What is Darwinism? Part 3

_Professor Huxley._

The second witness as to the character of Mr. Darwin's theory is Professor Huxley. We have some hesitation in including the name of this distinguished naturalist among the advocates of Darwinism.[19] On the one hand, in his Essay on the Origin of Species, printed in the "Westminster Review," in 1860, and reprinted in his "Lay Sermons,"

etc., in 1870, he says: "There is no fault to be found with Mr. Darwin's method, but it is another thing whether he has fulfilled all the conditions imposed by that method. Is it satisfactorily proved that species may[20] be originated by selection? that none of the phenomena exhibited by species are inconsistent with the origin of species in this way? If these questions can be answered in the affirmative, Mr. Darwin's view steps out of the rank of hypotheses into that of theories; but so long as the evidence at present adduced falls short of enforcing that affirmative, so long, to our minds, the new doctrine must be content to remain among the former,--an extremely valuable, and in the highest degree probable, doctrine; indeed, the only extant hypothesis which is worth anything in a scientific point of view; but still a hypothesis, and not yet a theory of species. After much consideration," he adds, "and a.s.suredly with no bias against Mr. Darwin's views, it is our clear conviction that, as the evidence now stands, it is not absolutely proven that a group of animals, having all the characters exhibited by species in Nature, has ever been originated by selection, whether artificial or natural."[21]

Again, in his work on "Man's Place in Nature," he expresses himself much to the same effect: "A true physical cause is admitted to be such only on one condition, that it shall account for all the phenomena which come within the range of its operation. If it is inconsistent with any one phenomenon it must be rejected; if it fails to explain any one phenomenon it is so far to be suspected, though it may have a perfect right to provisional acceptance.... Our acceptance, therefore, of the Darwinian hypothesis must be provisional so long as one link in the chain of evidence is wanting; and so long as all the animals and plants certainly produced by selective breeding from a common stock are fertile, and their progeny are fertile one with another, that link will be wanting. For so long selective breeding will not be proved to be competent to all that is required if it produce natural species."[22] In immediate connection with the above pa.s.sage, there is another which throws a clear light on Professor Huxley's cosmical views. "The whole a.n.a.logy of natural operations furnish so complete and crushing an argument against the intervention of any but what are called secondary causes, in the production of all the phenomena of the universe; that, in view of the intimate relations of man and the rest of the living world, and between the forces exerted by the latter and all other forces, I can see no reason for doubting that all are coordinate terms of nature's great progression, from formless to formed, from the inorganic to the organic, from blind force to conscious intellect and will."[23]

Ought not this to settle the matter? Are we to give up the Bible and all our hopes for the sake of an hypothesis that all living things, including man, on the face of the earth, are descended from a primordial animalcule, by natural selection, when such a man as Huxley, who (as Voltaire said of the prophet Habbakuk) is _capable de tout_, says that it has not been proved that any one species has thus originated?

But on the other hand, while he honestly admits that Darwin's doctrine is a mere hypothesis and not a theory, he has nevertheless written at least three essays or reviews in its exposition and vindication. He is freely referred to on the continent of Europe, at least, as an ardent advocate of the doctrine; and he quotes without protest such designations of himself. At any rate, as he a.s.sures his readers that he has no bias against Mr. Darwin's views, as he has devoted much time and attention to the subject, and as he is one of the most prominent naturalists of the age, there can be no question as to his competency as a witness as to what Darwinism is.

His testimony that Mr. Darwin's doctrine excludes all teleology, or final causes, is explicit. In his review of the "Criticisms on the Origin of Species," he says, "that when he first read Mr. Darwin's book, that which struck him most forcibly was the conviction that teleology, as commonly understood, had received its death-blow at Mr. Darwin's hands. For the teleological argument runs thus: An organ is precisely fitted to perform a function or purpose; therefore, it was specially constructed to perform that function. In Paley's famous ill.u.s.tration, the adaptation of all the parts of a watch to the function or purpose of showing the time, is held to be evidence that the watch was specially contrived to that end; on the ground that the only cause we know of competent to produce such an effect as a watch which shall keep time, is a contriving intelligence adapting the means directly to that end."[24]

This, Mr. Huxley tells us, is precisely what Darwin denies with reference to the organs of plants and animals. The eye was not formed for the purpose of seeing, or the ear for hearing. It so happened that a nerve became sensitive to light; then in course of time, it happened that a transparent tissue came over it; and thus in "millions of years"

an eye, as we have seen above, happened to be formed. No such organ was ever intended or designed by G.o.d or man. "An apparatus," says Professor Huxley, "thoroughly adapted to a particular purpose, might be the result of a method of trial and error worked by unintelligent agents, as well as by the application of means appropriate to the end by an intelligent agent." "For the notion that every organism has been created as it is and launched straight at a purpose, Mr. Darwin subst.i.tutes the conception of something, which may fairly be termed a method of trial and error. Organisms vary incessantly; of these variations the few meet with surrounding conditions which suit them, and thrive; the many are unsuited, and become extinguished." "For the teleologist an organism exists, because it was made for the conditions in which it is found; for the Darwinian an organism exists, because, out of many of its kind, it is the only one which has been able to persist in the conditions in which it is found." "If we apprehend," Huxley further says, "the spirit of the 'Origin of Species' rightly, then, nothing can be more entirely and absolutely opposed to teleology, as it is commonly understood, than the Darwinian theory." (p. 303)

It has already been stated that Mr. Wallace does not apply the doctrine of evolution to man; neither does Mr. Mivart, a distinguished naturalist, who is a member of the Latin Church. The manner in which Professor Huxley speaks of these gentlemen shows how thoroughly, in his judgment, Mr. Darwin banishes G.o.d from his works: "Mr. Wallace and Mr.

Mivart are as stout evolutionists as Mr. Darwin himself; but Mr. Wallace denies that man can have been evolved from a lower animal by that process of natural selection, which he, with Mr. Darwin, holds to be sufficient for the evolution of all animals below man; while Mr. Mivart, admitting that natural selection has been one of the conditions of the animals below man, maintains that natural selection must, even in their case, have been supplemented by some other cause,--of the nature of which, unfortunately, he does not give us any idea. Thus Mr. Mivart is less of a Darwinian than Mr. Wallace, for he has faith in the power of natural selection. But he is more of an evolutionist than Mr. Wallace, because Mr. Wallace thinks it necessary to call in an intelligent agent, a sort of supernatural Sir John Sebright, to produce even the animal frame of man; while Mr. Mivart requires no Divine a.s.sistance till he comes to man's soul."[25]

In the "Academy" for October, 1869, there is a review by Professor Huxley of Dr. Haeckel's "Naturlische Schopfungsgeschichte," in which he says: "Professor Haeckel enlarges on the service which the 'Origin of Species' has done in favoring what he terms 'the causal or mechanical'

view of living nature as opposed to the 'teleological or vitalistic'

view. And no doubt it is quite true the doctrine of evolution is the most formidable of all the commoner and coa.r.s.er forms of teleology.

Perhaps the most remarkable service to the philosophy of Biology rendered by Mr. Darwin is the reconciliation of Teleology and Morphology, and the explanation of the facts of both which his view offers.

"The teleology which supposes that the eye, such as we see it in man or in the higher vertebrata, was made with the precise structure which it exhibits, to make the animal which possesses it to see, has undoubtedly received its death-blow. But it is necessary to remember that there is a higher teleology, which is not touched by the doctrine of evolution, but is actually based on the fundamental proposition of evolution. That proposition is, that the whole world, living and not living, is the result of the mutual interaction, according to definite laws, of forces possessed by the molecules of which the primitive nebulosity of the universe was composed. If this be true, it is no less certain that the existing world lay potentially in the cosmic vapor; and that a sufficient intelligence could, from a knowledge of the properties of that vapor, have predicted, say, the state of fauna of Great Britain in 1869, with as much certainty as one can say what will happen to the vapor of the breath on a cold winter's day." This is the doctrine of the self-evolution of the universe. We know not what may lie behind this in Mr. Huxley's mind; but we are very sure that there is not an idea in the above paragraph which Epicurus of old, and Buchner, Vogt, Haeckel, and other "Materialisten von Profession," would not cheerfully adopt. His distinction between a higher and lower teleology is of no account in this discussion. What is the teleology to which, he says, Mr. Darwin has given the death-blow, the extracts given above clearly show. The eye, Huxley says, was not made for the purpose of seeing, or the ear for the purpose of hearing. "According to teleology," he says, "each organism is like a rifle bullet fired straight at a mark; according to Darwin, organisms are like grapeshot, of which one hits something and the rest fall wide."[26]

FOOTNOTES:

[19] Mr. Huxley, if we may judge from what he says of himself, is somewhat liable to be misunderstood. He says he was fourteen years laboring to resist the charge of Positivism made against the cla.s.s of scientific men to which he belongs. He also tells us in his letter to Professor Tyndall, prefixed to his volume of _Lay Sermons and Addresses_, that the "Essay on the Physical Basis of Life," included in that volume, was intended as a protest, from the philosophical side, against what is commonly called Materialism. It turned out, however, that the public regarded it as an argument in favor of Materialism. This we think was a very natural, if not an unavoidable mistake, on the part of the public. For in that Essay, he says that Protoplasm, or the physical basis of life, "is a kind of matter common to all living beings, that the powers or faculties of all kinds of living matter, diverse as they may be in degree, are substantially of the same kind."

Protoplasm as far as examined contains the four elements,--carbon, hydrogen, oxygen, and nitrogen. These are lifeless bodies, "but when brought together under certain conditions, they give rise to the still more complex body Protoplasm; and this protoplasm exhibits the phenomena of life." There is no more reason, he teaches, for a.s.suming the existence of a mysterious something called vitality to account for vital phenomena, than there is for the a.s.sumption of something called Aquasity to account for the phenomena of water. Life is said to be "the product of a certain disposition of material molecules." The matter of life is "composed of ordinary matter, differing from it only in the manner in which its atoms are aggregated. I take it," he says, "to be demonstrable that it is utterly impossible to prove that anything whatever may not be the effect of a material and necessary cause, and that human logic is equally incompetent to prove that any act is really spontaneous. A really spontaneous act is one, which, by the a.s.sumption, has no cause; and the attempt to prove such a negative as this, is on the face of the matter absurd. And while it is thus a philosophical impossibility to demonstrate that any given phenomenon is not the effect of a material cause, any one who is acquainted with the history of science will admit that its progress has, in all ages, meant, and now more than ever means, the extension of what we call matter and causation, and the concomitant gradual banishment from all regions of human thought of what we call spirit and spontaneity."

[20] It cannot escape the attention of any one that Mr. Darwin, Mr.

Wallace, Professor Huxley, and all the other advocates or defenders of Darwinism, do not pretend to prove anything more than that species _may_ be originated by selection, not that there is no other satisfactory account of their origin. Mr. Darwin admits that referring them to the intention and efficiency of G.o.d, accounts for everything, but, he says, that is not science.

[21] _Lay Sermons, Addresses, and Reviews_. By Thomas Henry Huxley, LL.

D., F. R. S. London, 1870, p. 323.

[22] _Evidence of Man's Place in Nature_. London, 1864, p. 107.

[23] Since writing the above paragraph our eye fell on the following note on the 89th page of the Duke of Argyle's _Reign of Law_, which it gives us pleasure to quote. It seems that a writer in the _Spectator_ had charged Professor Huxley with Atheism. In the number of that paper for February 10, 1866, the Professor replies: "I do not know that I care very much about popular odium, so there is no great merit in saying that if I really saw fit to deny the existence of a G.o.d I should certainly do so, for the sake of my own intellectual freedom, and be the honest atheist you are pleased to say I am. As it happens, however, I cannot take this position with honesty, inasmuch as it is, and always has been, a favorite tenet, that Atheism is as absurd, logically speaking, as Polytheism." In the same paper he says, "The denying the possibility of miracles seems to me quite as unjustifiable as speculative Atheism." How this can be reconciled with the pa.s.sages quoted above, we are unable to see.

[24] _Lay Sermons_, etc., p. 330.

[25] _Contemporary Review_, vol. xviii. 1871, p. 444. In this same article Mr. Huxley says: "Elijah's great question, Will ye serve G.o.d or Baal? Choose ye, is uttered audibly enough in the ears of every one of us as we come to manhood. Let every man who tries to answer it seriously ask himself whether he can be satisfied with the Baal of authority, and with all the good things his worshippers are promised in this world and the next. If he can, let him, if he be so inclined, amuse himself with such scientific implements as authority tells him are safe and will not cut his fingers; but let him not imagine that he is, or can be, both a true son of the Church and a loyal soldier of science." "And, on the other hand, if the blind acceptance of authority appear to him in its true colors, as mere private judgment _in excelsis_, and if he have courage to stand alone face to face with the abyss of the Eternal and Unknowable, let him be content, once for all, not only to renounce the good things promised by 'Infallibility,' but even to bear the bad things which it prophesies; content to follow reason and fact in singleness and honesty of purpose, wherever they may lead, in the sure faith that a h.e.l.l of honest men will to him be more endurable than a paradise full of angelic shams." There can be no doubt that the Apostle Paul believed in the infallibility of the Scriptures. Imagine Professor Huxley calling St. Paul to his face, a sham! What are all the Huxleys who have ever lived or ever can live, to that one Paul in power for good over human thought, character, and destiny!

Professor Huxley goes on in the next paragraph to say: "Mr. Mivart a.s.serts that 'without belief in a personal G.o.d there is no religion worthy of the name.' This is a matter of opinion. But it may be a.s.serted, with less reason to fear contradiction, that the worship of a personal G.o.d, who, on Mr. Mivart's hypothesis, must have used words studiously calculated to deceive his creatures and worshippers, is 'no religion worthy of the name.' 'Incredibile est, Deum illis verbis ad populum fuisse locutum quibis deciperetur,' is a verdict in which for once Jesuit casuistry concurs with the healthy moral sense of all mankind." (p. 458). Mr. Huxley calls believers in the Scriptures, and (apparently) believers in a personal G.o.d, bigots, old ladies of both s.e.xes, bibliolators, fools, etc., etc.

[26] _Lay Sermons_, etc. p. 331.

_Buchner._

Dr. Louis Buchner, president of the medical a.s.sociation of Hessen-Darmstadt, etc., etc., is not only a man of science but a popular writer. Perhaps no book of its cla.s.s, in our day, has been so widely circulated as his volume on "Kraft und Stoff," Matter and Force. It has been translated into all the languages of Europe. He holds that matter and force are inseparable; there cannot be the one without the other; both are eternal and imperishable; neither can be either increased or diminished; life originated spontaneously by the combination of molecules of matter under favorable conditions; all the phenomena of the universe, inorganic and organic, whether physical, vital, or mental, are due to matter and its forces. Consequently there is no G.o.d, no creation, no mind distinct from matter, no conscious existence of man after death.

All this is a.s.serted in the most explicit terms. Dr. Buchner has published a work on Darwinism in two volumes. Darwin's theory, he says, "is the most thoroughly naturalistic that can be imagined, and far more atheistic than that of his decried predecessor Lamarck, who admitted at least a general law of progress and development; whereas, according to Darwin, the whole development is due to the gradual summation of innumerable minute and accidental operations."[27]

FOOTNOTE:

[27] _Sechs Vorlesungen uber die Darwinische Theorie_. Von Ludwig Buchner. Zweite Auflage, Leipzig, 1848, vol. i. p. 125.

_Carl Vogt._

In his preface to his work on the "Descent of Man," Mr. Darwin quotes this author as a high authority. We see him elsewhere referred to as one of the first physiologists of Germany. Vogt devotes the concluding lecture of the second volume of his work on Man, to the consideration of Darwinism. He expresses his opinion of it, after high commendation, in the following terms. He says that it cannot be doubted that Darwin's "theory turns the Creator--and his occasional intervention in the revolutions of the earth and in the production of species--without any hesitation out of doors, inasmuch as it does not leave the smallest room for the agency of such a Being. The first living germ being granted, out of it the creation develops itself progressively by natural selection, through all the geological periods of our planets, by the simple law of descent--no new species arises by creation and none perishes by divine annihilation--the natural course of things, the process of evolution of all organisms and of the earth itself, is of itself sufficient for the production of all we see. Thus Man is not a special creation, produced in a different way, and distinct from other animals, endowed with an individual soul and animated by the breath of G.o.d; on the contrary, Man is only the highest product of the progressive evolution of animal life springing from the group of apes next below him."[28]

After this no one can be surprised to hear him say, that "the pulpits of the orthodox, the confessionals of the priests, the platforms of the interior missions, the presidential chairs of the consistories, resound with protestations against the a.s.saults made by Materialism and Darwinism against the very foundations of society." (p. 286) This he calls "Das Wehgeschrei der Moralisten" (the Wail of the Moralists). The designation Moralists is a felicitous one, as applied to the opponents of Vogt and his a.s.sociates. It distinguishes them as men who have not lost their moral sense; who refuse to limit their faith to what can be proved by the five senses; who bow to the authority of the law written by the finger of G.o.d, on the hearts of men, which neither sophistry nor wickedness can effectually erase. All Vogt thinks it necessary to reply to these Moralists is, "La.s.st sie bellen, bis sie ausgebellt haben" (Let them bark till they are tired). "Ende."

FOOTNOTE:

[28] _Vorlesungen uber den Menschen, seine Stellung in der Schoepfung und in der Geschichte der Erde_. Von Carl Vogt. Giessen, 1863, vol. ii.

p. 260.

_Haeckel._

Dr. Ernst Haeckel, Professor in the University of Jena, is said to stand at the head of the living naturalists of Germany. His work on "Natural History of Creation" contains a course of lectures delivered to the professors, students, and citizens of Jena. It is, therefore, somewhat popular in its character. The ability of the writer is manifest on every page. The distinctness of his perceptions, precision of language, perspicuity of style, and the strength of his convictions, give the impression of a man fully master of his subject, who has thought himself through, and is perfectly satisfied with the conclusions at which he has arrived. At the same time it is the impression of a man who is developed only on one side; who never looks within; who takes no cognizance of the wonders revealed in consciousness; to whom the intuitions of reason and of the conscience, the sense of dependence on a will higher than our own--the sense of obligation and responsibility are of no account,--in short a man to whom the image of G.o.d enstamped on the soul of man is invisible. This being the case, he that is least in the kingdom of heaven is greater than he.

Haeckel admits that the t.i.tle of his book, "Natural Creation," _i. e._ creation by natural laws, is a contradiction. He distinguishes, however, between the creation of substance and the creation of form. Of the former he says science knows nothing. To the scientist matter is eternal. If any one chooses to a.s.sume that it was created by an extramundane power, Haeckel says he will not object. But that is a matter of faith; and "where faith begins, science ends." The very reverse of this is true. Science must begin with faith. It cannot take a single step without it. How does Haeckel know that his senses do not deceive him? How does he know that he can trust to the operations of his intellect? How does he know that things are as they appear? How does he know that the universe is not a great phantasmagoria, as so many men have regarded it, and man the mere sport of chimeras? He must believe in the laws of belief impressed on his nature. Knowledge implies a mind that knows, and confidence in the act of knowing implies belief in the laws of mind. "An inductive science of nature," says President Porter, "presupposes a science of induction, and a science of induction presupposes a science of man."[29] Haeckel, however, says faith is the mere product of the poetic imagination; science, of the understanding; if its conclusions come into conflict with the creations of the imagination, the latter, of course, must give way.[30]

He says, there have ever been two conflicting theories of the universe: the one, monistic; the other, dualistic. The one admits of only one substance, matter; the other of two, matter and mind. He prefers to call the former monism rather than materialism, because the latter term often includes the idea of moral materialism, _i. e._ the doctrine that sensual pleasure is the end of life; a doctrine, he says, much more frequently held by princely church-men than by men of science. He maintains, however, that "all knowable nature is one; that the same eternal, immutable (ehernen, brazen) laws are active in the life of animals and plants, in the formation of crystals, and the power of steam; in the whole sphere of biology, zoology, and botany. We have, therefore, the right to hold fast the monistic and mechanical view, whether men choose to brand the system as Materialism or not. In this sense, all natural science, with the law of causation at its head, is thoroughly materialistic." (p. 32)

The monistic theory he calls "mechanical or causal," as distinguished from the dualistic theory, which he calls "teleological or vitalistic."

According to the latter, "the vegetable and animal kingdoms are considered as the products of a creative agency, working with a definite design. In looking on an organism, the conviction seems unavoidable that so skilfully constructed a machine, such a complicated working apparatus, as an organism is, could be produced only by an agency a.n.a.logous to, although far more perfect than the agency of man." "This,"

he says, "supposes the Creator to be an organism a.n.a.logous to man, although infinitely more perfect; who contemplates his formative powers, lays the plan of the machine, and then, by the use of appropriate means, produces an effect answering to the preconceived plan.... However highly the Creator may be exalted, this view involves the ascription to Him of human attributes, in virtue of which he can form a plan, and construct organisms to correspond with it. That is the view to which Darwin's doctrine is directly opposed, and of which Aga.s.siz is, among naturalists, the most important advocate. The famous work of Aga.s.siz, 'Essay on Cla.s.sification,' which is in direct opposition to Darwin's, and appeared about the same time, has carried out logically to the utmost the absurd anthropomorphic doctrine of a Creator." (p. 17)

The monistic theory is called "mechanical and causal," because it supposes that all the phenomena of the universe, organic and inorganic, vegetable and animal, vital and mental, are due to mechanical or necessarily operating causes (causae efficientes); just as the dualistic theory is called "teleological or vitalistic," because it refers natural organisms to causes working for the accomplishment of a given end (causae finales). (p. 67)

The grand difficulty in the way of the mechanical or monistic theory was the occurrence of innumerable organisms, apparently at least, indicative of design. To get over this difficulty, Haeckel says, some who could not believe in a creative and controlling mind adopted the idea of a metaphysical ghost called vitality. The grand service rendered by Darwin to science is, that his theory enables us to account for the appearances of design in nature without a.s.suming final causes, or, a mind working for a foreseen and intended end. "All that had appeared before Darwin," he says, "failed to secure success, and to meet with general acceptance of the doctrine of the mechanical production of vegetable and animal organisms. This was accomplished by Darwin's theory." (p. 20)

The precise difficulty which Mr. Darwin's doctrine has, according to Haeckel, enabled men of science to surmount, is thus clearly stated on p. 633. It is, "that organs for a definite end should be produced by undesigning or mechanical causes." This difficulty is overcome by the doctrine of evolution. "Through the theory of descent, we are for the first time able to establish the monistic doctrine of the unity of nature, that a mechanic-causal explanation of the most complicated organisms, _e. g._ the formation and const.i.tution of the organs of sense, have no more difficulty for the common understanding, than the mechanical explanation of any physical process, as, for example, earthquakes, the direction of the winds, or the currents of the sea. We thus arrive at the conviction of the last importance, that all natural bodies with which we are acquainted are equally endowed with life (gleichma.s.sig belebt sind); that the distinction between living and dead matter does not exist. When a stone is thrown into the air and falls by certain laws to the ground, or when a solution of salt forms a crystal, the result is neither more nor less a mechanical manifestation of life, than the flowering of a plant, the generation or sensibility of animals, or the feelings or the mental activity of man. In thus establishing the monistic theory of nature lies the highest and most comprehensive merit of the doctrine of descent, as reformed by Darwin." (p. 21) "As to the much vaunted design in nature, it is a reality only for those whose views of animal and vegetable life are to the last degree superficial.

Any one who has gone deeper into the organization and vital activity of animals and plants, who has made himself familiar with the action and reaction of vital phenomena, and the so-called economy of nature, comes of necessity to the conclusion, that design does not exist, any more than the vaunted goodness of the Creator" (die vielgeruhmte Allgute des Schopfers). (p. 17)

Professor Huxley, in his review of this work of Haeckel, already quoted, says: "I do not like to conclude without reminding the reader of my entire concurrence with the general tenor and spirit of the work, and of my high estimate of its value." If you take out of Haeckel's book its doctrine of Monism, which he himself says means Materialism, it has no "tenor or spirit" in it. It is not, however, for us to say how far Professor Huxley intended his indors.e.m.e.nt to go.

Haeckel says that Darwin's theory of evolution leads inevitably to Atheism and Materialism. In this we think he is correct. But we have nothing to do with Haeckel's logic or with our own. We make no charge against Mr. Darwin. We cite Haeckel merely as a witness to the fact that Darwinism involves the denial of final causes; that it excludes all intelligent design in the production of the organs of plants and animals, and even in the production of the soul and body of man. This first of German naturalists would occupy a strange position in the sight of all Europe, if, after lauding a book to the skies because it teaches a certain doctrine, it should turn out that the book taught no such doctrine at all.

FOOTNOTES:

[29] _The Science of Nature versus the Science of Man_. By Noah Porter, President of Yale College. New York, 1871, p. 29.

[30] _Naturlische Schopfungsgeschichte_. Von Dr. Ernst Haeckel, Professor in der Universitat Jena. Zweite Auflage, Berlin, 1873, pp. 8, and 9.