Ideal chemistry; a lecture

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IDEAL CHEMISTRY.

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BY

Sir B. C. BRODIE, Bart., D.C.L., F.R.S.,

Professor of Che??tistry in the University of Oxford,

2a^ = a + a^

MACMILLAN AND CO.

1880.

The Right of Translation and Reproduction is Reserved.

5 85 0

LONDON :

R. Clay, Sons, and Taylor,

BREAD STREET HILL, E C.

3T
H

PREFACE.

The following Lecture was delivered before
the Chemical Society on June 6, 1867, after
the presentation to the Royal Society of my
first Memoir on the Calculus of Chemical Opera-
tions. The Lecture, however, has not been
published except in a report which appeared
in the Chemical News of June 14, 1867. This
report I have in the main followed. It is,
however, far from presenting a satisfactory
account of the Lecture; and indeed, in several
important passages entirely fails to represent
my meaning. I publish this Lecture now,
partly that the views given in it may be correctly
apprehended, and also that I think it will
have a wider interest, and be more generally

appreciated by those who are curious in these

A 2

iv PREFACE.

questions than at the time it was delivered,
when the whole subject was new, and imper-
fectly understood. Also, although the Lecture
is short, it touches upon two or three topics
of fundamental importance, which I have not
elsewhere discussed in the same way. Of these,
there are three which I may especially indicate.
Firstly, the application which I have made of
the symbol xy regarded as a chemical symbol ;
secondly, the meaning to be assigned to the
term " ideal element," and lastly, the suggestion
which is here made, I believe for the first
time (excepting in the few words at the con-
clusion of Part I. of the Memoir referred to
above), of the possible decomposition, at the
elevated temperature of the sun, of certain
chemical elements, and of the existence in
that luminary of their constituents in indepen-
dent forms.

February iG, 1SS0.

IDEAL CHEMISTRY.

A Lecture delivered before the Chemical Society, on

Thursday, June 6th, 1867.

Mr. President, — I feel that I have undertaken
this evening a truly difficult task, to give to the
Chemical Society, in the brief space of one hour,
an account of an abstruse and difficult subject,
the exact comprehension of which requires that
it should be minutely considered in all its details.
I should not, however, shrink from this, if I did
not feel that the subject is really before those
even who are competent to judge of it, in a
somewhat imperfect form ; that I have as yet
offered to the chemical world the first part only
of the method of which I am about to speak ;
and that this method will be much better
comprehended, both from a mathematical and

6 IDEAL CHEMISTRY.

chemical point of view, when you have before
you the subsequent parts which I hope to
present hereafter.

I am to speak of a method of representing
the facts of chemistry, which is fundamentally
different from the method at present in use.
Let me say a few words upon the past history
of chemical theories.

I believe theory to be essential to the
existence of chemistry. The birth of the science
was inaugurated by the construction of a definite
theory of chemistry — the first theory which had
ever been proposed, and which sought to give a
definite and rational account of the facts of the
science. This theory was the once world-famous
doctrine of Phlogiston. In this theory the facts
of chemistry were explained by the agency of
a subtle, all-pervading, hypothetical principle, by
the transference of which, from one chemical
substance to another, it was assumed that the
facts of chemistry were correctly accounted for.
It is easy, from our present point of view, to pa
critical remarks upon the doctrine of Phlogiston,

IDEAL CHEMISTRY. 7

but it is not quite so easy really to comprehend
that doctrine and to put ourselves in the position
of those great chemists who worked and who
studied through its agency. If ever any one be
tempted to speak slightingly of the doctrine of
Phlogiston, let him remember that through the
instrumentality of this doctrine the great dis-
coverer of chlorine, the chemist Scheele, worked.
Let him remember that the exact mind of
Cavendish was contented with this doctrine. Let
him remember again that the illustrious Priestley,
that transcendentally inventive genius, in posses-
sion of this doctrine, made the great discovery
of oxygen : and that not only was he then con-
tented with this theory but that he died a firm
believer in and adherent to it. However, the
doctrine of Phlogiston, like many human surmises,
was destined to pass away — Lavoisier shattered
Phlogiston. For no inconsiderable period after
this chemists appear to have worked, if I may
so say, without a theory; that is to say, that,
as during the long alchemical ages chemists were
occupied in collecting together those facts which

8 IDEAL CHEMISTRY.

were afterwards to be embodied in the theory of
Phlogiston ; so for a period of above thirty or
forty years — that is to say, from the time of
Lavoisier to the time of Dalton — chemists were
employed in collecting together that exacter
system of facts which was to form the basis of
a far wider, and far more comprehensive theory,
namely, the great atomic doctrine. However,
Davy appears to have worked and to have made
his great discoveries without a theory. Davy
never admitted the atomic theory, but rested
content simply with the facts of numerical
analysis and the laws of combination deduced
from them.

In the year 1808 appeared that famous book,
A New System of Chemical Philosophy, which
contained the germs — indeed, I may say, almost
the full development — of the atomic theory itself.
In this atomic doctrine Dalton took up the
conception of combination, which was introduced
into the science by means of the theory of
Phlogiston. He took up that doctrine of com-
bination, and moulded it into a new and more

IDEAL CHEMISTRY. 9

definite form. It would be useless for me, before
the Chemical Society, to dwell upon the atomic
theory. It is a theory with which every one is
familiar, for every chemist of this day has worked
with that theory, has conceived his science
from the points of view of that theory ; and,
indeed, I believe, in the opinion of many, it
is almost impossible that that doctrine should
ever fall to the ground. This doctrine of
Dalton, however, was a doctrine far more
audacious than that of Stahl. In the theory
of Phlogiston, Stahl at least considered that he
had visible and palpable evidence of the trans-
ference of his Phlogiston from chemical system
to chemical system ; but Dalton told us that this
notion of the continuity of matter — that obvious
fact which our senses teach us — was simply an
illusion, and that, if only we could see things
aright, we should see that this world, which
appears to us so connected and so continuous,
was really made up of disjointed fragments.

From the point of view of the atomic theory,
chemists have worked for a period now of about

io IDEAL CHEMISTRY.

sixty years, and the progress of chemical theory
has consisted in the almost constant and unre-
mitting development of this doctrine. I cannot
say, however, that this has been an unremitting
progress. It has rather been a succession of
changes. System has followed system, doctrine
has followed doctrine ; but these doctrines have,
one after another, fallen to the ground. We
have had but little that is permanent, and at
the present moment the theory of chemistry is
built upon the ruin of other theories. Now no
one can have more respect for these great ideas
which were thus ushered into the science by
Dalton, than I myself have. It cannot be neces-
sary for me to express to this Society of
Chemists the admiration which I as a chemist
feel for that theory ; but, nevertheless, it is no
disparagement to say that I think the atomic
doctrine has proved itself unable to deal with
the complicated system of chemical facts, which
has been brought to light by the efforts of
modern chemists, and has not succeeded in con-
structing an adequate, a worthy, or even a

IDEAL CHEMISTRY. u

thoroughly useful representation of those facts,
although for sixty years the united efforts of
chemists, including many of the most able men
in science, have been devoted to the development
of this doctrine, and have founded their repre-
sentations upon it. Now, let me read to you an
account of the last modern representation of
the atomic doctrine, and the chemical symbols
in which the atomic doctrine has resulted. I
will read to you a paragraph headed " Glyptic
Formulae ; " it is given in a scientific journal,
The Laboratory. Here is the paragraph : —

" Those teachers who think, with Dr. Frankland
and Dr. Crum Brown, that the fundamental facts
of chemical combination may be advantageously
symbolized by balls and wires, and those prac-
tical students who require tangible demonstration
of such facts, will learn with pleasure that a set
of models for the construction of glyptic formulae
may now be obtained for a comparatively small
sum. At first sight the collection of bright-
coloured and silvered balls suggests anything
but abstract chemical truth." ....

12 IDEAL CHEMISTRY.

And so on. The writer proceeds to inform
us what we may procure for our money : —

"There are seventy balls in all for the re-
presentation of atoms — monads, dyads, triads,
tetrads, pentads, and hexads, being distinguished
by the number of holes pierced in the balls. To
connect these into rational formulae" — [which I
confess I should imagine to be a truly difficult
problem] — " brass rods, straight or bent, and
occasionally flexible bands, are employed."

However, the editor seems to have had some
misgivings, for he proceeds to say : —

" Whether they are calculated to induce erro-
neous conceptions is a question about which
much might be said/' Now, however much
might be said upon this subject, I certainly
am not going to say a great deal to the
Society about it ; but it is truly a remarkable
fact, that the atomic theory, after so many
efforts at completion should have resulted in
such a thoroughly materialistic bit of joiner's
work as this. Indeed I cannot but say
that the promulgation of such ideas — even the

IDEAL CHEMISTRY. 13

partial reception of such views — indicates that
the science must have got, somehow or another,
upon a wrong track ; that the science of chem-
istry I say must have got, in its modes of
representation, off the rails of philosophy, for it
really could only be a long series of errors and
of misconceptions which could have landed us
in such a bathos as this.

You may, however, ask me, and with reason,
" In what way, then, are we to represent the
facts of chemistry, if we are not to represent
them in this way ? Do you mean to deal with
this complicated system of facts, and to offer us
no mode of representing these facts, and no
mode of conceiving these facts ? " Now, I
quite admit that any person who seriously
attacks these ideas, is bound to show some
other, and, even some better way of representing
the facts. He is bound to do this, or to refrain
from his attacks. You ask me, how are we to
represent the facts of the science ? It is to that
question that I wish to offer an answer to-night.
I say that we are to express the numerical facts

H IDEAL CHEMISTRY.

of the science by means of symbols ; but I
attach to the term " symbol " a very special
signification. We have plenty of what are called
"chemical symbols'' already; but these chemical
symbols are not, from my point of view, symbols
at all, and you will presently see why. Now a
symbol may be regarded as a mark by which
we express the objects of our thoughts for the
purpose of reasoning about those objects ; and
one which is capable of being combined with
other similar marks according to certain definite
laws of combination ; which laws of combination
are to be possible, through the interpretation of
the symbol, in the subject matter which is
symbolized. That is what I mean by a symbol.

You will readily see that our present notation
really can hardly be called, even in courtesy, a
symbolic representation. The reason is, in the
first place, that these letters H, O, &c. are not
capable of being combined with other letters, or
other marks according to any definite laws ; and,
in the second place, so far are they from having
any definite signification or meaning attached

IDEAL CHEMISTRY. 15

to them, that every chemist thinks himself at
liberty to deal with them in this respect just as
he pleases, according to his fancy. I wish to
put a restriction upon that mode of dealing with
the subject, and to bring my fellow-chemists
and myself, when we have to deal with symbols,
under some definite rules. Symbols are of two
kinds. We may have symbols of things, and
we may have symbols of operations. Symbols
of operations are simply symbols of what we do
to things. Take a popular case; ordinary lan-
guage is an imperfect symbolic system, and here
we have just these two kinds of symbols. A
" dog " is the symbol of a thing, and " beating,"
" caning," " coaxing," and so on, are the symbols
of operations, or of something which we may do
to a dog. We have marks by which we express
things, and marks by which we may express
what we do to things. We might also have a
third kind of symbol ; we might have the
symbol of an operation and a thing together.

Now before I commence my explanations, I
should like to remove one or two popular errors

1 6 IDEAL CHEMISTRY.

upon this subject. I believe there is no error
more ingrained in the popular mind than that
the marks +, — , x, =, are necessarily the sym-
bols of adding, subtracting, multiplying, and
identification or equalization ; I mean that these
marks are purely arithmetical symbols, and are
to be used for purposes of arithmetic alone, and
that in any other subject matter to which they
are applied it is essential for us to give these
symbols their arithmetical signification. If that
were true, the application of symbols to the
science of chemistry in any extended sense
would simply be, from my point of view, an
impossibility.

Perhaps I shall best illustrate this matter by
giving you from another subject an example of
the mode of constructing a symbol and of what
we mean by a symbol. It is an example which
will bring before you clearly how independent
the application of symbols is of arithmetical
meaning and interpretation. I say of arithmeti-
cal meaning not of arithmetical laws, which is
another thing. In the ordinar\- ometrical

IDEAL CHEMISTRY. 17

interpretation of algebra we denote by the mark

a the operation of conferring upon the unit of

length a certain specified length. To fix our

ideas let us take this length as three inches.

The mark a then, will thus stand for a

straight line, three inches in length. Now the

symbol + is what may be termed a directive

symbol and indicates to us the direction in

which the line a is to be drawn towards, let us

say, some specified point in the horizon. Hence,

if the line AB

A B

a
be a line three inches long, AB will be properly
represented by the letter a, and + a will repre-
sent that line drawn from A to B ; and assum-
ing, as I said, the symbol — to be similarly a
directive symbol, telling us to draw the line in
the opposite direction to that indicated by +,
— a will indicate a line three inches long drawn
from A to C

CAB

— a + a

B

1 8 IDEAL CHEMISTRY.

Similarly, by the mark b we may represent a
line five inches long, drawn in the same direction
as a. Now, if we ask the meaning of the ex-
pression a -f- b or + a + b, the symbols inform
us, putting BC as a line five inches long, that
we are to commence by drawing as before from
A to B the line a, and then to proceed to
draw another line from B to C equal in length
to by as indicated below :

ABC.

a

It follows that a + b = b + a and + a + b =

+ (a + /;), since it is indifferent as regards the
total length and direction of the line, whether
we commence by drawing the line a and con-
tinue by drawing b, or commence with /; and
then proceed to draw the line a ; one peculiarity
of this treatment of the subject, which is the
ordinary geometrical application of algebra to geo-
metry, being that we may always replace, without
affecting the truth of the statement, the letfa

IDEAL CHEMISTRY. 19

a and b by the arithmetical value of the length
of the lines indicated by them.

We might also have argued thus : Let a be
the operation performed upon a point by which
a straight line three inches in length is generated.
This operation is the transference of a point from
one position to another without changing the
direction of the transference. Again, let + be
a directive symbol indicating the direction in
which the transference occurs. We have then,
referring to the figures above, + a as the symbol
of the transference of a point from A to B, by
which the line AB or #, is generated, and + b
the symbol of the transference of a point from
B to C, by which the line BC or b, is generated.
A little consideration will show that the laws
previously enunciated, a + b = b + a, + a -h b
— + (a + b), hold equally good with this inter-
pretation as with that previously given. In this
case also we can always substitute for the letter
by which the line is represented, the number
which expresses its length. It is, however, to
be noticed that we cannot, by the instrumentality

B 2

20 IDEAL CHEMISTRY.

alone of the symbols hitherto employed, express
lines drawn in any other direction than that
indicated by the symbols + or — , namely, lines
drawn in a specified direction and the opposite
of that direction.

But another kind of algebraical geometry has
been invented (what is termed double algebra),
in which the symbols a, b, c, and so on, indicate
to us not length alone but direction also,
and are to be interpreted as the operations of
conferring upon the unit of length, not only
certain lengths, but certain lengths in any speci-
fied direction. So that, taking AB as s. line
three inches long, drawn in the direction indicated
by the operation a, and A C as a line five
inches long, drawn from the point a in the direc-
tion indicated by the operation b, the symbols a
and b will indicate the lines AB, AC, as shown
in the annexed figure :

IDEAL CHEMISTRY. 21

and the same principle of interpretation will
prevail in the case of any number of symbols
a, bj c> d, e.

It is to be observed that in this method lines
are said to have the same direction which are
parallel to one another. This method is termed
Double Algebra, " from its meanings requiring
us to consider space of two dimensions (or area),
whereas all that ordinary algebra requires can
be represented in space of one dimension (or
length)." x

Let us now consider how, on these principles,
the symbol a + b is to be interpreted, a tells
me to draw a line from the starting point, the
line A By three inches long. The symbol + b
tells me to go on and draw at the termination
B of the line AB the line BC (in the direction
indicated by b) five inches long, which we may
consider effected in the figure below. The direc-
tion of the line b being here assumed to be

1 De Morgan, Trigonometry and Double Algebra, 1849,
p. 117.

22 IDEAL CHEMISTRY.

that of a line inclined to a at an angle of

35°.

Join AC Now, I say that the line AC re-
presents and is identical with the result of the
algebraical sum of the operations a and b, that
is, a + b} or, which is the same thing, + a + b.

The reason of this statement may be thus given.
Regarding a and b as the symbols of the opera-
tions of the transference of points by which the
straight lines AB and BC are generated, the
straight line AC is generated by the aggregate
of these operations ; the result being precisely
the same in both as regards the direction and
quantity of motion whether we transfer the point

IDEAL CHEMISTRY. 23

from A to B along the straight line AB and
then by a second transference from B to C
along the straight line BC> or transfer the point
immediately from A to C along the straight
line AC. This diagonal, however, is not equal
in length to the sum of the sides of the paral-
lelogram ACy but nevertheless this statement is
correct ; what we here denominate addition
being truly not addition of magnitude to pro-
duce magnitude, but junction of effects to
produce joint effect.1

Those persons, however, who consider it neces-
sary that all algebraical symbols should admit
of an arithmetical interpretation, must, if con-
sistent, reject an algebra founded upon these
principles.

We may note in passing, that these observa-
tions apply to the geometrical application of
algebra alone. In the application of algebra to
mechanics, for example, the diagonal actually
represents, not only from the point of view of
algebra, but also of arithmetic, the aggregate of
1 De Morgan, lib. cit.> p. 118,

24

IDEAL CHEMISTRY.

the forces represented by the sides of the paral-
lelogram. Here is not the place to pursue this

-a

subject, but the above diagram will convey all
the information in regard to it necessary for my
present purpose.

IDEAL CHEMISTRY. 25

Having made these few observations in refer-
ence to symbols in general, let me proceed to
explain more precisely what I mean by a
chemical symbol. The object, I should say, of
the first part of this method (to which I must
refer you for fuller explanations) is mainly to
discover a proper system of symbols by which
we may express the units of chemical substances.
I may put this in another way, and say that
we wish to discover what is the nature and the
number of the operations by which chemical sub-
stances are made or constructed. That is the
first object of our method. I should, perhaps,
limit myself a little further, for I should say
that (in order to fix our ideas) before we begin
to consider such questions at all I shall conceive
of chemical substances as brought into the con-
dition of perfect gases. The main reason of this
is the simplicity of the laws to which gaseous
compounds are subject, which simplicity was first
discovered by the great chemist, Gay-Lussac, and
which greatly facilitate the study of the question.
Of course, we may, if we please, deal with the

26 IDEAL CHEMISTRY.

properties of the combinations of solids and
liquids, and regard the units of matter as exist-
ing in these forms. But here it is far more
difficult for us to arrive at any intelligible and
simple results ; and therefore, before beginning to
think about the transformations of a chemical
substance, I, for my part, always conceive it as
brought into the condition of a gas. And to go
a little further, and to speak a little more defi-
nitely still, we shall always consider the chemical
substance as brought into the condition of a
gas, as the standard temperature of o degrees,
and at a pressure of 760 millimetres. The units
of all chemical substances are thus regarded
from the same point of view, without which no
comparison of these changes is possible. This is
the sort of chemical world with which wc have
to deal, a world of gases.

First, let me give you the definition of a unit
of matter; for it is absolutely essential, before
we attempt to assign symbols to units of matter
to know precisely what we mean by the unit
which we arc about to consider and symbol:.

IDEAL CHEMISTRY. 27

That definition is of such great importance that
I have had the words placed up before you in
a diagram.

The unit of ponderable matter ; is that portion of
ponderable matter, zvhich, in the condition of a
perfect gas, at a temperature of o degrees, and at
a pressure of 760 millimetres of mercury, occupies
a space of 1,000 cubic centimetres.

From considering the unit of matter, I pass
now to the consideration of a unit of another
kind, and that is what I have termed the unit
of space, which is the volume of 1,000 cubic cen-
timetres of empty space. Now, we cannot work
on this method until we have got hold of this
unit of space, which is the subject on which the
chemical operations by which the units of matter
are constructed, are performed, and constitutes a
fundamental conception peculiar to this calculus ;
let us therefore endeavour clearly to understand
what the unit of space means. Now, that there
may be no doubt upon this point, I have brought
you a very good image of the unit of space
which is represented by this hollow cube with

28 IDEAL CHEMISTRY.

glass walls, and of the dimensions above
assigned to the unit of space.

You must, however, go a step further. It is,
indeed, the space of 1,000 cubic centimetres which
is confined within these glass walls ; but, before
you can get at the unit of space, you must, by
the process of imagination, or by the efforts of
reason, divest this cube of glass of weight, and
take out of it all the ponderable matter which it
contains, and conceive the space within its walls
divested of matter altogether. Now, this unit of
space is fundamentally important to us, and
I shall begin by giving it a mark to itself. The
mark which I give to that unit of space is for
certain good reasons which I will not explain
now, but which I have fully given elsewhere,
the mark I. When you see that mark, it is to
recall to your mind the matter contained in the
unit of space. Now, what is that matter ? Ob-
viously, as there is no ponderable matter in it,
that matter is no matter at all. The mark 1,
therefore, is the symbol of the unit of no
matter.

IDEAL CHEMISTRY. 29

Perhaps, however, if I were to speak a little
more precisely, I should say, for the benefit of
those persons who may be more philosophically
inclined, that the mark 1, from the point of view
of operations, is to be defined- as the symbol of
the operation of taking the unit of space as it
is. The symbol 1, therefore, tells us to take the
unit of space as it is, and do nothing at all
with it.

However, we have not to consider units of
space, the consideration of which alone would
lead us to very little, but we are going to consider
the units of matter. Now, how are we to conceive
of space becoming matter, or of matter getting
into space — chemically, I mean ? I shall think
of this through the aid of an operation, and I
shall define by a mark the operation by which
this empty unit of space is turned into a unit of
ponderable matter. For example, I will take x
as such a mark. This is the mark of the operation
by which the unit of space becomes a unit of
ponderable matter of a certain specified kind and
density.

30 IDEAL CHEMISTRY.

Assuming, then, x as the symbol of such an
operation ; how are we to symbolize the per-
forming of this operation upon the unit of space ?
I shall do this in the usual way in which the
performance of operations on any given subject is
symbolized, by writing the letter x before the
symbol of the unit of space, thus : x I, and that
indicates to me a unit of matter of a certain
kind x, at o° C. and at 760 millimetres pres-
sure.

But we may be called on to represent a unit
of matter double the density, but the same in
kind as x. How i$ this to be effected ? Having
once conferred upon the unit of space this den-
sity x, we have then to perform the operation
x a second time. Hence, to double the density
we have only to write x again ; thus, x x 1, or
x1 1. This will symbolize that we confer on
the unit of space a certain density, and having
done that, we confer that density on it again ;
that is, we make it double the density. Similarly
xxx 1, or x2 1, will mean that we give it three
times the density, and so on. If you compare

IDEAL CHEMISTRY. 31

these operations with the symbols which express
the densities, you will see that the symbols of the
units of matter which we have thus constructed
stand to the numbers which express the densities
of that matter, in the same relation as numbers
to their logarithms.

We will now take another kind of matter:
y 1, y2 1, y3 1. These, again, would be the sym-
bols of portions of ponderable matter which
would be contained in this glass box at the
pressure and temperature before-named of the
kind indicated by y, and of the relative density
indicated by the number of units of y. In these
cases we have considered the construction of
matter of one kind, but of different densities.

If we proceed further upon the same lines we
come to consider the symbol of units of space
containing two kinds of matter. Reasoning on
the same principles as before, we have xy 1 as
the symbol of the unit of space containing the
matter of x, and also containing the matter of
y ; that is to say, having the density which is
the sum of the densities of x and y. And, we

32 IDEAL CHEMISTRY.

can in this way symbolize also the unit of
space filled with the matter x and y in various
proportions.

You will see that there is a real analogy
between the symbols which I am here employing,
and the symbols which I used just now in my
illustration derived from double algebra : we have
the chemical symbol xy, the product of two
chemical operations subject to the same alge-
braical laws as the arithmetical symbol x y, the
product of two numbers, but with a totally
different interpretation ; and just as the symbols
of double algebra indicate to us, not only the
length of a line, but also its direction or position,
so these chemical symbols indicate to us, not
only the weight, but also the kind of matter.
You are not to confound them with the numbers
which express the densities, or the letters by
which we might express those numbers; but
they are, I say, symbols which express to us,
at one and the same time, the nature of the
matter and the density of the matter, having
this double signification.

IDEAL CHEMISTRY. ^o

Before we go further, let me say a word about
the nature of these operations x, yy and the
like ; I am here symbolizing the unit of matter
by the aid of the symbols of the operation by
which the unit of matter is made. The question
arises, what is that operation ? The operation
is one which, speaking with a certain degree of
freedom, I may term a "packing" operation. It
is the operation by which matter is " packed "
into space, being, in fact, the operation with
which every chemist is familiar under the name
of combination, which is an operation precisely
of this kind. But it is necessary for the
comprehension of the methods of this calculus
to enlarge our view of the nature of combination
so as to include under this term (what is truly
included under the same fundamental conception),
not only the combination of matter with matter,
but the combination also of matter with space.

We are getting thus at a definition of our
unit in terms perhaps more in accordance with
ordinary language. We will call the matter of
x} A, and the matter of y, B ; and the matter of

C

34 IDEAL CHEMISTRY.

the unit of space O. What, then, does x stand
for, considered from the point of view of com-
bination ? It is the operation of combining the
matter A with any substance which we please
to write after the symbol of the letter ; and
y is the symbol of similarly combining the
matter B. Now, if we write x before the sym-
bol of the unit of space I, thus: xi, x I tells
us that we are to take the matter A and
combine it with the matter of the unit of
space, that is to say, to pack it into that
empty box which I have symbolized as I, the
result being to constitute the matter A. If,
having done that, I write y to it, thus : x y I,
this symbol tells me to take the matter />
and combine that also with the matter of the
unit of space. If you do that, the result is
the matter of A combined with the matter of
B and the matter of the unit of space o. That
is to say, those three things are combined together.
Do not imagine there is anything mysterious
about these terms. They arc operations about
which you think even' da)' of your life ; and,

IDEAL CHEMISTRY. - 35

if you want to think to any purpose about
chemistry by means of symbols, you must em-
body in your symbols the very thing which you
are thinking about, namely, the processes with
which you have to deal.

If some curious person wishes to penetrate
further still into the problem, and inquires in
what the operation of combination consists, the
only kind of reply I can make to him is to

show him the result of combination and to ex-
plode, we will say, 2 vols, of hydrogen, and
I vol. of oxygen, and exhibit to him the 2 vols,
of water which is the result of this experiment.
The combination, I say, of 2 vols, of hydrogen,
and 1 vol. of oxygen, being merely the name
given to the operation performed upon these
quantities of these gases which produces this
result. Various hypotheses, both metaphysical
and atomic, have been framed to explain what
combination consists in, but such hypotheses have
not, at least in my judgment, thrown the slightest
light upon the question.

The views of chemists as to the use of the

C 2

36 IDEAL CHEMISTRY.

apposition of letters as the symbol of combination
are of a very vague character. Berzelius, the
author of our present notation, regarded the
expression HC1 as an abbreviated form for
H -f CI. The late Sir John Herschel was very
unwilling to admit the expression at all, and
took the same view of it. The statements made
on the subject in some of our chemical manuals
are almost unmeaning. All that it is necessary
to say on this point is that a system of chemical
symbols which contains no distinctive symbol
of combination, omits the most essential point
to be considered, and that an indefinite sym-
bolism to which no exact meaning is attached
is necessarily of little value.

I must not seek to explain to you now the
process or method by which we arrive at the
symbols of chemical substances, that is to say,
why I write the unit of hydrochloric acid as
a% and the unit of chlorine as a%\ To explain
the process on the board, and to do it any
justice, would occupy far more time than is at
my disposal, and it has been fully explained

IDEAL CHEMISTRY. 37

elsewhere. I will only ask you to allow me now
simply to explain wrhat we mean by the sym-
bols of chemical substances in one or two
special cases, and then to consider the general
results to which this mode of representation
conducts us.

As to the mode of constructing these symbols,
it is quite a mistake to suppose that our sym-
bols are the result of invention or hypothesis.
They are based in the most absolute sense
upon facts. We do not imagine or invent a
symbol at all. We look for the symbol and
find it. But where are we to look for the sym-
bols of the operations by which units of matter
are made ? Plainly in the very facts of com-
bination, to which I have just now referred.
That is the source, and the only source open
to us, whence to derive the symbol. The
facts referred to in the case of gaseous com-
binations are such as these : 2 units of hydro-
chloric acid consist of the same ponderable
matter, as 1 unit of hydrogen, and I unit of
chlorine ; 2 units of gaseous water consist of

38 IDEAL CHEMISTRY.

the same ponderable matter as 2 units of
hydrogen and I unit of oxygen. Again, 2 units
of ammonia consist of the same ponderable
matter as 3 units of hydrogen and 1 unit of
nitrogen. These are the facts, and chemistry
supplies us with a large number of such facts.
The method which I have ventured to give is
merely a method of expressing these facts in
the symbol of the substance. It is simply and
purely, I say, a method of taking an equation
expressing a chemical metamorphosis, and of
embodying in the symbol certain facts of the
equation. Through the facts of the equation
we construct the symbols of the units of pon-
derable matter. We then take the symbols out
of the equations, and thus separate and analyse
the facts one from the other. It is an analysis
of a peculiar kind.

I have constructed some tables expressive of
the general nature of the conclusions at which
we arrive through the aid of this method, as to
the composition of these units of matter. I have
had a good many of these symbols written out,

IDEAL CHEMISTRY. 39

for really it is easier for you, by looking at these
tables, to see the general results which we arrive
at by this method, than it would be for me to
enter into a long explanation of the process.
Here you see are the symbols of the chemical
substances. We start with the symbol of the
unit of space : —

Symbols of the Units of Chemical

Substances.

Unit of Space 1

Hydrogen a

Oxygen . f2

Water . . . af

Peroxide of Hydrogen . . . a£2

Sulphur 02

Protosulphide of Hydrogen . . a0

Bisulphide of Hydrogen . . . aO2

Sulphurous Anhydride . . . Of;2

Sulphuric Anhydride .... Of;3

Sulphurous Acid a6P*

Sulphuric Acid a0^

Chlorine aX2

40 IDEAL CHEMISTRY.

Hydrochloric Acid ax

Hydrochlorous Acid .... ayj;

Chlorous Acid «%|2

Chlorosulphurous Acid . . . a^20£

Hypochlorosulphurous Acid . «%#£3

Chlorosulphuric Acid .... a^B^2

Iodine aw2

Bromine a/32

Nitrogen av2

In the next Table is another system of symbols,
those of the combinations of carbon, hydrogen,
and two or three other elements : —

Carbon k

Acetylene ax1

Marsh Gas a2 k

defiant Gas a2/c2

Carbonic Oxide k%

Carbonic Acid /cp

Alcohol a3*2!

Ether a*Vf

Glycol aVJ£2

Glycerine a4/cn£

IDEAL CHEMISTRY. 41

Anhydrous Acetic Acid ... . aVf 3

Tetrachloride of Carbon . . . a2^tc2

Chloroform a2%s/c

Chloracetic Acid a2%/c2|2

Trichloracetic Acid .... a2xS/c2£2

Chloride of Benzoyl .... cl^x^^

Cyanogen clv2k2

Hydrocyanic Acid .... avic

Methylamine a2vfc

Mercuric Ethide a5/c4S

You must regard these symbols as being, if I
may so say, chemical equations turned into another
form, and divested of a certain amount of super-
fluous and useless matter, which we do not want
now to consider or think about. Nature does
not supply us with the key-note to enable us to
construct any one system of chemical symbols,
necessarily true to the exclusion of every other
system. Nature does not tell us absolutely —
though I think she does tell us probably — how
we are to proceed to construct such a system.
In order to be able to construct a chemical system

42 IDEAL CHEMISTRY.

we must start with an hypothesis. As we go on
constructing our symbols, our hypothesis, in so
far as we prove it, approximates more and more
to fact ; but we must, at any rate, start with the
assumption that we know one symbol. We may
construct a complete chemical system from one
symbol ; and we may view all these symbols as
the result of one hypothesis, combined with the
facts given to us and supplied by the equations.
Now, the hypothesis here made is that the sym-
bol of the unit of hydrogen is expressed by one
letter, a That is my starting-point ; and I
should say that the symbols which you see in the
tables, as indicating simple chemical operations,
and expressed by one letter, are to be regarded as
symbols of primary operations, that is to say,
operations which you cannot resolve or decompose
into any other operations by known methods.

They are symbols of primary operations ; and
when I say that the symbol of hydrogen can be
expressed in chemical equations by one letter, I
mean that in the changes and transformations of
chemistry that unit of hydrogen is never broken

IDEAL CHEMISTRY. 43

up ; that it moves as a whole from system to
system, and is never decomposed or resolved into
parts. Hydrogen is constructed at once, by one
operation. Imagine yourself witnessing the for-
mation of hydrogen. To form some substances
you want many operations ; but to form hydrogen
you want only one operation. That [striking a
blow on the glass model of the unity of space]
represents the formation of hydrogen — one opera-
tion. It is one act. If we could witness chemical
transformations, and nature should become vocal
to us, and indicate each combination as it occurred
by a musical note, that [again striking a blow]
is what you would hear when hydrogen was
formed. Now, as we go on we come to much
more complex substances. Let us take oxygen.
This is a substance very different indeed from
hydrogen in its chemical properties ; and as you
can conceive of the unit of hydrogen being made
at once by one operation, so I say that it is
impossible for you to conceive of the unit of
oxygen being made by less than two operations.
To return to our metaphor. When you take water

44 IDEAL CHEMISTRY.

and decompose it, so that oxygen is formed, you
ought to hear two notes. That is what I mean
when in this language I say that oxygen is made
by two operations. Again, the unit of water is
made by two operations like the unit of oxygen ;
but it differs from the unit of oxygen in this
respect, that one of those operations is the same
as that by which hydrogen is made. That is to
say, in the operation by which water was formed
you would hear two notes, one different from the
other, a, £.

The symbol of chlorine is a^2. Chlorine, from
this point of view, is to be conceived as made up |
by three operations. You are to hear ^, ^, a. One
of these operations is the same as that by which
hydrogen is made, and the other is an operation
peculiar to chlorine itself, namely, %. Again, a
unit of hydrochloric acid is to be conceived of as
made by two operations, a and %.

To go one step further : let me refer you to
this Table : —

Nitrogen av*

Ammonia a'V

IDEAL CHEMISTRY. 45

Protoxide of Nitrogen . . . ai>2£

Nitrous Acid ...... avf

Nitric Acid ai>£3

Phosphorus a<2(p4

Phosphide of Hydrogen . . a2<£

Hypophosphorous Acid . . a2$|2

Orthophosphoric Acid . . . a2<£J4

Terchloride of Phosphorus . cf^y*

Pentachloride of Phosphorus . a3^>%

5

Nitrogen is to be conceived of here as made by
three operations, vy v, a. In the formation of the
unit of ammonia also three operations concur ; one
of them being one of the operations of nitrogen,
vy and the other two being the operations by which
hydrogen is formed, a.

I must not enter into further details upon this
subject, but I have little doubt that, with this
explanation, you will readily appreciate the mean-
ing of the symbols which are written up before
you. You will see that, by following this process
of taking the facts of the equations and turning
them into the language of symbols, we arrive at

46 IDEAL CHEMISTRY.

a peculiar view as to the nature of matter, which
view is embodied in those symbols.

Now, as to the view of the nature of the
elemental bodies which is here indicated ; for that,
perhaps, will occur to many persons as the most
important point to be considered, for, seeing that
it is out of these elemental bodies that everything
else is made, and that into them all things are
capable of being resolved ; the view which we take
of these bodies gives us implicitly the view which
we are to take of the composition of every other
body whatever. To understand this it is only
necessary to appreciate the view which is here
given of the nature of the elements themselves,
and everything else follows from that. We are
led to the following singular results, — that,
speaking generally, there are, perhaps, four — and
certainly, at least three — fundamentally distinct
classes of elements.

First of all, the elements, the units of which are
made by one individual operation. These bodies
are represented to us by mercury and hydrogen.
To this class also probably belong such elements

IDEAL CHEMISTRY. 47

as zinc, cadmium, and tin ; but we cannot speak
with great confidence on that point.

Secondly, we have a class of, so to say, double
elements formed by two similar operations ; these
are such as oxygen, f2, sulphur, &2> selenium, A,2.
Carbon we are not certain about ; it belongs, in
all probability, to the first or second class, we do
not quite know which ; but I have symbolized it
as tc2.

But we have another and a very large class —
perhaps the largest of all the groups of the ele-
ments— and we may take the elements chlorine
and nitrogen as representatives of it. Here is
the symbol of the element chlorine, a%2 ; here is
nitrogen, av2 ; here is iodine, ato\ and so on. You
will see that the symbols of these elements occupy
a certain intermediate portion between the group
of elements, a, S, f, &c, and the group of ele-
ments £2, ff\ X2, &c. We have many compound
substances which are in every way analogous to
this group of elements — analogous as to their
properties, analogous as to their symbols. Of
this class we have a most interesting and striking

48 IDEAL CHEMISTRY.

example in the peroxide of hydrogen ; which is
symbolized here as a£2. You see the peroxide
of hydrogen is really to be regarded as the com-
bination of one unit of the element hydrogen with
one unit of oxygen — which things really exist, —
just as the element chlorine may be regarded as
a combination of the unit of hydrogen a with the
unit of a substance which does not exist, and
which I have symbolized as %2. The unit of
nitrogen is to be regarded as similarly composed,
av2. We may regard it as a combined with the
unknown element v.

There is one question which must occur to
every one, the explanation of which is of funda-
mental importance to the comprehension of this
system. You may ask me, " What reality do you
attach to these symbols? When you call chlorine
a^ ; nitrogen, av2 ; oxygen, fa ; do you make the
hypothesis that there are certain real bits of
matter actually, or even possibly, existing capable
of being brought to the lecture-room and exhibited
on the table — bits of matter which you represent
by a, % v, and the like; do you mean this ? or i

IDEAL CHEMISTRY. 49

you mean that these things do not exist, that they
are the mere creation of your imagination, fictions,
illusions ? We like Dalton," perhaps you may say
to me — "we like Dalton far better than we do
you ; for Dalton made no such claims on our
imagination. He, at any rate, was intelligible, and
dealt with realities, or possible realities, alone.
He showed us the elemental matter of which all
substances are made ; and even in his atoms
Dalton dealt with what he believed to be realities.
Neither he nor we indeed have ever seen these
things ; yet, nevertheless, we most perfectly believe
them to exist. To impress their reality upon the
mind Dalton drew pictures of them, and made bits
of wood to represent them ; by which he certainly
went so far as to express his belief that they were
real material things of definite form. Now can you
also do this for us ? can you show us the matter
of which these elements, £, % co, v . . . . consist ?
Will you take a piece of chalk and draw upon
that board some picture, or figure, or diagram to
render clear to us what these things are ? " To
these perplexing questions I cannot give a direct

D

So IDEAL CHEMISTRY.

answer. The symbol of a simple weight is not
necessarily the symbol of a real thing. I have
never assumed it to be so, and I have never
attempted to prove it to be so. I cannot draw a
picture, or represent by a model the structure of

a thing which is not real. On the other hand,
these symbols are not the creation of my imagi-
nation. I did not invent them ; I only found them
in the course of an analytical process. It is,
therefore, equally untrue to speak of them as un-
real, for I do not know this to be the case. Now, a
thing which is neither real nor unreal, but may be
either, is that which I here term an " ideal " thing ;
and for this reason I speak of the factors by which
in this calculus the symbols of the units of matter
are expressed as " Ideal" factors, and in this they
essentially differ from the corresponding represen-
tations, afforded by the atomic theory, which,
being a theory or hypothesis as to the constitution
of matter, deals with realities alone. The essen-
tial point is that in this calculus it is not necessary
to pronounce any further opinion upon this ques-
tion, for it is proved that, so far as all analytical

IDEAL CHEMISTRY. 51

ends are concerned in considering and reasoning
upon the problems of chemistry by means of
analytical processes, it is totally unnecessary to
raise this question, and we may confidently deal
with the ideal factor as with real factors, satisfied
that we cannot be led into error by so doing.
The ideal weight is a thing which may exist or
may not exist, as an external reality, but for
those purposes of reasoning with which we are
here concerned it satisfies all the analytical con-
ditions supplied to us by chemical equations, and
we are bound to accept it as a member of the
general system of symbols.

I will venture to give you an illustration on
this subject which was suggested to me by some
remarks of Professor G. G. Stokes, with whom I
have had the great advantage of discussing
several of these abstruse questions. The fol-
lowing statement is a mathematical truth invari-
ably admitted : every straight line cuts every conic
section in two poiiits. This assertion may be con-
sidered to correspond to my statement that the
unit of every chemical substance is compounded

D 2

52 IDEAL CHEMISTRY.

of an integral number of simple weights. But
you say, " Do you mean that every straight line
cuts every conic section in two real points ? If
so, you should be able to explain by means
of a geometrical diagram how and where it
cuts it." To this I reply, that my assertion
cannot be represented at all by means of a
geometrical diagram : that the statement is not
a geometrical but an algebraical truth. I never
said that the straight line really cut the conic
section at all. I said that it ait the conic
section, and I will supplement my previous
statement by saying that every straight line
cuts every conic section in two points, which
are real, coincident, or imaginary. Similarly,
I say that every unit of matter is made up of
an integral number of simple weights not nee
sarily real, but which may be cither real or
imaginary, although we have not the data to
determine to which class they belong. Now, as
the statement that every straight line cuts every
conic section in two points is not a geometrical
but an analytical, or symbolical truth, and we

IDEAL CHEMISTRY. 53

cannot, speaking generally, and without reference
to a particular case, draw a geometrical diagram
indicating these points, so also in the simple
weights of chemistry we cannot draw on the
board visible pictures to represent them. This
is possible in the case of the Daltonian atom.
But the only possible representation of the
simple weights of this calculus is the symbols
by which they are expressed in the analytical
system of which they are members, and any
other representation must necessarily mislead.

Now, although it is essential carefully to
discriminate between the symbolical expression
employed in this calculus, and any physical
hypothesis based on this analytical expression,
yet we cannot altogether disregard the alterna-
tive that the portions of matter symbolized by
a, % f* , v . . . . may be real physical existences.
This hypothesis cannot be established by means
of any symbolical calculus, for we cannot infer
because the symbol of chlorine may be ex-
pressed in every chemical operation by the three
letters a, %, ^, that the matter of chlorine is

54 IDEAL CHEMISTRY.

made up of three real distinct bits of matter
into which in chemical transformation it is re-
solved, and which are capable of a real and
independent existence ; but, nevertheless, there
are very forcible reasons which (when once we
are in possession of this symbolical system)
lead us to suspect that chemical substances are
really composed of a primitive system of ele-
mental bodies, analogous in their general nature
to our present elements, some of which we
possess, but of which we possess only a few.
I will take the case of peroxide of hydrogen.
Neglecting oxygen and a great class of oxy-
genated combinations, I will suppose for the
moment that I have these combinations in my
hand — hydrogen, water, peroxide of hydrogen,
and certain other substances which I could specif}-.
If I were to apply my method to finding the
symbol of peroxide of hydrogen, not regarding
the oxygen at all, the symbol at which we should
arrive for peroxide of hydrogen is af2. Then
the same question would arise about peroxide of
hydrogen as now arises about chlorine, namely,

IDEAL CHEMISTRY. 55

whether the bit of matter represented by £ were
real or imaginary. In the case of peroxide of
hydrogen we have, however, really succeeded in
separating the elements which it contains, and
this fact among others leads us to the suspicion
that some of these bodies which we speak of as
elements may in fact be compounds. In short,
we are led, through our method, to a certain
physical hypothesis as to the origin and causes
of chemical phenomena.

Now, what I am going to suggest you must
consider to be put before you with reservation,
but we may conceive, that, in remote time, or in
remote space, there did exist formerly, or pos-
sibly do exist now, certain simpler forms of
matter than we find on the surface of our globe
—a, %, £, v, and so on — I say, we may at least
conceive of, or imagine, the existence, in time
and space, of these simpler forms of being, of
which we have some records remaining to us in
such elements as hydrogen and mercury. We
may consider that in remote ages the tempera-
ture of matter was much higher than it is now,

56 IDEAL CHEMISTRY,

and that these other things existed then in the
state of perfect gases — separate existences — un-
combined. This is the furthest barrier to which
in the way of analysis theory can reach. Beyond,
all is conjecture. There may be something
further, but if so, we have no suspicion of it
from the facts of the science. We may, then,
conceive that the temperature began to fall and
these things to combine with one another and
to enter into new forms of existence, appropriate
to the circumstances in which they were placed.
We may suppose that at this time water (a£),
hydrochloric acid (a^)» and many other bodies
began to exist. We may further consider
that, as the temperature went on falling, certain
forms of matter became more permanent and
more stable, to the exclusion of other forms.
We have evidence on the surface of our globe
itself, of the permanence of certain forms of
matter to the exclusion of others. We may
conceive of this process of the lowering of the
temperature going on, so that these substances,
ax2, and ar, when once formed, could never be

IDEAL CHEMISTRY. 57

decomposed — in fact, that the resolution of these
bodies into their component elements could
never occur again. You would then have some-
thing of our present system of things. You
might further imagine that it would be possible,
on looking carefully at chemical equations, and
minutely studying them, to recover from the
equations the record of the truths which were
buried and preserved in the equations ; and
some analyst might come and say, "These equa-
tions are only consistent with this hypothesis,
that chlorine is composed of a and j^2," or, at
least, it might be said that the equations are
consistent with that hypothesis, for I do not
want to go further than that. We can conceive,
I say, of such a state of things. Now, this is
not purely an imagination, for when we look
upon the surface of our globe, we have, as 1
said before, actual evidence of similar changes in
nature. We talk of the elemental bodies as
though they were existing things ; but where
are they ? We have oxygen, nitrogen, sulphur,
certain metals, and certain bodies which we

58 IDEAL CHEMISTRY.

could specify, but what has become of the
others ? Where is hydrogen ? Where is chlo-
rine ? Where is fluorine ? Where are these
things ? They are locked up in combination in
such a way that it is only within the last
hundred years that the art of the chemist has
revealed them to mankind. Now, if in our
globe there had been more hydrogen — if there
had been an excess of hydrogen present in the
matter from which our globe was made — and
if we suppose it to be true that the gases con-
dense in the solid matter of our globe, we cannot
doubt that the whole of the free oxygen would
have been carried away from our planet, and that
we should have had simply oxygen stored up in
the form of water. We should have had water,
but no oxygen at all ; the hydrogen would have
combined with it and carried it all away.

When we look at some of the facts which
have been revealed to us, by the extraordinary
analyses which have been made of the matter of
distant worlds and nebuLne, by means of the
spectroscope, it does not seem incredible to me

IDEAL CHEMISTRY. 59

that there may even be evidence, some day, of
the independent existence of such things as ^
and v. We know that Dr. Miller and Mr.
Huggins saw a most wonderful hydrogen com-
bustion— at least what they imagined to be a
hydrogen combustion — taking place in a variable
star. Now this hydrogen combustion might be
actually hydrogen combining with these unknown
elements, and carrying them away in the form of
chlorine, nitrogen, and the like. One of the
nebulae examined by Dr. Miller and Mr. Huggins
afforded them the spectrum of an ignited gas,
and in the spectrum of this nebula they saw one
of the lines of nitrogen alone. This suggested
to them that the line might have been produced
by one of the elements of nitrogen. That might
have been the element, v. This as yet is a mere
suggestion, but it seems to me eminently probable
that if we follow up the subject we may from
this source have one day revealed to us, indepen-
dent evidence of the existence of these elements
in the sun or stars. (See Note A.)

Let me, in conclusion, make one or two

60 IDEAL CHEMISTRY.

observations upon a point which must occur to
every chemist who has studied this method.
If we had not taken a as the symbol of hydro-
gen, but had started with a different hypo-
thesis, namely, that the symbol of hydrogen
was a'2, we should have arrived at a different
symbolic system analogous in its form to our
present system. We should have hydrogen as
a/2, water as a'2£, and so on. In fact, we should
have been led to develop a system different from
that which I have brought before you.

In the following Table are given a few examples
of symbols constructed on this hypothesis : —

Hydrogen a*

Chlorine x~

Hydrochloric Acid a'x

llydrochlorous Acid .... a>'x%
Chlorosulphurous Acid . . . X^Z
Hydrochlorosulphurous Acid . a'x'^l'

Iodine a/2

Nitrogen v*

Acetylene a

Marsh Gas 1a'

IDEAL CHEMISTRY. 61

Cyanogen v'2k2

Hydrocyanic Acid a'vic

Ammonia a'V

Methylamine a'V/e

You may with reason ask me, " Why do you
prefer one of these systems to the other ? or
do you prefer it ? or what view do you take of
that question ?" Let me say, in the first place,
that I cannot as yet give a complete answer to
this question. For, I have not placed before you
and others the ideas upon which a judgment can
properly be formed upon it.1 .

I will, however, make one remark which will
be sufficient to convince those who have so far
followed me of the essential difference between
the two systems. On comparing the second sys-
tem, "system a2" with the first system, " system
a," it will be seen that we may always, by a
mere process of substitution, pass from the former
to the latter, that is to say, every combination of

1 This has since been done in Part II. of this Calculus.
I refer especially to the discussion contained in it as to
the origin of the law of even numbers.

62 IDEAL CHEMISTRY.

the latter system will have its counterpart in
the former — the combinations being expressed in
the two cases respectively by positive and integral
members of the prime factors of the systems :
but it is not true that every combination of the
former system will have a counterpart in the
latter, or can be expressed by the prime factors
of that system ; thus, for example, the combina-
tion v'£, which is a combination found in the
system a'2, has no counterpart in the system a,
and cannot be expressed in it. The system a2
is therefore more comprehensive than the system a.
This observation disposes at once of the remarks
of those critics who maintain that because we can
pass by a simple process of translation from the
system a2 to the system a, these systems are to
be regarded as meaning the same thing, it being
perfectly indifferent to which we adhere. Such
persons are really in the position of those wise-
acres who maintain that because all A is B all
B is A. When we have to select between two such
hypotheses, the more restricted hypothesis, which
in this case is system a, is always to be preferred.

IDEAL CHEMISTRY. 63

The reason of this restriction is that system a
excludes all those combinations which do not
satisfy the law of even numbers, of which the
system a2 takes no notice. At this point I
must leave the subject for fuller consideration
hereafter.

Note A. — Since this Lecture was delivered, further
researches have been made in this direction, and in an
article by myself in the Philosophical Magazine of June,.
1879, tne following passage occurs : —

It is a significant fact that a very large proportion of
the class of elements which I have termed composite
elements have not been found in the sun.

In reply to inquiries on my part, Mr. W. Huggins
writes to me thus : —

"So far as I know, nitrogen, phosphorus, arsenic, anti-
mony, boron, chlorine, iodine, bromine, have not been
found in the sun. In one paper Lockyer suspects iodine.
Dr. Miller and I found coincidence of three lines of anti-
mony, with three lines in Aldebaran. Though this obser-
vation would show considerable probability of antimony in
this star, I do not think the spectroscope (two dense prisms
of flint glass) was sufficiently powerful to make its existence
there certain. In the case of nitrogen, no coincidence was
observed in any of the stars. In my paper in the Trans-
actions of the Royal Society, on Spectra of Nebulae, I show
coincidence of principal line with the strong line in spectrum
of nitrogen. Now> this line of nitrogen is a double one ;

64 IDEAL CHEMISTRY,

and I was not at first able to be certain if the line in the
nebula was similarly double. Subsequently, with the powerful
spectroscope I used for the motions of the stars, I was
able to make a certain determination of this point {Pro-
ceedings R. S., 1872, p. 385). I found the line in the nebula
single and coincident with the middle of the less refrangible
of the components of the double line.

Nitrogen Red

II

Nebula

I say ( middle/ because the line in the nebula is narrower
and more defined than either of the two lines forming the
double line. I made experiments to see if, under any con-
ditions of pressure and temperature, the more refrangible
of the two lines fades out, so as to leave only the one with
which the line in the nebula is incident. I did not succeed.
So the matter stands : Is nitrogen compound ? Are there
any conditions under which the one line only appears ?
Has the line in the nebula no connection with nitrogen
further than being sensibly of the same refrangibility ? "

Now we must either consider that the matter of these
elements, so abundant on the earth, does not exist in the
sun or stars (which is not probable), or that they have
passed into forms of combination in which they cannot
be recognised by the spectroscope (which is also hardly
admissible at that elevated temperature), or that they
have been decomposed. — Philosophical Magazine, 1879,
p. 130.

LONDON: K. CLAV, SON.^, AND lAYLOh, KKINT1

DATE DUE

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Brodie, Benjamin

Ideal chemistry; a lecture.

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