of the most distinct and useful domestic breeds. That many of the breeds produced by man have to a large extent the character of natural species, is shown by the inextricable doubts whether very many of them are varieties or aboriginal species.

There is no obvious reason why the principles which have acted so efficiently under domestication should not have acted under nature. In the preservation of favoured individuals and races, during the constantly-recurrent Struggle for Existence, we see the most powerful and ever-acting means of selection. The struggle for existence inevitably follows from the high geometrical ratio of increase which is common to all organic beings. This high rate of increase is proved by calculation, by the effects of a succession of peculiar seasons, and by the results of naturalisation, as explained in the third chapter. More individuals are born than can possibly survive. A grain in the balance will determine which individual shall live and which shall die,—which variety or species shall increase in number, and which shall decrease, or finally become extinct. As the


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 of the same species come in all respects into the closest competition with each other, the struggle will generally be most severe between them; it will be almost equally severe between the varieties of the same species, and next in severity between the species of the same genus. But the struggle will often be very severe between beings most remote in the scale of nature. The slightest advantage in one being, at any age or during any season, over those with which it comes into competition, or better adaptation in however slight a degree to the surrounding physical conditions, will turn the balance.

With animals having separated sexes there will in most cases be a struggle between the males for possession of the females. The most vigorous individuals, or those which have most successfully struggled with their conditions of life, will generally leave most progeny. But success will often depend on having special weapons or means of defence, or on the charms of the males; and the slightest advantage will lead to victory.

As geology plainly proclaims that each land has undergone great physical changes, we might have expected that organic beings would have varied under nature, in the same way as they generally have varied under the changed conditions of domestication. And if there be any variability under nature, it would be an unaccountable fact if natural selection had not come into play. It has often been asserted, but the assertion is quite incapable of proof, that the amount of variation under nature is a strictly limited quantity. Man, though acting on external characters alone and often capriciously, can produce within a short period a great result by adding up mere individual differences in his domestic productions; and every one admits that there are at least individual differences in species under nature. But, besides such differences, all naturalists


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 have admitted the existence of varieties, which they think sufficiently distinct to be worthy of record in systematic works. No one can draw any clear distinction between individual differences and slight varieties; or between more plainly marked varieties and sub-species, and species. Let it be observed how naturalists differ in the rank which they assign to the many representative forms in Europe and North America.

If then we have under nature variability and a powerful agent always ready to act and select, why should we doubt that variations in any way useful to beings, under their excessively complex relations of life, would be preserved, accumulated, and inherited? Why, if man can by patience select variations most useful to himself, should nature fail in selecting variations useful, under changing conditions of life, to her living products? What limit can be put to this power, acting during long ages and rigidly scrutinising the whole constitution, structure, and habits of each creature,—favouring the good and rejecting the bad? I can see no limit to this power, in slowly and beautifully adapting each form to the most complex relations of life. The theory of natural selection, even if we looked no further than this, seems to me to be in itself probable. I have already recapitulated, as fairly as I could, the opposed difficulties and objections: now let us turn to the special facts and arguments in favour of the theory.

On the view that species are only strongly marked and permanent varieties, and that each species first existed as a variety, we can see why it is that no line of demarcation can be drawn between species, commonly supposed to have been produced by special acts of creation, and varieties which are acknowledged to have been produced by secondary laws. On this same view we can understand how it is that in each region


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 where many species of a genus have been produced, and where they now flourish, these same species should present many varieties; for where the manufactory of species has been active, we might expect, as a general rule, to find it still in action; and this is the case if varieties be incipient species. Moreover, the species of the larger genera, which afford the greater number of varieties or incipient species, retain to a certain degree the character of varieties; for they differ from each other by a less amount of difference than do the species of smaller genera. The closely allied species also of the larger genera apparently have restricted ranges, and they are clustered in little groups round other species—in which respects they resemble varieties. These are strange relations on the view of each species having been independently created, but are intelligible if all species first existed as varieties.

As each species tends by its geometrical ratio of reproduction to increase inordinately in number; and as the modified descendants of each species will be enabled to increase by so much the more as they become more diversified in habits and structure, so as to be enabled to seize on many and widely different places in the economy of nature, there will be a constant tendency in natural selection to preserve the most divergent offspring of any one species. Hence during a long-continued course of modification, the slight differences, characteristic of varieties of the same species, tend to be augmented into the greater differences characteristic of species of the same genus. New and improved varieties will inevitably supplant and exterminate the older, less improved and intermediate varieties; and thus species are rendered to a large extent defined and distinct objects. Dominant species belonging to the larger groups tend to give birth to new and dominant


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 forms; so that each large group tends to become still larger, and at the same time more divergent in character. But as all groups cannot thus succeed in increasing in size, for the world would not hold them, the more dominant groups beat the less dominant. This tendency in the large groups to go on increasing in size and diverging in character, together with the almost inevitable contingency of much extinction, explains the arrangement of all the forms of life, in groups subordinate to groups, all within a few great classes, which we now see everywhere around us, and which has prevailed throughout all time. This grand fact of the grouping of all organic beings seems to me utterly inexplicable on the theory of creation.

As natural selection acts solely by accumulating slight, successive, favourable variations, it can produce no great or sudden modification; it can act only by very short and slow steps. Hence the canon of "Natura non facit saltum," which every fresh addition to our knowledge tends to make more strictly correct, is on this theory simply intelligible. We can plainly see why nature is prodigal in variety, though niggard in innovation. But why this should be a law of nature if each species has been independently created, no man can explain.

Many other facts are, as it seems to me, explicable on this theory. How strange it is that a bird, under the form of woodpecker, should have been created to prey on insects on the ground; that upland geese, which never or rarely swim, should have been created with webbed feet; that a thrush should have been created to dive and feed on sub-aquatic insects; and that a petrel should have been created with habits and structure fitting it for the life of an auk or grebe! and so on in endless other cases. But on the view of each


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 species constantly trying to increase in number, with natural selection always ready to adapt the slowly varying descendants of each to any unoccupied or ill-occupied place in nature, these facts cease to be strange, or perhaps might even have been anticipated.

As natural selection acts by competition, it adapts the inhabitants of each country only in relation to the degree of perfection of their associates; so that we need feel no surprise at the inhabitants of any one country, although on the ordinary view supposed to have been specially created and adapted for that country, being beaten and supplanted by the naturalised productions from another land. Nor ought we to marvel if all the contrivances in nature be not, as far as we can judge, absolutely perfect; and if some of them be abhorrent to our ideas of fitness. We need not marvel at the sting of the bee causing the bee's own death; at drones being produced in such vast numbers for one single act, and being then slaughtered by their sterile sisters; at the astonishing waste of pollen by our fir-trees; at the instinctive hatred of the queen bee for her own fertile daughters; at ichneumonidæ feeding within the live bodies of caterpillars; and at other such cases. The wonder indeed is, on the theory of natural selection, that more cases of the want of absolute perfection have not been observed.

The complex and little known laws governing variation are the same, as far as we can see, with the laws which have governed the production of so-called specific forms. In both cases physical conditions seem to have produced but little direct effect; yet when varieties enter any zone, they occasionally assume some of the characters of the species proper to that zone. In both varieties and species, use and disuse seem to have produced some effect; for it is difficult to resist this


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 when we look, for instance, at the logger-headed duck, which has wings incapable of flight, in nearly the same condition as in the domestic duck; or when we look at the burrowing tucutucu, which is occasionally blind, and then at certain moles, which are habitually blind and have their eyes covered with skin; or when we look at the blind animals inhabiting the dark caves of America and Europe. In both varieties and species correlation of growth seems to have played a most important part, so that when one part has been modified other parts are necessarily modified. In both varieties and species reversions to long-lost characters occur. How inexplicable on the theory of creation is the occasional appearance of stripes on the shoulder and legs of the several species of the horse-genus and in their hybrids! How simply is this fact explained if we believe that these species have descended from a striped progenitor, in the same manner as the several domestic breeds of pigeon have descended from the blue and barred rock-pigeon!

On the ordinary view of each species having been independently created, why should the specific characters, or those by which the species of the same genus differ from each other, be more variable than the generic characters in which they all agree? Why, for instance, should the colour of a flower be more likely to vary in any one species of a genus, if the other species, supposed to have been created independently, have differently coloured flowers, than if all the species of the genus have the same coloured flowers? If species are only well-marked varieties, of which the characters have become in a high degree permanent, we can understand this fact; for they have already varied since they branched off from a common progenitor in certain characters, by which they have come to be specifically distinct from each other;


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 and therefore these same characters would be more likely still to be variable than the generic characters which have been inherited without change for an enormous period. It is inexplicable on the theory of creation why a part developed in a very unusual manner in any one species of a genus, and therefore, as we may naturally infer, of great importance to the species, should be eminently liable to variation; but, on my view, this part has undergone, since the several species branched off from a common progenitor, an unusual amount of variability and modification, and therefore we might expect this part generally to be still variable. But a part may be developed in the most unusual manner, like the wing of a bat, and yet not be more variable than any other structure, if the part be common to many subordinate forms, that is, if it has been inherited for a very long period; for in this case it will have been rendered constant by long-continued natural selection.

Glancing at instincts, marvellous as some are, they offer no greater difficulty than does corporeal structure on the theory of the natural selection of successive, slight, but profitable modifications. We can thus understand why nature moves by graduated steps in endowing different animals of the same class with their several instincts. I have attempted to show how much light the principle of gradation throws on the admirable architectural powers of the hive-bee. Habit no doubt sometimes comes into play in modifying instincts; but it certainly is not indispensable, as we see, in the case of neuter insects, which leave no progeny to inherit the effects of long-continued habit. On the view of all the species of the same genus having descended from a common parent, and having inherited much in common, we can understand how it is that allied species, when placed under considerably different conditions of life,


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 yet should follow nearly the same instincts; why the thrush of South America, for instance, lines her nest with mud like our British species. On the view of instincts having been slowly acquired through natural selection we need not marvel at some instincts being apparently not perfect and liable to mistakes, and at many instincts causing other animals to suffer.

If species be only well-marked and permanent varieties, we can at once see why their crossed offspring should follow the same complex laws in their degrees and kinds of resemblance to their parents,—in being absorbed into each other by successive crosses, and in other such points,—as do the crossed offspring of acknowledged varieties. On the other hand, these would be strange facts if species have been independently created, and varieties have been produced by secondary laws.

If we admit that the geological record is imperfect in an extreme degree, then such facts as the record gives, support the theory of descent with modification. New species have come on the stage slowly and at successive intervals; and the amount of change, after equal intervals of time, is widely different in different groups. The extinction of species and of whole groups of species, which has played so conspicuous a part in the history of the organic world, almost inevitably follows on the principle of natural selection; for old forms will be supplanted by new and improved forms. Neither single species nor groups of species reappear when the chain of ordinary generation has once been broken. The gradual diffusion of dominant forms, with the slow modification of their descendants, causes the forms of life, after long intervals of time, to appear as if they had changed simultaneously throughout the world. The fact of the fossil remains of each formation being in some degree intermediate in character between the


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 fossils in the formations above and below, is simply explained by their intermediate position in the chain of descent. The grand fact that all extinct organic beings belong to the same system with recent beings, falling either into the same or into intermediate groups, follows from the living and the extinct being the offspring of common parents. As the groups which have descended from an ancient progenitor have generally diverged in character, the progenitor with its early descendants will often be intermediate in character in comparison with its later descendants; and thus we can see why the more ancient a fossil is, the oftener it stands in some degree intermediate between existing and allied groups. Recent forms are generally looked at as being, in some vague sense, higher than ancient and extinct forms; and they are in so far higher as the later and more improved forms have conquered the older and less improved organic beings in the struggle for life. Lastly, the law of the long endurance of allied forms on the same continent,—of marsupials in Australia, of edentata in America, and other such cases,—is intelligible, for within a confined country, the recent and the extinct will naturally be allied by descent.

Looking to geographical distribution, if we admit that there has been during the long course of ages much migration from one part of the world to another, owing to former climatal and geographical changes and to the many occasional and unknown means of dispersal, then we can understand, on the theory of descent with modification, most of the great leading facts in Distribution. We can see why there should be so striking a parallelism in the distribution of organic beings throughout space, and in their geological succession throughout time; for in both cases the beings have been connected by the bond of ordinary generation, and the means of


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 modification have been the same. We see the full meaning of the wonderful fact, which must have struck every traveller, namely, that on the same continent, under the most diverse conditions, under heat and cold, on mountain and lowland, on deserts and marshes, most of the inhabitants within each great class are plainly related; for they will generally be descendants of the same progenitors and early colonists. On this same principle of former migration, combined in most cases with modification, we can understand, by the aid of the Glacial period, the identity of some few plants, and the close alliance of many others, on the most distant mountains, under the most different climates; and likewise the close alliance of some of the inhabitants of the sea in the northern and southern temperate zones, though separated by the whole intertropical ocean. Although two areas may present the same physical conditions of life, we need feel no surprise at their inhabitants being widely different, if they have been for a long period completely separated from each other; for as the relation of organism to organism is the most important of all relations, and as the two areas will have received colonists from some third source or from each other, at various periods and in different proportions, the course of modification in the two areas will inevitably be different.

On this view of migration, with subsequent modification, we can see why oceanic islands should be inhabited by few species, but of these, that many should be peculiar. We can clearly see why those animals which cannot cross wide spaces of ocean, as frogs and terrestrial mammals, should not inhabit oceanic islands; and why, on the other hand, new and peculiar species of bats, which can traverse the ocean, should so often be found on islands far distant from any continent. Such facts


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 as the presence of peculiar species of bats, and the absence of all other mammals, on oceanic islands, are utterly inexplicable on the theory of independent acts of creation.

The existence of closely allied or representative species in any two areas, implies, on the theory of descent with modification, that the same parents formerly inhabited both areas; and we almost invariably find that wherever many closely allied species inhabit two areas, some identical species common to both still exist. Wherever many closely allied yet distinct species occur, many doubtful forms and varieties of the same species likewise occur. It is a rule of high generality that the inhabitants of each area are related to the inhabitants of the nearest source whence immigrants might have been derived. We see this in nearly all the plants and animals of the Galapagos archipelago, of Juan Fernandez, and of the other American islands being related in the most striking manner to the plants and animals of the neighbouring American mainland; and those of the Cape de Verde archipelago and other African islands to the African mainland. It must be admitted that these facts receive no explanation on the theory of creation.

The fact, as we have seen, that all past and present organic beings constitute one grand natural system, with group subordinate to group, and with extinct groups often falling in between recent groups, is intelligible on the theory of natural selection with its contingencies of extinction and divergence of character. On these same principles we see how it is, that the mutual affinities of the species and genera within each class are so complex and circuitous. We see why certain characters are far more serviceable than others for classification;—why adaptive characters, though of paramount importance to the being, are of hardly any


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 importance in classification; why characters derived from rudimentary parts, though of no service to the being, are often of high classificatory value; and why embryological characters are the most valuable of all. The real affinities of all organic beings are due to inheritance or community of descent. The natural system is a genealogical arrangement, in which we have to discover the lines of descent by the most permanent characters, however slight their vital importance may be.

The framework of bones being the same in the hand of a man, wing of a bat, fin of the porpoise, and leg of the horse,—the same number of vertebræ forming the neck of the giraffe and of the elephant,—and innumerable other such facts, at once explain themselves on the theory of descent with slow and slight successive modifications. The similarity of pattern in the wing and leg of a bat, though used for such different purpose,—in the jaws and legs of a crab,—in the petals, stamens, and pistils of a flower, is likewise intelligible on the view of the gradual modification of parts or organs, which were alike in the early progenitor of each class. On the principle of successive variations not always supervening at an early age, and being inherited at a corresponding not early period of life, we can clearly see why the embryos of mammals, birds, reptiles, and fishes should be so closely alike, and should be so unlike the adult forms. We may cease marvelling at the embryo of an air-breathing mammal or bird having branchial slits and arteries running in loops, like those in a fish which has to breathe the air dissolved in water, by the aid of well-developed branchiæ.

Disuse, aided sometimes by natural selection, will often tend to reduce an organ, when it has become useless by changed habits or under changed conditions


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 of life; and we can clearly understand on this view the meaning of rudimentary organs. But disuse and selection will generally act on each creature, when it has come to maturity and has to play its full part in the struggle for existence, and will thus have little power of acting on an organ during early life; hence the organ will not be much reduced or rendered rudimentary at this early age. The calf, for instance, has inherited teeth, which never cut through the gums of the upper jaw, from an early progenitor having well-developed teeth; and we may believe, that the teeth in the mature animal were reduced, during successive generations, by disuse or by the tongue and palate having been fitted by natural selection to browse without their aid; whereas in the calf, the teeth have been left untouched by selection or disuse, and on the principle of inheritance at corresponding ages have been inherited from a remote period to the present day. On the view of each organic being and each separate organ having been specially created, how utterly inexplicable it is that parts, like the teeth in the embryonic calf or like the shrivelled wings under the soldered wing-covers of some beetles, should thus so frequently bear the plain stamp of inutility! Nature may be said to have taken pains to reveal, by rudimentary organs and by homologous structures, her scheme of modification, which it seems that we wilfully will not understand.

I have now recapitulated the chief facts and considerations which have thoroughly convinced me that species have changed, and are still slowly changing by the preservation and accumulation of successive slight favourable variations. Why, it may be asked, have all the most eminent living naturalists and geologists rejected this view of the mutability of species? It cannot be


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 asserted that organic beings in a state of nature are subject to no variation; it cannot be proved that the amount of variation in the course of long ages is a limited quantity; no clear distinction has been, or can be, drawn between species and well-marked varieties. It cannot be maintained that species when intercrossed are invariably sterile, and varieties invariably fertile; or that sterility is a special endowment and sign of creation. The belief that species were immutable productions was almost unavoidable as long as the history of the world was thought to be of short duration; and now that we have acquired some idea of the lapse of time, we are too apt to assume, without proof, that the geological record is so perfect that it would have afforded us plain evidence of the mutation of species, if they had undergone mutation.

But the chief cause of our natural unwillingness to admit that one species has given birth to other and distinct species, is that we are always slow in admitting any great change of which we do not see the intermediate steps. The difficulty is the same as that felt by so many geologists, when Lyell first insisted that long lines of inland cliffs had been formed, and great valleys excavated, by the slow action of the coast-waves. The mind cannot possibly grasp the full meaning of the term of a hundred million years; it cannot add up and perceive the full effects of many slight variations, accumulated during an almost infinite number of generations.

Although I am fully convinced of the truth of the views given in this volume under the form of an abstract, I by no means expect to convince experienced naturalists whose minds are stocked with a multitude of facts all viewed, during a long course of years, from a point of view directly opposite to mine. It is so easy


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 to hide our ignorance under such expressions as the "plan of creation," "unity of design," &c., and to think that we give an explanation when we only restate a fact. Any one whose disposition leads him to attach more weight to unexplained difficulties than to the explanation of a certain number of facts will certainly reject my theory. A few naturalists, endowed with much flexibility of mind, and who have already begun to doubt on the immutability of species, may be influenced by this volume; but I look with confidence to the future, to young and rising naturalists, who will be able to view both sides of the question with impartiality. Whoever is led to believe that species are mutable will do good service by conscientiously expressing his conviction; for only thus can the load of prejudice by which this subject is overwhelmed be removed.

Several eminent naturalists have of late published their belief that a multitude of reputed species in each genus are not real species; but that other species are real, that is, have been independently created. This seems to me a strange conclusion to arrive at. They admit that a multitude of forms, which till lately they themselves thought were special creations, and which are still thus looked at by the majority of naturalists, and which consequently have every external characteristic feature of true species,—they admit that these have been produced by variation, but they refuse to extend the same view to other and very slightly different forms. Nevertheless they do not pretend that they can define, or even conjecture, which are the created forms of life, and which are those produced by secondary laws. They admit variation as a vera causa in one case, they arbitrarily reject it in another, without assigning any distinction in the two cases. The day will come when this will be given as a curious illustration of


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 the blindness of preconceived opinion. These authors seem no more startled at a miraculous act of creation than at an ordinary birth. But do they really believe that at innumerable periods in the earth's history certain elemental atoms have been commanded suddenly to flash into living tissues? Do they believe that at each supposed act of creation one individual or many were produced? Were all the infinitely numerous kinds of animals and plants created as eggs or seed, or as full grown? and in the case of mammals, were they created bearing the false marks of nourishment from the mother's womb? Although naturalists very properly demand a full explanation of every difficulty from those who believe in the mutability of species, on their own side they ignore the whole subject of the first appearance of species in what they consider reverent silence.

It may be asked how far I extend the doctrine of the modification of species. The question is difficult to answer, because the more distinct the forms are which we may consider, by so much the arguments fall away in force. But some arguments of the greatest weight extend very far. All the members of whole classes can be connected together by chains of affinities, and all can be classified on the same principle, in groups subordinate to groups. Fossil remains sometimes tend to fill up very wide intervals between existing orders. Organs in a rudimentary condition plainly show that an early progenitor had the organ in a fully developed state; and this in some instances necessarily implies an enormous amount of modification in the descendants. Throughout whole classes various structures are formed on the same pattern, and at an embryonic age the species closely resemble each other. Therefore I cannot doubt that the theory of descent with modification


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 embraces all the members of the same class. I believe that animals have descended from at most only four or five progenitors, and plants from an equal or lesser number.

Analogy would lead me one step further, namely, to the belief that all animals and plants have descended from some one prototype. But analogy may be a deceitful guide. Nevertheless all living things have much in common, in their chemical composition, their germinal vesicles, their cellular structure, and their laws of growth and reproduction. We see this even in so trifling a circumstance as that the same poison often similarly affects plants and animals; or that the poison secreted by the gall-fly produces monstrous growths on the wild rose or oak-tree. Therefore I should infer from analogy that probably all the organic beings which have ever lived on this earth have descended from some one primordial form, into which life was first breathed.

When the views entertained in this volume on the origin of species, or when analogous views are generally admitted, we can dimly foresee that there will be a considerable revolution in natural history. Systematists will be able to pursue their labours as at present; but they will not be incessantly haunted by the shadowy doubt whether this or that form be in essence a species. This I feel sure, and I speak after experience, will be no slight relief. The endless disputes whether or not some fifty species of British brambles are true species will cease. Systematists will have only to decide (not that this will be easy) whether any form be sufficiently constant and distinct from other forms, to be capable of definition; and if definable, whether the differences be sufficiently important to deserve a specific name. This latter point will become a far more essential


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 than it is at present; for differences, however slight, between any two forms, if not blended by intermediate gradations, are looked at by most naturalists as sufficient to raise both forms to the rank of species. Hereafter we shall be compelled to acknowledge that the only distinction between species and well-marked varieties is, that the latter are known, or believed, to be connected at the present day by intermediate gradations, whereas species were formerly thus connected. Hence, without quite rejecting the consideration of the present existence of intermediate gradations between any two forms, we shall be led to weigh more carefully and to value higher the actual amount of difference between them. It is quite possible that forms now generally acknowledged to be merely varieties may hereafter be thought worthy of specific names, as with the primrose and cowslip; and in this case scientific and common language will come into accordance. In short, we shall have to treat species in the same manner as those naturalists treat genera, who admit that genera are merely artificial combinations made for convenience. This may not be a cheering prospect; but we shall at least be freed from the vain search for the undiscovered and undiscoverable essence of the term species.

The other and more general departments of natural history will rise greatly in interest. The terms used by naturalists of affinity, relationship, community of type, paternity, morphology, adaptive characters, rudimentary and aborted organs, &c., will cease to be metaphorical, and will have a plain signification. When we no longer look at an organic being as a savage looks at a ship, as at something wholly beyond his comprehension; when we regard every production of nature as one which has had a history; when we contemplate every complex structure


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 and instinct as the summing up of many contrivances, each useful to the possessor, nearly in the same way as when we look at any great mechanical invention as the summing up of the labour, the experience, the reason, and even the blunders of numerous workmen; when we thus view each organic being, how far more interesting, I speak from experience, will the study of natural history become!

A grand and almost untrodden field of inquiry will be opened, on the causes and laws of variation, on correlation of growth, on the effects of use and disuse, on the direct action of external conditions, and so forth. The study of domestic productions will rise immensely in value. A new variety raised by man will be a far more important and interesting subject for study than one more species added to the infinitude of already recorded species. Our classifications will come to be, as far as they can be so made, genealogies; and will then truly give what may be called the plan of creation. The rules for classifying will no doubt become simpler when we have a definite object in view. We possess no pedigrees or armorial bearings; and we have to discover and trace the many diverging lines of descent in our natural genealogies, by characters of any kind which have long been inherited. Rudimentary organs will speak infallibly with respect to the nature of long-lost structures. Species and groups of species, which are called aberrant, and which may fancifully be called living fossils, will aid us in forming a picture of the ancient forms of life. Embryology will reveal to us the structure, in some degree obscured, of the prototypes of each great class.

When we can feel assured that all the individuals of the same species, and all the closely allied species of most genera, have within a not very remote period


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 from one parent, and have migrated from some one birthplace; and when we better know the many means of migration, then, by the light which geology now throws, and will continue to throw, on former changes of climate and of the level of the land, we shall surely be enabled to trace in an admirable manner the former migrations of the inhabitants of the whole world. Even at present, by comparing the differences of the inhabitants of the sea on the opposite sides of a continent, and the nature of the various inhabitants of that continent in relation to their apparent means of immigration, some light can be thrown on ancient geography.

The noble science of Geology loses glory from the extreme imperfection of the record. The crust of the earth with its embedded remains must not be looked at as a well-filled museum, but as a poor collection made at hazard and at rare intervals. The accumulation of each great fossiliferous formation will be recognised as having depended on an unusual concurrence of circumstances, and the blank intervals between the successive stages as having been of vast duration. But we shall be able to gauge with some security the duration of these intervals by a comparison of the preceding and succeeding organic forms. We must be cautious in attempting to correlate as strictly contemporaneous two formations, which include few identical species, by the general succession of their forms of life. As species are produced and exterminated by slowly acting and still existing causes, and not by miraculous acts of creation and by catastrophes; and as the most important of all causes of organic change is one which is almost independent of altered and perhaps suddenly altered physical conditions, namely, the mutual relation of organism to organism,—the improvement of one being entailing the improvement or the extermination of


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 others; it follows, that the amount of organic change in the fossils of consecutive formations probably serves as a fair measure of the lapse of actual time. A number of species, however, keeping in a body might remain for a long period unchanged, whilst within this same period, several of these species, by migrating into new countries and coming into competition with foreign associates, might become modified; so that we must not overrate the accuracy of organic change as a measure of time. During early periods of the earth's history, when the forms of life were probably fewer and simpler, the rate of change was probably slower; and at the first dawn of life, when very few forms of the simplest structure existed, the rate of change may have been slow in an extreme degree. The whole history of the world, as at present known, although of a length quite incomprehensible by us, will hereafter be recognised as a mere fragment of time, compared with the ages which have elapsed since the first creature, the progenitor of innumerable extinct and living descendants, was created.

In the distant future I see open fields for far more important researches. Psychology will be based on a new foundation, that of the necessary acquirement of each mental power and capacity by gradation. Light will be thrown on the origin of man and his history.

Authors of the highest eminence seem to be fully satisfied with the view that each species has been independently created. To my mind it accords better with what we know of the laws impressed on matter by the Creator, that the production and extinction of the past and present inhabitants of the world should have been due to secondary causes, like those determining the birth and death of the individual. When I view all beings not as special creations, but as the lineal descendants of some few beings which lived long before the


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 first bed of the Silurian system was deposited, they seem to me to become ennobled. Judging from the past, we may safely infer that not one living species will transmit its unaltered likeness to a distant futurity. And of the species now living very few will transmit progeny of any kind to a far distant futurity; for the manner in which all organic beings are grouped, shows that the greater number of species of each genus, and all the species of many genera, have left no descendants, but have become utterly extinct. We can so far take a prophetic glance into futurity as to foretel that it will be the common and widely-spread species, belonging to the larger and dominant groups, which will ultimately prevail and procreate new and dominant species. As all the living forms of life are the lineal descendants of those which lived long before the Silurian epoch, we may feel certain that the ordinary succession by generation has never once been broken, and that no cataclysm has desolated the whole world. Hence we may look with some confidence to a secure future of equally inappreciable length. And as natural selection works solely by and for the good of each being, all corporeal and mental endowments will tend to progress towards perfection.

It is interesting to contemplate an entangled bank, clothed with many plants of many kinds, with birds singing on the bushes, with various insects flitting about, and with worms crawling through the damp earth, and to reflect that these elaborately constructed forms, so different from each other, and dependent on each other in so complex a manner, have all been produced by laws acting around us. These laws, taken in the largest sense, being Growth with Reproduction; Inheritance which is almost implied by reproduction; Variability from the indirect and direct action of the external


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490 of life, and from use and disuse; a Ratio of Increase so high as to lead to a Struggle for Life, and as a consequence to Natural Selection, entailing Divergence of Character and the Extinction of less-improved forms. Thus, from the war of nature, from famine and death, the most exalted object which we are capable of conceiving, namely, the production of the higher animals, directly follows. There is grandeur in this view of life, with its several powers, having been originally breathed into a few forms or into one; and that, whilst this planet has gone cycling on according to the fixed law of gravity, from so simple a beginning endless forms most beautiful and most wonderful have been, and are being, evolved.


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 Rh For this purpose I have chosen many letters and mere notes, illustrating his domestic and gossipy moods, for that element was in his mixed nature, inherited from the lively maternal side, and even the colloquial vulgarity (using the word in its strict sense of "popular speech") that he sometimes allowed himself. In his last years he revolted a little at this turn of his thoughts, and, as Channing relates, "rubbed out the more humorous parts of his essays, originally a relief to their sterner features, saying, 'I cannot bear the levity I find; to which Channing replied that he ought to spare it, even to the puns, in which he abounded almost as much as Shakespeare. His friend was right,—the obvious incongruity was as natural to Thoreau as the grace and French elegance of his best sentences. Thus I have not rejected the common and trivial in these letters; being well assured that what the increasing number of Thoreau's readers desire is to see this piquant original just as he was,—not arrayed in the paradoxical cloak of the Stoic sage, nor sitting complacent in the cynic earthenware cave of Diogenes, and bidding Alexander stand out of his sunshine.


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Rh These eyes, fresh-opened, spied the far-off Sea, That like a silent godfather did stand, Nor uttered one explaining word to me, While introducing straight godmother Land. And yonder still stretches that silent Main, With many glancing ships besprinkled o'er: And earnest still I gaze and gaze again Upon the selfsame waves and friendly shore. Infinite work my hands find there to do, Gathering the relicts which the waves upcast: Each storm doth scour the sea for something new,— And every time the strangest is the last. My neighbors sometimes come with lumbering carts, As if they wished my pleasant toil to share; But straight they go again to distant marts,— For only weeds and ballast are their care.

"Only weeds and ballast?" that is exactly what Thoreau's neighbors would have said he was gathering, for the most of his days; yet now he is seen to have collected something more durable and precious than they with their implements and market-carts. If they viewed him with a kind of scorn and pity, it must be said that he returned the affront; only time seems to have sided with the poet in the controversy that he maintained against his busy age.


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 viii or attractive. "In his own home," says Ellery Channing, who knew him more inwardly than any other, "he was one of those characters who may be called household treasures; always on the spot, with skillful eye and hand, to raise the best melons in the garden, plant the orchard with choicest trees, or act as extempore mechanic; fond of the pets, his sister's flowers, or sacred Tabby; kittens were his favorites,—he would play with them by the half-hour. No whim or coldness, no absorption of his time by public or private business, deprived those to whom he belonged of his kindness and affection. He did the duties that lay nearest, and satisfied those in his immediate circle; and whatever the impressions from the theoretical part of his writings, when the matter is probed to the bottom, good sense and good feeling will be detected in it." This is preëminently true; and the affectionate conviction of this made his sister Sophia dissatisfied with Emerson's rule of selection among the letters. This she confided to me, and this determined me, should occasion offer, to give the world some day a fuller and more familiar view of our friend.


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x He did those acts also; but they were not the whole man. He was far more poet than cynic or stoic; he had the proud humility of those sects, but still more largely that unconscious pride which comes to the poet when he sees that his pursuits are those of the few and not of the multitude. This perception came early to Thoreau, and was expressed in some unpublished verses dating from his long, solitary rambles, by night and day, on the seashore at Staten Island, where he first learned the sombre magnificence of Ocean. He feigns himself the son of what might well be one of Homer's fishermen, or the shipwrecked seaman of Lucretius,—

and then goes on thus with his parable:—

Within a humble cot that looks to sea Daily I breathe this curious warm life, Beneath a friendly haven's sheltering lea My noiseless day with mystery still is rife. 'T is here, they say, my simple life began,— And easy credence to the tale I lend, For well I know 't is here I am a man,— But who will simply tell me of the end?


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 xii Superiority,—moral elevation, without peevishness or condescension,—this was Thoreau's distinguishing quality. He softened it with humor, and sometimes sharpened it with indignation; but he directed his satire and his censure as often against himself as against mankind; men he truly loved,—if they would not obstruct his humble and strictly-chosen path. The letters here printed show this, if I mistake not,—and the many other epistles of his, still uncollected, would hardly vary the picture he has sketched of himself, though they would add new facts. Those most to be sought for are his replies to the generous letters of his one English correspondent.

The profile-portrait engraved for this volume is less known than it should be,—for it alone of the four likenesses extant shows the aquiline features as his comrades of the wood and mountain saw them,—not weakened by any effort to bring him to the standard of other men in garb or expression. The artist, Mr. Walton Ricketson, knew and admired him. F. B. S. 1em


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8 hay. At the same time the raising of stock has been encouraged as much as possible. There are now owned by reservation Indians 199,700 horses, 2,870 mules, 68,891 head of cattle, 32,537 swine, and 863,525 sheep, the latter principally by the Navajoes. The five civilized tribes in the Indian Territory are reported to have 45,500 horses, 5,500 mules, 272,000 head of cattle, 190,000 swine, and 32,400 sheep. Provision has been made for an additional distribution of 11,300 head of stock cattle among the uncivilized tribes, preference being given to those individual Indians who have taken the best care of their stock heretofore. The complaints frequently made in former times that the Indians would slaughter their cows and eat them has ceased almost entirely. On the contrary, it is found that they are beginning to take excellent care of their domestic animals, and to be proud of the increase of their stock. Many have commenced raising swine and poultry, and it is thought expedient to encourage such beginnings in every possible way. The cultivation of garden vegetables among them is also rapidly spreading. Preparations have been made to increase the area of cultivated soil very largely next year. Considerable quantities of agricultural tools and implements have been distributed, and the demand is constantly growing.

For the first time this year the uncivilized tribes in the Indian Territory were induced to take some part in the agricultural and industrial fair at Muskogee. Several of them sent delegations, and although their contributions were at first very limited it is expected that the repetition of the experiment will stimulate a spirit of rivalry among them. Another agricultural fair was held by the Chippewas on the White Earth reservation in Minnesota, where the contributions of agricultural products, of stock, and articles of domestic industry came exclusively from Indians, and where Indians acted as managers and judges. According to all accounts, the exhibition was surprisingly successful. Some of the Sioux chiefs in Southern Dakota on the occasion of my visit a few months ago expressed a desire to have an agricultural fair on their reservation next year, which might seem somewhat premature, as they are just starting in civilized pursuits; but their ambition in this respect is laudable and deserves every encouragement.

The building of houses to supersede the traditional wigwams and to cultivate the love of, and attachment to permanent and comfortable homes is pushed with energy wherever it is possible. Several of the more advanced tribes, not speaking of the civilized tribes of the Indian Territory, are all completely housed or nearly so, and other tribes will be in the same condition in less than a year.

INDIAN FREIGHTING AND MECHANICAL PURSUITS.

Agriculture and herding, however, are not the only fields on which Indian labor has been introduced. In my last annual report I mentioned that late in the autumn of 1878 the conveyance of supplies from the Missouri


text: Familiar Letters of Henry David Thoreau

title: Familiar Letters of Henry David Thoreau


text: Familiar Letters of Henry David Thoreau/Introduction


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Author:James McGranahan

Hymn tune

 * "The Crowning Day"
 * "I Know Whom I Have Believed", also called "El Nathan"
 * "I'll Stand By You"
 * "Sometime We'll Understand"
 * musical setting for "There Shall Be Showers of Blessing"

title: Author:James McGranahan


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Portal:Goncourt brothers

Author pages

 * Edmond de Goncourt (1822–96)
 * Jules de Goncourt (1830–70)

title: Portal:Goncourt brothers


text: Index:Deux Mémoires de Henri Poincaré.djvu


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by H. A. Lorentz

The following pages cannot at all give a complete idea of what theoretical physics owes to Poincaré. I would have been happy to pay homage to his memory by presenting to the reader such a general picture, but I moved back in front of this task, that cannot be done with dignity without long and serious studies for which there was no time for me. I limited thus myself to two papers, that on the Dynamics of the electron, written in 1905 and published the following year in Rendiconti del Circolo Matematico di Palermo, and the study on the quantum theory which appeared in the Journal de Physique at the beginning of 1912.

To fully appreciate the first of this works, I will have to enter in some details on the ideas whose development led to the principle of relativity. Thus let us speak a little about the part that I contributed to this development, I must say first that I have found a valuable encouragement in the benevolent interest that Poincaré constantly took with my studies. Moreover, we will see soon by which degree he surpassed me.

It is known that Fresnel had based the explanation of the astronomical aberration on the assumption of a motionless ether that the celestial bodies would cross without entraining it. We also know his famous theorem, a necessary complement of this fundamental assumption, of the partial entrainment of light waves by moving matter. An transparent body animated by translation will communicate to the rays only a fraction of its own speed, a fraction which


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 is determined by the "coefficient of Fresnel" $$1\tfrac{1}{n^ {2}}$$, in which $$N$$ is the index of refraction of the medium.

When, thanks to the work of Clerk Maxwell, our views on the nature of light had been profoundly changed, it was natural to try a deduction of this coefficient based on the principles of the electromagnetic theory. That's the goal I set myself, which could be achieved without too much difficulty in the theory of electrons.

The majority of the phenomena which are connected to aberration, and in particular the absence of an influence of the earth's motion in all the experiments where the collective system of devices is at rest in respect to our planet, could now be explained in a satisfactory way. It was only necessary to make the restriction, that the considered effects were of first order of magnitude compared to the speed of the Earth divided by the speed of light, terms of the second order have been neglected in calculations.

However, in 1881 Mr. Michelson succeeded to interfere two light rays, that were departed from a single point and came back after following rectilinear and mutually perpendicular paths of equal length. He found that the observed phenomena are again insensitive to the earth's motion; the interference fringes preserved the same positions, whatever were the directions of the arms of the device.

This time it was indeed an effect of the second order and it was easy to see that the hypothesis of the stationary aether alone is not sufficient for the explanation of the negative result. I was obliged to make a new assumption which consists in admitting, that the translation of a body through the aether produces a slight contraction of the body in the direction of motion. This assumption was indeed the only possibility; it had also been imagined by Fitzgerald and it found the approval of Poincaré, who however did not conceal the lack of satisfaction that the theories gave him in which one multiplies special assumptions invented for particular phenomena. This criticism was for me an additional reason to seek a general theory, in which the same principles would lead to the explanation of the experiment of Mr. Michelson and all those that were undertaken after him to discover effects of the second order. In the theory that I proposed, the absence of phenomena due to the collective motion of a system should be demonstrated for any value of speed less than that of light.

The method to be followed was indeed indicated. It was obviously necessary to demonstrate that


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 the phenomena which take place in a material system can be represented by equations of the same form, the system may be at rest or being animated by a uniform translatory motion, and this equality of form has to be obtained using a suitable substitution of new variables. It was a question of finding transformation formulas, suitable for the independent variables, the coordinates x, y, z and time t, as well as for the various physical magnitudes, speeds, forces, etc, and by showing the invariance of the equations for these transformations.

The formulas that I established for coordinates and time can be put as

where ε, k, l are constants which are, however, reduced to one. We see immediately that the origin of the new coordinates ($$x'=0$$) is

so the point moves in the system x, y, z, t with speed -ε in the direction of the x-axis. The coefficient k is defined by

and ε is a function of l that has the value 1 for ε = 0. I initially left it undetermined, but I found in the course of my calculations, that to obtain the invariance (that I had in mind) we must put l = 1.

These were the considerations published by me in 1904 which gave place to Poincaré to write his paper on the dynamics of the electron, in which he attached my name to the transformation to which I will come to speak. I must notice on this subject that the same transformation was already present in an article of Mr. Voigt published in 1887, and that I did not draw from this artifice all the possible parts. Indeed, for some of the physical quantities which enter the formulas, I did not indicate the transformation which suits best. That was done by Poincaré and then by Mr. Einstein and Minkowski.

To find the "transformations of relativity", as I will call them now, it is sufficient in some cases to describe the phenomena in the


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 system $$x',y',z',t' $$ exactly in the same way as we do it in system x, y, z, t. Let us consider, for example, the motion of a point. If, in time dt the coordinates x, y, z undergo the changes dx, dy, dz, then we have for the velocity components

$$\xi=\frac{dx}{dt},\ \eta=\frac{dy}{dt},\ \zeta=\frac{dz}{dt}$$

However, by these relations the variations dx, dy, dz, dt contain the changes

of the new variables. It is natural to define the velocity components in the new system by the formulas

which gives us

To have another example, we can imagine a great number of mobile points whose velocities are continuous functions of the coordinates and time. Let dτ an element of volume located at point x, y, z and let us fix the attention to the points of the system which are in this element at one given moment t. Let $$t'_0$$ be the special value of $$t'$$ which corresponds to x, y, z, t by the equations (1), and consider for the various points the values of $$x', y', z'$$ which correspond to the given value $$t'=t'_0$$; in other words, let us consider the positions of the points in the new system, all taken for the same value of "time" $$t'$$. One might ask after the extension of the element $$d\tau'$$ of space $$x', y', z'$$, in which are at this moment $$t'_0$$ the selected points which are in dτ at the time t. A simple calculation, which I omit here, led to the relation

Finally, let us suppose that the points in question carry equal electric charges, and admit that in two systems x, y, z, t and $$x', y', z', t'$$ we attribute the same numerical values to these charges. If the points are sufficiently close to each other, we obtain a continuous distribution of electricity and it is clear that the charge contained in the element dτ


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 at the moment t is equal to that which is in $$d\tau'$$ at the moment $$t'$$. Consequently, if ρ and $$\rho'$$ are the densities of these charges,

and, by virtue of (5)

By this formula, combined with (4), we deduce again

These are the transformation formulas for the convection current.

For other physical quantities such as electric and magnetic forces, it is necessary to follow a less direct method; we will seek, perhaps with a little groping, the formulas of transformation suitable to ensure the invariance of the electromagnetic equations.

The formulas (4) and (7) are not in my memoir of 1904. Because I had not thought of the direct way which led there, and because I had the idea that there is an essential difference between systems x, y, z, t and $$x', y', z', t'$$. In one we use - such was my thought - coordinate axes which have a fixed position in the aether and which we can call "true" time; in the other system, on the contrary, we would deal with simple auxiliary quantities whose introduction is only a mathematical artifice. In particular, the variable $$t'$$ could not be called "time" in the same way as the variable t.

In this order of ideas I did not think of describing the phenomena in the system $$x', y', z', t',$$ exactly in the same way as in system x, y, z, t, and I did not define by the equations (3) and (7) the quantities ξ', η', ζ', ρ' which will correspond to ξ, η, ζ, ρ. It is rather by groping that I arrived at my formulas of transformation which, with our current notation, take the form

and that I wanted to choose, so as to obtain in the new system the simplest equations. Later, I could see in the paper of Poincaré that when proceeding more systematically I could have reached an even greater


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 simplification. Not having noticed it, I did not succeed in obtaining the exact invariance of the equations; my formulas remained encumbered with certain terms which should have disappeared. These terms were too small to have an appreciable effect on the phenomena and I could thus explain the independence of the earth's motion that was revealed by observations, but I did not establish the principle of relativity as rigorously and universally true.

Poincaré, on the contrary, obtained a perfect invariance of the equations of electrodynamics, and he formulated the "postulate of relativity", terms which he was the first to employ. Indeed, stating from the point of view that I had missed, he found the formulas (4) and (7). Let us add that by correcting the imperfections of my work he never reproached me for them.

I can not explain here all the beautiful results obtained by Poincaré. Let us insist however on some points. Initially, he was not satisfied to show that the transformations of relativity leave intact the form of the electromagnetic equations. He explains the success of substitutions by noticing that these equations can be put in the form of the principle of least action and that the fundamental equation which expresses this principle, as well as the operations by which we deduce the field equations, are the same in systems x, y, z, t and $$x', y', z', t'$$.

In the second place, in accordance with the title of his paper, Poincaré particularly considers the way in which the deformation of a moving electron occurs, comparable with that of the arms of the device of Mr. Michelson, which is required by the postulate of relativity. Two different assumptions had been proposed on this subject. According to both an electron, presumably spherical in the state of rest, would change by a translation into an oblated ellipsoid of revolution, the axis of symmetry coincide with the direction of motion and the ratio of this axis to the diameter of the equator being given by $$\sqrt{1-v^{2}},$$, if v is the velocity. But the assumptions differed between them with regard to the length of the axes and consequently the volume of the electron. While I had been led to admit that the radius of the equator remains equal to that of the original sphere, Mr. Bucherer and Mr. Langevin rather wanted to assign a constant size with volume. The first assumption corresponds to l = 1, the second with $$kl^3 =1$$. Let us immediately add that the first value is the only one which is compatible with the postulate of relativity.


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 If one wants to realize the persistence and the balance of an electron while making use of the ordinary notions of mechanics, it is obviously not sufficient to consider the electrodynamic actions. The particle - that we consider here as a sphere carrying a surface charge - would immediately explode because of the mutual repulsions or, which is to same, of the stresses of Maxwell exerted on its surface. Therefore another concept should also be introduced, and Poincaré distinguishes at this place between the "bindings" and the "supplementary forces". He initially supposed that there is only the connection represented by the equation

$$r = b\theta^m$$

r is the semi-axis of the electron, rθ its equatorial radius, b and m variables that remain constant when r and θ (or one of these quantities) vary with the translation speed v. This granted, we know for any value of v the dimensions of the electron - because we know that $$\theta=\left(1-v^{2}\right)^{-\frac{1}{2}}$$ - and by the ordinary formulas of electromagnetic field, the energy, momentum and the Lagrange function can be calculated. Between these values, considered as functions of v, there must be well known relations. Poincaré shows that they are verified only for $$m=-\tfrac{2}{3}$$, which brings us back to the constancy of volume, that is to say, the hypothesis of Mr. Bucherer and Langevin. But we know already that it is not this hypothesis, but only that of a constant equatorial radius, which is in agreement with the postulate of relativity. It is thus necessary to have recourse to additional forces.

By supposing that they depend on a potential of the form $$Ar^\alpha \theta^\beta$$, where A, α and β are constants, Poincaré finds that the constancy of the equatorial radius requires α = 3, β = 2, i.e. the potential in question must be proportional to volume. It results from it that the sought supplementary forces are equivalent to a pressure or a normal tension exerted on the surface and whose magnitude per unit of area remains constant, whatever the speed of translation. It is immediately seen that only a tension directed towards the interior is appropriate; we will determine the magnitude by the condition of an electron at rest and which has consequently the shape of a sphere, and it must be in equilibrium with the electrostatic repulsions. So when the particle is set into motion, the stress of Poincaré is united with the electrodynamic actions,


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 and will inevitably produce the oblateness which is required by the principle of relativity.

After having found his supplementary force, Poincaré showed that the transformations of relativity do not change the form of the terms which it represents; thus he showed that arbitrary motions of a system of electrons can take place in the completely same manner in system x, y, z, t and in the system $$x', y', z', t'$$.

I already spoke about the necessity for posing l = 1 (constancy of the equatorial radius of the electron). I will not repeat here the demonstration given by Poincaré and I will only say that he showed the mathematical origin of this condition. One can consider all the transformations which are represented by formulas (1), with different values for speed -ε, and the corresponding values of k and l, this last coefficient has to be regarded as a function of ε; we can add to it other similar transformations which we deduce from (1) by changing the directions of the axes, and finally by arbitrary rotations. The postulate of relativity requires that all these transformations form a group and that is only possible if l has the constant value 1.

The "group of relativity" obtained, consists of linear substitutions which do not affect the quadratic form

$$x^2 + y^2 + z^2 - t^2$$

The paper ends with the application of the postulate of relativity on the phenomena of gravitation. Here, it is the question of finding the rule which determines the propagation of it, and the formulas which express the components of the force according to the coordinates and the speed, as well as of the attracted body as of the attracting body. By considering these questions, Poincaré starts by seeking the invariants of the group of relativity; indeed, it is clear that it must be possible to represent the phenomena by equations which contain only these invariants. However, the problem is undetermined. It is natural to admit that the propagation velocity is equal to that of light and that the variations of the law of Newton must be of second-order magnitude in respect to the velocities. But even with these restrictions, there is the choice between several assumptions, among which there are two that were especially indicated by Poincaré.

In this last part of the article one finds some new concepts which I must especially announce. Poincaré notices, for example, if


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 x, y, z and $$t\sqrt{-1}$$ are considered as the coordinates of a point in four-dimensional space, the transformations of relativity are reduced to rotations in this space. He also had the idea of adding to the three force-components X, Y, Z the magnitude

$$T = X\xi + Y\eta + Z\zeta\,$$

which is nothing but the work of the force per unit time and which we can (to some extent) regard as a fourth component. When we ask after the force that a body experiences per unit volume, the magnitudes X, Y, Z, T$$\sqrt{-1}$$ are affected by a transformation of relativity in the same way as the magnitudes x, y, z, t$$\sqrt{-1}$$.

I recall these ideas of Poincaré because they are similar to methods that Minkowski and other scientists have later used to facilitate mathematical operations that arise in the theory of relativity.

Let us pass now to the paper on the quantum theory. Towards the end of 1911 Poincaré had attended the meeting of the Council of Physics convened in Brussels by Mr. Solvay, in which we had especially dealt with the phenomena of the calorific radiation and the hypothesis of the elements or quanta of energy imagined by Mr. Planck to explain them. In the discussions, Poincaré had shown all the promptness and the penetration of his spirit and we had admired the facility with which he could enter the most difficult questions of Physics, even in those which were new for him. At the return to Paris, he did not cease dealing with the problem of which he felt the high importance. If the hypothesis of Mr. Planck were true, "the physical phenomena would cease obeying laws expressed by differential equations, and it would be, undoubtedly, the greatest and most profound revolution that natural philosophy suffered since Newton".

But are these new conceptions really inevitable and is there no way to arrive at the radiation law without introducing these discontinuities which are in direct opposition with the notions of traditional mechanics? Here is the question that Poincaré poses in his paper and to which he gives an answer that I will allow myself to briefly summarize.


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 Let us consider a system made up of n resonators of Planck and p molecules, n and p being very great numbers; let us suppose that all the resonators are equal between them and that it is the same for the molecules. Let us indicate by $$\xi_{1},\dots,\xi_{p}$$ the energies of the molecules and by $$\eta_{1},\dots,\eta_{n}$$ those of the resonators; each one of these variables will be able to take all the positive values.

Poincaré showed first that the probability so that the quantities of energy are between the limits $$\xi_{1}$$ and $$\xi_{1}+d\xi_{1},\dots,\xi_{p}$$, and $$\xi_{p}+d\xi_{p}$$, $$\eta_{1}$$ and $$\eta_{1}+d\eta_{1},\dots,\eta_{n} $$, $$\eta_{n}$$ and $$\eta_{n}+d\eta_{n}$$, can be represented by

$$\omega\left(\eta_{1}\right)\dots\omega\left(\eta_{n}\right)d\eta_{1}\dots d\eta_{n}d\xi_{1}\dots d\xi_{p}$$

where ω is a function for which we can make different hypotheses.

Once we know this function we can tell how much energy h will be distributed over the molecules and resonators. For this purpose, we can imagine a space of p + n dimensions, $$\xi_{1},\dots,\xi_{\rho},\eta_{1},\dots,\eta_{n}$$, the infinitely thin layer S, in which the total energy

$$\xi_{1}+\dots+\xi_{p}+\eta_{1}+\dots+\eta_{n}$$

lies between h and an infinitely close value h + dh. The three integrals will be calculated

$$\begin{array}{l} I=\int\omega\left(\eta_{1}\right)\dots\omega\left(\eta_{n}\right)d\eta_{1}\dots d\eta_{n}d\xi_{1}\dots d\xi_{p}\\ \\I'=\int x\omega\left(\eta_{1}\right)\dots\omega\left(\eta_{n}\right)d\eta_{1}\dots d\eta_{n}d\xi_{1}\dots d\xi_{p}\\ \\I''=\int(h-x)\omega\left(\eta_{1}\right)\dots\omega\left(\eta_{n}\right)d\eta_{1}\dots d\eta_{n}d\xi_{1}\dots d\xi_{p}\end{array}$$

$$\left(x=\eta_{1}+\dots+\eta_{n}\right)$$

extended to the layer S, and we have $$\tfrac{I'}{I}$$ for the energy that the resonators take, and $$\tfrac{I''}{I}$$ for that of all the molecules. Therefore, if Y is the mean energy of a resonator, and X is that of a molecule,

$$nYI=I',\ pXI=I''$$

To calculate the integral I, we may first give fixed values to variables $$\eta_{1},\dots,\eta_{n}$$ and consequently to their sum x, and extend the integration over ξ for all positive values of these variables, for which the sum $$\xi_{1}+\dots+\xi_{p}$$ is between h - x and h - x + dh. This gives us

$$\int d\xi_{1}\dots d\xi_{p}=\frac{1}{(p-1)!}(h-x)^{p-1}dh$$


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 Then we can calculate the integral

$$\int\omega\left(\eta_{1}\right)\dots\omega\left(\eta_{n}\right)d\eta_{1}\dots d\eta_{n}$$

extended to positive values of η such that $$\eta_{1}+\dots+\eta_{p}$$ lies between x and x + dx. Let

$$\varphi$$ is a function that depends on the function ω and we have

$$I=\frac{dh}{(p-1)!}\int_{0}^{h}(h-x)^{p-1}\varphi(x)dx$$

$$I'$$ and $$I$$ are calculated in the same manner, we only need to introduce under the sign of integration the factor x or the factor h - x''. Ultimately, we can write

where the factor C is the same in both cases. We do not have to deal with it because it is sufficient to determine the ratio of X to Y.

Now we obtain the Planck formula - which can be regarded as an expression of reality - if we make on the function ω the following hypothesis, which is consistent with quantum theory.

Let ε be the magnitude of the quantum of energy which is specific to the resonators considered, and denote by δ an infinitely small quantity. The function ω is zero, except in the intervals

$$k\epsilon < \eta < k\epsilon + \delta\,$$

and for each of these intervals the integral $$\int_{k\epsilon}^{k\epsilon+\delta}\omega\ d\eta$$ has the value 1.

These data are sufficient for determining the function $$\varphi$$ and the ratio $$\tfrac{Y}{X}$$ for which we find, as I said before, the value given


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 by Planck's theory. I did not stop at these calculations and I pass immediately to the principal question, whether the discontinuities that I just mentioned must necessarily be admitted.

I will reproduce the reasoning of Poincaré, but I will at first say that in the formulas that we will encounter, α indicates a complex variable of which the real part $$\alpha_r$$ is always positive. In the representation we will limit ourselves to the half of plane α characterized by $$\alpha_r>0$$, and in integrations in respect to α we will follow a straight line l perpendicular to the axis of real α, and prolonged indefinitely on the two sides. The values of the integrals will be independent of the length of the distance $$\alpha_r>0$$ of this line at the origin of α.

Poincaré introduced an auxiliary function that defines the equation

and demonstrated that the function ω and the derived function $$\varphi$$ can be be expressed by using Φ.

We obtain at first, by inverting (11)

For a similar formula for $$\varphi(x)$$ we notice that in equation (11) we can replace η by any of the variables $$\eta_{1},\dots,\eta_{n}$$. Multiplying the n equations which we obtained, we find

$$\left[\Phi(\alpha)\right]^{n}=\int_{0}^{\infty}\dots\int_{0}^{\infty}\omega\left(\eta_{1}\right)\dots\omega\left(\eta_{n}\right)e^{-\alpha x}d\eta_{1}\dots d\eta_{n}$$

or, by virtue of the formula (8)

$$\left[\Phi(\alpha)\right]^{n}=\int_{0}^{\infty}\varphi(x)^{-\alpha x}dx$$

and by inversion

$$\varphi(x)=\frac{1}{2\pi i}\int_{(L)}\left[\Phi(\alpha)\right]^{n}e^{\alpha x}d\alpha$$

The formulas (9) and (10) now become

$$\begin{array}{l} nY=\frac{C}{2i\pi}\int_{0}^{h}\int_{(L)}x(h-x)^{p-1}[\Phi(\alpha)]^{n}e^{\alpha x}dx\ d\alpha\\ \\pX=\frac{C}{2i\pi}\int_{0}^{h}\int_{(L)}(h-x)^{p}[\Phi(\alpha)]^{n}e^{\alpha x}dx\ d\alpha\end{array}$$