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.
The most elementary form is that of the person who tells you where you can
get something that you want--a simple statement that someone is a barber
or an inn-keeper, or gives music lessons, or has shoes for sale. This may
be accompanied by an effort to show that the goods offered are of
specially good quality or have some feature that makes them particularly
desirable, either to consumers in general or to those of a certain class.
This is all surely economic, so long as nothing but the truth is told.
Next we have an effort not only to supply existing wants and to direct
them into some particular channel, but to create a new field, to make
people realize a lack previously not felt; in other words to make people
want something that they need. This may be done simply by exhibiting or
describing the article or it may require long and skillful presentation of
the matter. All this is still economic. But it requires only a step to
carry us across the line. Next the enthusiastic advertiser strives to make
someone want that which he does not need. As may be seen, the line here is
difficult to determine, but this sort of advertising is surely not
economic. So long as the thing not needed is not really injurious,
however, the advertising cannot be called illegitimate. It is simply
uneconomic. The world would be better off without it, but we may look for
its abolition only to the increase of good judgment and intelligence among
consumers. When an attempt however, is made to cause a man to want
something that is really injurious, then the act becomes illegitimate and
should be prevented. Another class of illegitimate advertising is that
which would be perfectly allowable if it were truthful and becomes
objectionable only because its representations are false. It may be
ostensibly of any of the types noted above.
As we have already noted, the material objects distributed by the
librarian are valued not for their physical characteristics but for a
different reason altogether, the fact that they contain stored ideas.
Ideas which, according to some, are merely the relative positions of
material particles in the brain, and which are indisputably accompanied
and conditioned by such positions, here subsist in the form of peculiar
and visible arrangements of particles of printer's ink upon paper, which
are capable under certain conditions of generating in the human brain
ideas precisely similar to those that gave them birth. And although the
book cannot think for itself, but must merely preserve the idea intrusted
to it, without change, it is vastly superior in stability to the brain
that gave it birth, so that thousands of years after that brain has
mouldered into dust it is capable of reproducing the original ideas in a
second brain where they may germinate and bear fruit. How familiar all
this is, and yet how perennially wonderful! The miracle of it is
sufficient excuse for this digression.
Now books, beside this modern form of distribution by loan, are widely
distributed commercially both by loan and by sale, and especially in the
latter form advertisement is now very extensively used in connection with
the distribution. In fact we have all the different types specified
above--economic, uneconomic and illegitimate, both through
misrepresentation and the harmful character of the subject matter. The
reason for all illegitimate forms of advertising is of course not a desire
to misrepresent or to do harm per se, but to make money, the profit to the
distributor being proportioned to the amount of distribution done and not
at all dependent on its economic value. Distribution by public officers is
of course not open to this objection, nor are the distributors subject to
temptation, since their compensation does not depend on the amount of
distribution. If they are capable and interested, furthermore, they are
particularly desirous to increase the economic value of the work that they
are doing. Since this is so and since the danger of uneconomic or harmful
forms of advertising is thus reduced to a minimum, there would seem to be
special reason why the economic forms should be employed very freely. But
the fact is that they have been used sparingly, and by some librarians
shunned altogether.
Let us see what library advertising of the economic types may mean. In the
first place it means telling those who want books where they may get them.
This simple task is rarely performed completely or satisfactorily. It is
astonishing how many inhabitants of a large town do not even know where
the public library is. Everyone realizes this who has ever tried to find a
public library in a strange place. I once asked repeatedly of passers-by
in a crowded city street a block distant from a library (in this case not
architecturally conspicuous) before finding one who knew its whereabouts;
in another city I inquired in vain of a conductor who passed the building
every few hours in his car. In the latter case the library was a beautiful
structure calculated to move the curiosity of a less stolid citizen. In
New York inquiry would probably cause you to reach the nearest branch
library, anything more remote than that being beyond the local
intelligence. Sometimes I think we had better drop all our far-reaching
plans for civic betterment and devote our time for a few years to causing
citizens, lettered and unlettered alike to memorize some such simple
formula as this: "There is a Public Library. It is on Blank street. We may
borrow books there, free."
You will notice that I have inserted in this formula one item of
information that pertains to use, not location. For of those who know of
the existence and location of the Public Library there are many whose
ideas of its contents and their uses, and of the conditions and value of
such uses, are limited and crude. The advertising that succeeds in
bettering this state of things is surely doing an economic service. All
these things the self-respecting citizen should know. But beyond and above
all this there is the final economic service of advertising--the causing a
man to want that which he needs but does not yet desire. Every man, woman
and child in every town and village needs books in some shape, degree,
form or substance. And yet the proportion of those who desire them is yet
outrageously small, though encouragingly on the increase. Here no
memorizing of a formula, even could we compass it, could suffice. This
kind of advertising means the realization of something lacking in a life.
Is the awakening of such a realization too much for us? Are we to stand by
and see our neighbors all about us awakening to the undoubted fact that
they need telephones in their houses, and electric runabouts, and
mechanical fans in hot weather, and pianolas, and new kinds of breakfast
food, while we despair of awakening them to their needs of books--quite as
undoubted? Are we to admit that personal gain, which was the victorious
motive that spurred on the commercial advertisers in these and countless
other instances, is to be counted more mighty than the desire to do a
service to our fellowmen and to fulfill the duties of our positions--which
should spur us on?
I am not foolish enough to suppose that by placarding the fences with the
words "Books! Books!" as the patent medicine man does with "Curoline!
Curoline!" we shall make any progress. The patent medicine man is right;
he wants to excite curiosity and familiarize the public with the name of
his nostrum. They all know what a book is--and alas the name is not even
unknown and mysterious--would that it were! It calls up in many minds
associations which, if we are to be successful we must combat, overthrow,
and replace by others. To many--sad it is to say it--a book is an
abhorrent thing; to more still, it is a thing of absolute indifference. To
some a book is merely a collection of things, having no ascertainable
relationships, that one is required to memorize; to others it is a
collection of statements, difficult to understand, out of which the
meaning must be extracted by hard study; to very few indeed does the book
appear to be what it really is--a message from another mind. People will
go to a seance and listen with thrills to the silliest stuff purporting to
proceed from Plato or Daniel Webster or Abraham Lincoln, when in the
Public Library, a few blocks away are important and authentic messages
from those same persons, to which they have never given heed. Such a
message derives interest and significance from circumstances outside
itself. Very few books create their own atmosphere unaided. They
presuppose a system of abilities, opinions, prejudices, likes and
dislikes, intellectual connections and what not, that is little less than
appalling, if we try to follow it up. Dislike of books or indifference
toward them is often simply the result of a lack of these things or of
some component part of them. We must supply what is lacking if we are to
arouse a desire for books in those who do not yet possess it. I say that
such a labor is difficult enough to interest him whose pleasure it is to
essay hard tasks; it is noble enough to attract him who loves his
fellow-man; success in it is rare enough and glorious enough to stimulate
him who likes to succeed where others have failed. Advertising may be good
or bad, noble or ignoble, right or wrong, according to what is advertised
and our methods of advertising it. He who would scorn to announce the
curative powers of bottled spring-water and pink aniline dye; he who
regards it as a commonplace task to urge upon the spendthrift public the
purchase of unnecessary gloves and neckties, may well feel a thrill of
satisfaction and of anticipation in the task of advertising ideas and of
persuading the unheeding citizen to appropriate what he has been
accustomed to view with indifference.
To get at the root of the matter, let us inquire why it is that so many
persons do not care for books. We may divide them, I think, into two
classes--those who do not care, or appear not to care for ideas at all,
whether stored in books or not; and those who do care for ideas but who
either do not easily get them out of storage or do not realize that they
can be and are stored in books. Absolute carelessness of ideas is, it
seems to me, rather apparent than real. It exists only in the idiot. There
are those to be sure that care about a very limited range of ideas; but
about some ideas they always care.