Chapter IV: Part 4

We have, in the modern library, the very best way of perpetuating such relations as this and of ensuring that such as are preserved shall be worth preserving. When the ancients desired to make an idea carry as far as possible, they saw to the toughness and strength of the material object constituting the record; they cut it in stone or cast it in metal, forgetting that all matter is in a state of continual flux and change; it is the idea only that endures. Stone and metal will both one day pass away and unless some one sees fit to copy the inscription on a fresh block or tablet, the record will be lost. It is, then, only by continual renewal of its material basis that a record in written language can be made to last, and there is no reason why this renewal should not take place every few years, as well as every few centuries. There is even an advantage in frequent renewal; for this ensures that the value of the record shall be more frequently passed upon and prevents the preservation of records that are not worth keeping. This preservation by frequent renewal is just what is taking place with books; we make them of perishable materials; if we want to keep them, we reprint them; otherwise they decay and are forgotten.

We should not forget that by this plan the reader is usually made the judge of whether a book is worth keeping. Why do we preserve by continual reprinting Shakespeare and Scott and Tennyson and Hawthorne? The reprinting is done by publishers as a money-making scheme. It is profitable to them because there is a demand for those authors. If we cease to care for them and prefer unworthy writers, Shakespeare and Scott will decay and be forgotten and the unworthy ones will be preserved. Thus a great responsibility is thrown upon readers; so far they have judged pretty well.

Just now, however, we are confining ourselves to the use of books for information; and here there is less preservation than elsewhere. Especially in science, statements and facts quickly become out of date; here it is not the old but the new that we want--the new based on the accurate and enduring part of the old.

Before we leave this part of the subject it may be noted that many persons have no idea of the kinds of information that may be obtained from books. Even those who would unhesitatingly seek a book for data in history, art, or mathematics would not think of going to books for facts on plumbing, weaving, or shoe-making, for methods of shop-window decoration or of display-advertising, for special forms of bookkeeping suitable for factories or for stock-farms--for a host of facts relating to trades, occupations, and business in general. Yet there are books about all these things--not books perhaps to read for an idle hour, but books full of meat for them who want just this kind of food. If Book-taught Bilkins fails, after trying to utilize what such books have taught him, it is doubtless because he has previously failed to realize that books plus experience, or, to put it differently, the recorded experience of others plus our own is better than either could be separately. And the same is true of information that calls for no physical action to supplement it. Books plus thought--the thoughts of others plus our own--are more effective in combination than either could be by itself. Reading should provoke thought; thought should suggest more reading, and so on, until others' thoughts and our own have become so completely amalgamated that they are our personal intellectual possessions.

But we may not read for information at all--recreation may be what we are after. Do not misunderstand me. Many persons have an idea that if one reads to amuse himself he must necessarily read novels. I think most highly of good novels. Narrative is a popular form of literary expression; it is used by those who wish to instruct as well as to amuse. One may obtain plenty of information from novels--often in a form nowhere else available. If we want exact statement, statistical or otherwise, we do not go to fiction for it; but if we wish to obtain what is often more important--accurate and lasting general impressions of history, society, or geography, the novel is often the only place where these may be had. Likewise, one may amuse himself with history, travel, science, or art--even with mathematics. The last is rarely written primarily to amuse, although we have such a title as "Mathematical recreations," but there are plenty of non-fiction books written for entertainment and one may read for entertainment any book whatever. The result depends not so much on the book or its contents as on the reader.

Recreation is now recognized as an essential part of education. And just as physical recreation consists largely in the same muscular movements that constitute work, only in different combinations and with different ends in view, so mental recreation consists of intellectual exercise with a similar variation of combinations and aims.

Somebody says that "play is work that you don't have to do". So reading for amusement may closely resemble study--the only difference is that it is purely voluntary. Here again, however, the written language is only an intermediary; we have as before, the contact of two minds--only here it is often the lighter contact of good-fellowship. And one who reads always for such recreation is thus like the man who is always bandying trivialities, story-telling, and jesting--an excellent, even a necessary, way of passing part of one's time, but a mistaken way of employing all of it.

The best kind of recreation is gently stimulating, but stimulation may rise easily to abnormality. There are fiction drunkards just as there are persons who take too much alcohol or too much coffee. In fact, if one is so much absorbed by the ideas that he is assimilating that the process interferes with the ordinary duties of life, he may be fairly sure that it is injuring him. If one loves coffee or alcohol, or even candy, so dearly that one can not give it up, it is time to stop using it altogether. If a reader is so fond of an exciting story that he can not lay it aside, so that he sits up late at night reading it, or if he can not drop it from his mind when he does lay it aside, but goes on thinking about the deadly combat between the hero and Lord William Fitz Grouchy when he ought to be studying his lessons or attending to his business, it is time to cut out fiction altogether. This advice has absolutely nothing to do with the quality of the fiction. It will not do simply to warn the habitual drunkard that he must be careful to take none but the best brands; he must drop alcohol altogether. If you are a fiction drunkard, enhanced quality will only enslave you further. This sort of use is no more recreation in the proper sense of the word than is gambling, or drinking to excess, or smoking opium.

And now we come to a use of books that is more important--lies more at the root of things--than their use for either information or recreation--their use for inspiration. One may get help and inspiration along with the other two--reading about how to make a box may inspire a boy to go out and make one himself. It is this kind of thing that should be the final outcome of every mental process. Nothing that goes on in the brain is really complete until it ends in a motor stimulus. The action, it is true, may not follow closely; it may be the result of years of mental adjustment; it may even take place in another body from the one where it originated. The man who tells us how to make a box, and tells it so fascinatingly that he sets all his readers to box-making, presumably has made boxes with his own hands, but there may be those who are fitted to inspire action in others rather than to undertake it themselves. And the larger literature of inspiration is not that which urges to specific deeds like box-making, or even to classes of deeds, like caring for the sick or improving methods of transportation; rather does it include in its scope all good thoughts and all good actions. It makes better men and women of those who read it; it is revolutionary and evolutionary at the same time, in the best sense of both words.

What will thus inspire me, do you ask? It would be easy to try to tell you; it would also be easy to fail. Many have tried and failed. This is a deeply personal matter. I can not tell what book, or what passage in a book, will touch the magic spring that shall make your life useful instead of useless, that shall start your thoughts and your deeds climbing up instead of grovelling or passively waiting. Only search will reveal it. The diamond-miner who expects to be directed to the precise spot where he will find a gem will never pick one up. Only he who seeks, finds. There are, however, places to look and places to avoid. The peculiar clay in which diamonds occur is well known to mineralogists. He who runs across it, looks for diamonds, though he may find none. But he who hunts for them on the rock-ribbed hills of New Hampshire or the sea-sands of Florida is doing a foolish thing--although even there he may conceivably pick up one that has been dropped by accident.

So you may know where it is best to go in your search for inspiration from books, for we know where seekers in the past have most often found it. He who could read the Bible or Shakespeare without finding some of it is the exception. It may be looked for in the great poets--Homer, Virgil, Dante, Chaucer, Milton, Hugo, Keats, Goethe; or the great historians--Tacitus, Herodotus, Froissart, Macaulay, Taine, Bancroft; or in the great travellers from Sir John Mandeville down, or in biographies like Boswell's life of Johnson, or in books of science--Laplace, Lagrange, Darwin, Tyndall, Helmholtz; in the lives of the great artists; in the great novels and romances--Thackeray, Balzac, Hawthorne, Dickens, George Eliot. Yet each and all of these may leave you cold and you may pick up your gem in some out-of-the-way corner where neither you nor anyone else would think of looking for it.

Did you ever see a car-conductor fumbling about in the dark with the trolley pole, trying to hit the wire? While he is pulling it down and letting it fly up again, making fruitless dabs in the air, the car is dark and motionless; in vain the motorman turns his controller, in vain do the passengers long for light. But sooner or later the pole strikes the wire; down it flows the current that was there all the time up in the air; in a jiffy the car is in motion and ablaze with light. So your search for inspiration in literature may be long and unsuccessful; you are dark and motionless. But the life-giving current from some great man's brain is flowing through some book not far away. One day you will make the connection and your life will in a trice be filled with light and instinct with action.

And before we leave this subject of inspiration, let us dwell for a moment on that to be obtained from one's literary setting in general--from the totality of one's literary associations and impressions, as distinguished from that gained from some specific passage or idea.

It has been said that it takes two to tell the truth; one to speak and one to listen. In like manner we may say that two persons are necessary to a great artistic interpretation--one to create and one to appreciate. And of no art is this more true than it is of literature. The thought that we are thus cooperating with Shakespeare and Schiller and Hugo in bringing out the full effect of their deathless conceptions is an inspiring one and its consideration may aid us in realizing the essential oneness of the human race, so far as its intellectual life is concerned.

Would you rather be a citizen of the United States than, we will say, of Nicaragua? You might be as happy, as well educated, as well off, there as here. Why do you prefer your present status? Simply and solely because of associations and relationships. If this is sentiment, as it doubtless is, it is the kind of sentiment that rules the world--it is in the same class as friendship, loyalty, love of kin, affection for home. The links that bind us to the past and the threads that stretch out into the future are more satisfactory to us here in the United States, with the complexity of its interests for us, than they would be in Nicaragua, or Guam, or Iceland.

Then of what country in the realm of literature do you desire to be a citizen? Of the one where Shakespeare is king and where your familiar and daily speech is with the great ones of this earth--those whose wise, witty, good, or inspiring words, spoken for centuries past, have been recorded in books? Or would you prefer to dwell with triviality and banality--perhaps with Laura Jean Libbey or even with Mary J. Holmes, and those a little better than these--or a little worse.

I am one of those who believe in the best associations, literary as well as social. And associations may have their effect even if they are apparently trivial or superficial.

When the open-shelf library was first introduced we were told that one of its chief advantages was that it encouraged "browsing"--the somewhat aimless rambling about and dipping here and there into a book. Obviously this can not be done in a closed-shelf library. But of late it has been suggested, in one quarter or another, that although this may be a pleasant occupation to some, or even to most, it is not a profitable one. Opponents of the open shelf of whom there are still one or two, here and there, find in this conclusion a reason for negativing the argument in its favor, while those of its advocates who accept this view see in it only a reason for basing that argument wholly on other grounds.

Now those of us who like a thing do not relish being told that it is not good for us. We feel that pleasure was intended as an outward sign of benefits received and although it may in abnormal conditions deceive us, we are right in demanding proof before distrusting its indications. When the cow absorbs physical nutriment by browsing, she does so without further reason than that she likes it. Does the absorber of mental pabulum from books argue wrongly from similar premises?

Many things are hastily and wrongly condemned because they do not achieve certain results that they were not intended to achieve. And in particular, when a thing exists in several degrees or grades, some one of those grades is often censured, although good in itself, because it is not a grade or two higher. Obviously everything depends on what is required. When a shopper wants just three yards of cloth, she would be foolish to buy four. She would, of course, be even more foolish to imagine that, if she really wished four, three would do just as well. But if a man wants to go to the eighth story of a building, he should not be condemned because he does not mount to the ninth; if he wishes a light lunch, he should not be found fault with for not ordering a seven-course dinner. And yet we continually hear persons accused of "superficiality" who purposely and knowingly acquire some slight degree of knowledge of a subject instead of a higher degree. And others are condemned, we will say, for reading for amusement when they might have read for serious information, without inquiring whether amusement, in this instance, was not precisely what they needed.

It may be, therefore, that browsing is productive of some good result, and that it fails to effect some other, perhaps some higher, result which its critics have wrongly fixed upon as the one desirable thing in this connection.

When a name embodies a figure of speech, we may often learn something by following up the figure to see how far it holds good. What does an animal do, and what does it not do, when it "browses"? In the first place it eats food--fresh, growing food; but, secondly, it eats this food by cropping off the tips of the herbage, not taking much at once, and again, it moves about from place to place, eating now here and now there and then making selection, from one motive or another, but presumably following the dictates of its own taste or fancy. What does it not do? First, it does not, from choice, eat anything bad. Secondly, it does not necessarily consume all of its food in this way. If it finds a particularly choice spot, it may confine its feeding to that spot; or, if its owner sees fit, he may remove it to the stable, where it may stand all day and eat what he chooses to give it. The benefits of browsing are, first, the nourishment actually derived from the food taken, coupled with the fact that it is taken in small quantities, and in great variety; and secondly, the knowledge of good spots, obtained from the testing of one spot after another, throughout the whole broad pasture.

Now I submit that our figure of speech holds good in all these particulars. The literary "browser" partakes of his mental food from books and is thereby nourished and stimulated; he takes it here and there in brief quantities, moving from section to section and from shelf to shelf, selecting choice morsels of literature as fancy may dictate. He does not, if he is a healthy reader, absorb voluntarily anything that will hurt him, and this method of literary absorption does not preclude other methods of mental nourishment. He may like a book so much that he proceeds to devour it whole, or his superiors in knowledge may remove him to a place where necessary mental food is administered more or less forcibly. And having gone so far with our comparison, we shall make no mistake if we go a little further and say that the benefits of browsing to the reader are twofold, as they are to the material feeder--the absorption of actual nutriment in his own wilful, wayward manner--a little at a time and in great variety; and the knowledge of good reading obtained from such a wide testing of the field.

Are not these real benefits, and are they not desirable? I fear that our original surmise was correct and that browsing is condemned not for what it does, but because it fails to do something that it could not be expected to do. Of course, if one were to browse continuously he would be unable to feed in any other way. Attendance upon school or the continuous reading of any book whatever would be obviously impossible. To avoid misunderstanding, therefore, we will agree at this point that whatever may be said here in commendation of browsing is on condition that it be occasional and not excessive and that the normal amount of continuous reading and study proceed together with it.

Having settled, therefore, that browsing is a good thing when one does not occupy one's whole time with it, let us examine its advantages a little more in detail.

First: about the mental nourishment that is absorbed in browsing; the specific information, the appreciation of what is good, the intellectual stimulation--not that which comes from reading suggested or guided by browsing, but from the actual process itself. I have heard it strenuously denied that any such absorption occurs; the bits taken are too small, the motion of the browser is too rapid, the whole process is too desultory. Let us see. In the first place a knowledge of authors and titles and of the general character of their works is by no means to be despised. I heard the other day of a presumably educated woman who betrayed in a conversation her ignorance of Omar Khayyam--not lack of acquaintance with his works, but lack of knowledge that such a person had ever existed. If at some period in her life she had held in her hand a copy of "The Rubaiyat," and had glanced at its back, without even opening it, how much embarrassment she might have been spared! And if, in addition, she had glanced within for just ten seconds and had discovered that he wrote poetry in stanzas of four lines each, she would have known as much about Omar as do many of those who would contemptuously scoff at her ignorance. With so brief effort may we acquire literary knowledge sufficient to avoid embarrassment in ordinary conversation. Browsing in a good library, if the browser has a memory, will soon equip him with a wide range of knowledge of this kind. Nor is such knowledge to be sneered at as superficial. It is all that we know, or need to know, about scores of authors. One may never study higher mathematics, but it may be good for him to know that Lagrange was a French author who wrote on analytical mechanics, that Euclid was a Greek geometer, and that Hamilton invented quaternions. All this and vastly more may be impressed on the mind by an hour in the mathematical alcove of a library of moderate size. And it will do no harm to a boy to know that Benvenuto Cellini wrote his autobiography, even if the inevitable perusal of the book is delayed for several years, or that Felicia Hemans, James Thomson, and Robert Herrick wrote poetry, independently of familiarity with their works, or that "Lamia" is not something to eat or "As you like it" a popular novel. Information of this kind is almost impossible to acquire from lists or from oral statement, whereas a moment's handling of a book in the concrete may fix it in the mind for good and all. So far, we have not supposed that even a word of the contents has been read. What, now, if a sentence, a stanza, a paragraph, a page, passes into the brain through the eye? Those who measure literary effect by the thousand words or by the hour are making a great mistake. The lightning flash is over in a fraction of a second, but in that time it may reveal a scene of beauty, may give the traveller warning of the fatal precipice, or may shatter the farmer's home into kindling wood. Intellectual lightning may strike the "browser" as he stands there book in hand before the shelf. A word, a phrase, may sear into his brain--may turn the current of his whole life. And even if no such epoch-making words meet his eye, in how brief a time may he read, digest, appreciate, some of the gems of literature! Leigh Hunt's "Jennie kissed me" would probably take about thirty seconds; on a second reading he would have it by heart--the joy of a life-time. How many meaty epigrams would take as long? The whole of Gray's "Elegy" is hardly beyond the browser's limit.

In an editorial on the Harvard Classics in the "Chicago evening post", (April 22), we read, "the cultural tabloid has very little virtue;... to gain everything that a book has to give one must be submerged in it, saturated and absorbed". This is very much like saying, "there is very little nourishment in a sandwich; to get the full effect of a luncheon you must eat everything on the table". It is a truism to say that you can not get everything in a book without reading all of it; but it by no means follows that the virtue of less than the whole is negligible.

So much for the direct effect of what one may thus take in, bit by bit. The indirect effect is even more important. For by sampling a whole literature, as he does, he not only gets a bird's-eye view of it, but he finds out what he likes and what he dislikes; he begins to form his taste. Are you afraid that he will form it wrong? I am not. We are assuming that the library where he browses is a good one; here is no chance of evil, only a choice between different kinds of good. And even if the evil be there, it is astonishing how the healthy mind will let it slip and fasten eagerly on the good. Would you prefer a taste fixed by someone who tells the browser what he ought to like? Then that is not the reader's own taste at all, but that of his informant. We have too much of this sort of thing--too many readers without an atom of taste of their own who will say, for instance, that they adore George Meredith, because some one has told them that all intellectual persons do so. The man who frankly loves George Ade and can yet see nothing in Shakespeare may one day discover Shakespeare. The man who reads Shakespeare merely because he thinks he ought to is hopeless.

But what a triumph, to stand spell-bound by the art of a writer whose name you never heard, and then discover that he is one of the great ones of the world! Nought is comparable to it except perhaps to pick out all by yourself in the exhibition the one picture that the experts have chosen for the museum or to be able to say you liked olives the first time you tasted them.

Who are your favorites? Did some one guide you to them or did you find them yourselves? I will warrant that in many cases you discovered them and that this is why you love them. I discovered DeQuincey's romances, Praed's poetry, Béranger in French, Heine in German, "The Arabian nights", Molière, Irving's "Alhambra," hundreds of others probably. I am sure that I love them all far more than if some one had told me they were good books. If I had been obliged to read them in school and pass an examination on them, I should have hated them. The teacher who can write an examination paper on Gray's "Elegy", would, I firmly believe, cut up his grandmother alive before the physiology class.

And next to the author or the book that you have discovered yourself comes the one that the discoverer himself--your boy or girl friend--tells you about. _He_ knows a good thing--_she_ knows it! No school nonsense about that; no adult misunderstanding. I found out Poe that way, and Thackeray's "Major Gahagan", and many others.

To go back to our old illustration and consider for a moment not the book but the mind, the personality whose ideas it records, such association with books represents association with one's fellowmen in society--at a reception, in school or college, at a club. Some we pass by with a nod, with some we exchange a word; sometimes there is a warm handgrasp; sometimes a long conversation. No matter what the mental contact may be, it has its effects--we are continually gaining knowledge, making new friends, receiving fresh inspiration. The complexion of this kind of daily association determines the cast of one's mind, the thoroughness of his taste, the usefulness or uselessness of what he does. A man is known by the company he keeps, because that company forms him; he gets from it what becomes brain of his brain and soul of his soul.

And no less is he formed by his mental associations with the good and the great of all ages whom he meets in books and who talk to him there. More rather than less; for into a book the writer puts generally what is best in him, laying aside the pettiness, the triviality, the downright wickedness that may have characterized him in the flesh.

I have often heard the comment from one who had met face to face a writer whose work he loved--"Oh! he disappointed me so!" How disappointed might we be with Thackeray, with Dickens, even with Shakespeare, could we meet them in the flesh! Now they can not disappoint us, for we know only what they have left on record--the best, the most enduring part, purified from what is gross and earthly.

In and among such company as this it is your privilege to live and move, almost without money and without price. Thank God for books; let them be your friends and companions through life--for information, for recreation, but above all for inspiration.

ATOMIC THEORIES OF ENERGY[6]

[6] Read before the St. Louis Academy of Science.

A theory involving some sort of a discrete or discontinuous structure of energy has been put forward by Prof. Max Planck of the University of Berlin. The various aspects of this theory are discussed and elaborated by the late M. Henri Poincaré in a paper entitled "L'Hypothèse des Quanta," published in the _Revue Scientifique_ (Paris, Feb. 21, 1912).

A paper in which a discontinuous or "atomic" structure of energy was suggested was prepared by the present writer fifteen years ago but remains unpublished for reasons that will appear later. Although he has no desire to put in a claim of priority and is well aware that failure to publish would put any such claim out of court, it seems to him that in connection with present radical developments in physical theory the paper, together with some correspondence relating thereto, has historical interest. Planck's theory was suggested by thermodynamical considerations. In the paper now to be quoted the matter was approached from the standpoint of a criterion for determining the identity of two portions of matter or of energy. The paper is as follows:

_Some Consideration on the Identity of Definite Portions of Energy_

It has been remarked recently that physicists are now divided into two opposing schools according to the way in which they view the subject of energy, some regarding it as a mere mathematical abstraction and others looking upon it as a physical entity, filling space and continuously migrating by definite paths from one place to another. It may be added that there are numerous factions within these two parties; for instance, not all of those who consider energy to be something more than a mere mathematical expression would maintain that a given quantity of it retains its identity just as a given quantity of matter does. In fact a close analysis would possibly show that opinions are graded very closely and continuously from a view hardly differing from that of Lagrange, who clearly saw and freely used the mathematical considerations involving energy before the word had been invented or its physical meaning developed, up to that stated recently in its extreme form by Professor Ostwald, who would replace what he terms a mechanical theory of the universe by an "energetical" theory, and would dwell exclusively on energy as opposed to its vehicles.

Differences of opinion of this sort very frequently reduce to differences of definition, and in this case the meaning of the word "identity" or some similar word or phrase has undoubtedly much to do with the view that is taken of the matter. It may be interesting, for instance, to look for a moment at our ideas of the identity of matter and the extent to which they are influenced by the accepted theory of its constitution.

Very few persons would hesitate to admit that the matter that now constitutes the universe is identical in amount with that which constituted it one million years ago, and that any given portion of that matter is identical with an equal amount of matter that then existed, although the situations of the parts of that portion might be and probably were widely different in the two classes. To assert this is of course a very different thing from asserting that the identity of the two portions or any parts thereof could have been practically shown by following them during all their changes of location or state. That cannot be done even in the case of some simple changes that are effected in a fraction of a second. For instance, if water from the pail A be mixed with water from the pail B there is no possible way of telling which pail any given portion of the mixture came from or in what proportions, yet it is certain that such portion is identical with a portion of equal mass that recently occupied part of one or both pails.

How far our certainty as to this is influenced by our ideas regarding the ultimate constitution of the water is worthy of investigation. All who accept the molecular theory, for instance, will regard our inability to trace the elements of a mixture as due to purely physical limitations. A set of Maxwell's "demons" if bidden to watch the molecules of the water in pail A, one demon being assigned to each molecule, would be able to tell us at any time the precise proportions of any given part of the mixture. But if we should not accept the molecular theory and believe for instance, that water is a continuum, absolutely homogeneous, no matter how small portions of it be selected, then our demons would be as powerless as we ourselves now are to trace the constituents in the mixture.

We are now in a position to ask the question: Is the matter in a mixture of two continua identical with that of its constituents? The identity certainly seems of a different kind or degree from that which obtains in the first case, for there is no part, however small, that was derived from one pail alone. The mixture is something more than a mere juxtaposition of elements each of which has retained its identity; it is now of such nature that no part of it is identical with any part of A alone or of B alone, nor of A+B, where the sign + denotes simple juxtaposition. It is identical, to be sure, with a perfect mixture of certain parts of A and B, but this is simply saying that it is identical with what it is now, that is, with itself, not with something that went before.

Probably no one now believes that water or any other kind of matter is a continuum, but the bearing of what has been said may be seen when we remember that this is precisely the present stage of our belief regarding energy.

No one, so far as I know, has ventured to suggest what may be termed a molecular theory of energy, a somewhat remarkable fact when we consider the control now exercised over all thought in physics by molecular theories of matter. While we now believe, for instance, that a material body, say a crystal, can by no possibility increase continuously in mass, but must do so step by step, the minimum mass of matter that can be added being the molecule, we believe on the contrary that the energy possessed by the same body can and may increase with absolutely perfect continuity, being hampered by no such restriction.

It is not the purpose of this paper to discuss whether we have grounds for belief that there is such a thing as a minimum quantity, or atom, of energy, that does not separate into smaller parts, no matter what changes it undergoes. Suffice it to say that there appears to be no _a priori_ absurdity in such an idea. At first sight both matter and energy appear non-molecular in structure. But we have been forced to look upon the gradual growth of a crystal as a step-by-step process, and we may some day, by equally cogent considerations, be forced to regard the gradual increase of energy of an accelerating body as also a step-by-step process, although the discontinuity is as invisible to the eye in the latter case as in the former.

Without following this out any farther, however, the point may be here emphasized that it is hardly possible for one who, like the majority of physicists, regards matter as molecular and energy as a continuum, to hold the same ideas regarding the identity of the two. Efforts to show that definite portions of energy, like definite portions of matter, retain their identity have hitherto been made chiefly on the lines of a demonstration that energy travels by definite and continuous paths in space just as matter does. This is very well, but it would appear to be necessary to supplement it with evidence to show that the lines representing these paths do not form at their intersections continuous blurs that not only forbid any practical attempt at identification on emergence, but make it doubtful whether we can in any true sense call the issuing path identical with the entering one. Otherwise the identity of energy can be admitted to be only that kind of identity that could be preserved by matter if its molecular structure did not exist. One who can admit that this sort of identity is the same sort that can be preserved by molecular matter may be able to hold the identity of energy in the present state of the evidence, but the present attitude of physicists would seem to show that, whether they realize the connection of the two subjects or not, they cannot take this view. In other words, modern views of the identity of matter seem closely connected with modern views of its structure, and the same connection will doubtless hold good for energy.

Regarding the probable success of an attempt to prove that energy has a "structure" analogous to the molecular structure of matter, any prediction would doubtless be rash just now. The writer has been unable, up to the present time, to disprove the proposition, but the subject is one of corresponding importance to that of the whole molecular theory of matter and should not be entered upon lightly.

* * * * *

The writer freely acknowledges at present that the illustrations in the foregoing are badly chosen and some of the statements are too strong, but it still represents essentially his ideas on the subject. No reputable scientific journal would undertake to publish it. The paper was then sent to Prof. J. Willard Gibbs of Yale, and elicited the following letter from him:

"NEW HAVEN, JUNE 2, 1897.

"MY DEAR MR. BOSTWICK:

"I regret that I have allowed your letter to lie so long
unanswered. It was in fact not very easy to answer, and when one
lays a letter aside to answer, the weeks slip away very fast.

"I do not think that you state the matter quite right in regard to
the mixture of fluids if they were continuous. The mixing of water
as I regard it would be like this, if it were continuous and not
molecular. Suppose you should take strips of white and red glass
and heat them until soft and twist them together. Keep on drawing
them out and doubling them up and twisting them together. It would
soon require a microscope to distinguish the red and white glass,
which would be drawn out into thinner and thinner filaments if the
matter were continuous. But it would be always only a matter of
optical power to distinguish perfectly the portion of red and
white glass. The stirring up of water from two pails would not
really mix them but only entangle filaments from the pails.

"To come to the case of energy. All our ideas concerning energy
seem to require that it is capable of gradual increase. Thus the
energy due to velocity can increase continuously if velocity can.
Since the energy is as the square of the velocity, if the velocity
can only increase discontinuously by equal increments, the energy
of the body will increase by unequal increments in such a way as
to make the exchange of energy between bodies a very awkward
matter to adjust.

"But apart from the question of the increase of energy by
discontinuous increments, the question of relative and absolute
motion makes it very hard to give a particular position to energy,
since the 'energy' we speak of in any case is not one quantity but
may be interpreted in a great many ways. Take the important case
of two equal elastic balls. One, moving, strikes the other at
rest, we say, and gives it nearly all its energy. But we have no
right to call one ball at rest and we can not say (as anything
absolute) which of the balls has lost and which has gained energy.
If there is such a thing as absolute energy of motion it is
something entirely unknowable to us. Take the solar system,
supposed isolated. We may take as our origin of coordinates the
center of gravity of the system. Or we may take an origin with
respect to which the center of gravity of the solar system has any
(constant) velocity. The kinetic energy of the earth, for example,
may have any value whatever, and the principle of the conservation
of energy will hold in any case for the whole solar system. But
the shifting of energy from one planet to another will take place
entirely differently when we estimate the energies with reference
to different origins.

"It does not seem to me that your ideas fit in with what we know
about nature. If you ask my advice, I should not advise you to try
to publish them.

"At best you would be entering into a discussion (perhaps not in
bad company) in which words would play a greater part than precise
ideas.

"This is the way I feel about it.

"I remain,
"Yours faithfully,
"J.W. GIBBS."

Professor Gibbs's criticism of the illustration of water-mixture is evidently just. Another might well have been used where the things mixed are not material--for instance, the value of money deposited in a bank. If A and B each deposits $100 to C's credit and C then draws $10, there is evidently no way of determining what part of it came from A and what from B. The structure of "value", in other words, is perfectly continuous. Professor Gibbs's objections to an "atomic" theory of the structure of energy are most interesting. The difficulties that it involves are not overstated. In 1897 they made it unnecessary, but since that time considerations have been brought forward, and generally recognized, which may make it necessary to brave those difficulties.

Planck's theory was suggested by the apparent necessity of modifying the generally accepted theory of statistical equilibrium involving the so called "law of equipartition," enunciated first for gases and extended to liquids and solids.

In the first place the kinetic theory fixes the number of degrees of freedom of each gaseous molecule, which would be three for argon, for instance, and five for oxygen. But what prevents either from having the six degrees to which ordinary mechanical theory entitles it? Furthermore, the oxygen spectrum has more than five lines, and the molecule must therefore vibrate in more than five modes. "Why," asks Poincaré, "do certain degrees of freedom appear to play no part here; why are they, so to speak, 'ankylosed'?" Again, suppose a system in statistical equilibrium, each part gaining on an average, in a short time, exactly as much as it loses. If the system consists of molecules and ether, as the former have a finite number of degrees of freedom and the latter an infinite number, the unmodified law of equipartition would require that the ether should finally appropriate all energy, leaving none of it to the matter. To escape this conclusion we have Rayleigh's law that the radiated energy, for a given wave length, is proportional to the absolute temperature, and for a given temperature is in inverse ratio to the fourth power of the wave-length. This is found by Planck to be experimentally unverifiable, the radiation being less for small wave-lengths and low temperatures, than the law requires.

Still again, the specific heats of solids, instead of being sensibly constant at all temperatures, are found to diminish rapidly in the low temperatures now available in liquid air or hydrogen and apparently tend to disappear at absolute zero. "All takes place," says Poincaré, "as if these molecules lost some of their degrees of freedom in cooling--as if some of their articulations froze at the limit."

Planck attempts to explain these facts by introducing the idea of what he calls "quanta" of energy. To quote from Poincaré's paper:

"How should we picture a radiating body? We know that a Hertz resonator sends into the ether Hertzian waves that are identical with luminous waves; an incandescent body must then be regarded as containing a very great number of tiny resonators. When the body is heated, these resonators acquire energy, start vibrating and consequently radiate.

"Planck's hypothesis consists in the supposition that each of these resonators can acquire or lose energy only by abrupt jumps, in such a way that the store of energy that it possesses must always be a multiple of a constant quantity, which he calls a 'quantum'--must be composed of a whole number of quanta. This indivisible unit, this quantum, is not the same for all resonators; it is in inverse ratio to the wave-length, so that resonators of short period can take in energy only in large pieces, while those of long period can absorb or give it out by small bits. What is the result? Great effort is necessary to agitate a short-period resonator, since this requires at least a quantity of energy equal to its quantum, which is great. The chances are, then, that these resonators will keep quiet, especially if the temperature is low, and it is for this reason that there is relatively little short-wave radiation in 'black radiation'... The diminution of specific-heats is explained similarly: When the temperature falls, a large number of vibrators fall below their quantum and cease to vibrate, so that the total energy diminishes faster than the old theories require."

Here we have the germs of an atomic theory of energy. As Poincaré now points out, the trouble is that the quanta are not constant. In his study of the matter he notes that the work of Prof. Wilhelm Wien, of Würzburg, leads by theory to precisely the conclusion announced by Planck that if we are to hold to the accepted ideas of statistical equilibrium the energy can vary only by quanta inversely proportional to wave-length. The mechanical property of the resonators imagined by Planck is therefore precisely that which Wien's theory requires. If we are to suppose atoms of energy, therefore, they must be variable atoms. There are other objections which need not be touched upon here, the whole theory being in a very early stage. To quote Poincaré again:

"The new conception is seductive from a certain standpoint: for some time the tendency has been toward atomism. Matter appears to us as formed of indivisible atoms; electricity is no longer continuous, not infinitely divisible. It resolves itself into equally-charged electrons; we have also now the magneton, or atom of magnetism. From this point of view the quanta appear as _atoms_ of _energy_. Unfortunately the comparison may not be pushed to the limit; a hydrogen atom is really invariable.... The electrons preserve their individuality amid the most diverse vicissitudes, is it the same with the atoms of energy? We have, for instance, three quanta of energy in a resonator whose wave-length is 3; this passes to a second resonator whose wave-length is 5; it now represents not 3 but 5 quanta, since the quantum of the new resonator is smaller and in the transformation the number of atoms and the size of each has changed."

If, however, we replace the atom of energy by an "atom of action," these atoms may be considered equal and invariable. The whole study of thermodynamic equilibrium has been reduced by the French mathematical school to a question of probability. "The probability of a continuous variable is obtained by considering elementary independent domains of equal probability.... In the classic dynamics we use, to find these elementary domains, the theorem that two physical states of which one is the necessary effect of the other are equally probable. In a physical system if we represent by _q_ one of the generalized coordinates and by _p_ the corresponding momentum, according to Liouville's theorem the domain [double integral]_dpdq_, considered at given instant, is invariable with respect to the time if _p_ and _q_ vary according to Hamilton's equations. On the other hand _p_ and _q_ may, at a given instant take all possible values, independent of each other. Whence it follows that the elementary domain is infinitely small, of the magnitude _dpdq_.... The new hypothesis has for its object to restrict the variability of _p_ and _q_ so that these variables will only change by jumps.... Thus the number of elementary domains of probability is reduced and the extent of each is augmented. The hypothesis of quanta of action consists in supposing that these domains are all equal and no longer infinitely small but finite and that for each [double integral]_dpdq_ equals _h_, _h_ being a constant."

Put a little less mathematically, this simply means that as energy equals action multiplied by frequency, the fact that the quantum of energy is proportional to the frequency (or inversely to the wave-length as stated above) is due simply to the fact that the quantum of action is constant--a real atom. The general effect on our physical conceptions, however, is the same: we have a purely discontinuous universe--discontinuous not only in matter but in energy and the flow of time. M. Poincaré thus puts it: "A physical system is susceptible only of a finite number of distinct states; it leaps from one of these to the next without passing through any continuous series of intermediate states."

He notes later:

"The universe, then, leaps suddenly from one state to another; but in the interval it must remain immovable, and the divers instants during which it keeps in the same state can no longer be discriminated from one another; we thus reach a conception of the discontinuous variation of time--the atom of _time_."

I quote in conclusion, Poincaré's final remarks:

"The present state of the question is thus as follows: the old theories, which hitherto seemed to account for all the known phenomena, have met with an unexpected obstacle. Seemingly a modification becomes necessary. A hypothesis has presented itself to M. Planck's mind, but so strange a one that one is tempted to seek every means of escaping it; these means, however, have been sought vainly. The new theory, however, raises a host of difficulties, many of which are real and not simply illusions due to the indolence of our minds, unwilling to change their modes of thought....

"Is discontinuity to reign through out the physical universe, and is its triumph definitive? Or rather shall we find that it is but apparent and hides a series of continuous processes?... To try to give an opinion just now on these questions would only be to waste ink."

It only remains to call attention again to the fact that this conception of the discontinuity of energy, the acceptance of which Poincaré says would be "the most profound revolution that natural philosophy has undergone since Newton" was suggested by the present writer fifteen years ago. Its reception and serious consideration by one of the first mathematical physicists of the world seems a sufficient justification of its suggestion then as a legitimate scientific hypothesis.

THE ADVERTISEMENT OF IDEAS

Writing is a device for the storage of ideas--the only device for this purpose prior to the invention of the phonograph, and not now likely to be generally superseded. A book consists of stored ideas; sometimes it is like a box, from which the contents must be lifted slowly and with more or less toil; sometimes like a storage battery where one only has to make the right kind of contact to get a discharge. At any rate, if we want people to use books or to use them more, or to use them better, or to use a different kind from that which they now use, we must lose sight for a moment of the material part of the book, which is only the box or the lead and acid of the storage battery, and fix our attention on the stored ideas, which are what everybody wants--everybody, that is, except those who collect books as curiosities. The subject of this lecture is thus only library advertising, about which we have heard a good deal of late, but we shall try to confine its applications to this inner or ideal substance which it is our special business as librarians to purvey. And first, in considering the matter, it may be worth while to say a word about advertising in general. Practically an advertisement is an announcement by somebody who has something to distribute. Announcements of this kind may be classified, it seems to me, as economic, uneconomic and illegitimate.