Mathematics give us the "exact sciences." "Solid" as Prof.
Drummond tells us the laws of nature are, in mathematics at least they
are so, beyond the possibility of intelligent question. No one, that I
am aware, has ever accused them of poetic license, although poetry on
her side does not refuse their alliance. And as we build our
foundations of what we can find most solid, it need be no wonder that
in proportion as we go down to the foundations of the earth, so do we
find mathematics more and more revealing themselves in proportional
numbers and in geometric forms. Chemistry has become in our day
penetrated with arithmetic; and chemistry deals with those elementary
principles, the combination of which gives us the material world.
"Chemistry," says Herschel, is, in a most pre-eminent degree, the
science of quantity; and to enumerate the discoveries which have arisen
for it from the mere determination of weights and measures would be
nearly to give a synopsis of this branch of knowledge."
What
is this but as if you were to go into some ancient structure, as the
pyramids, and find upon the stones the builder's hieroglyph? We have
been only learning to find deeper truth than we were at all aware of in
the prophet's challenge, "Who hath measured the waters in the hollow of
His hand, and meted out heaven with a span, and comprehended the dust
of the earth in a measure, and weighed the mountains in scales, and the
hills in a balance?" (Is. xl. 12.) What science of the day in which
that question was asked knew any thing about such measurement? How many
centuries has it taken to bring man's tardy feet to where the prophet
stood? But we are able now to see that we may take this as true in the
most absolute way, that every bit of the earth's dust is weighed and
measured.
"The law of simple numerical ratios," says Dr.
Cooke, "Is the fundamental law of crystallography, and gives to the
science a mathematical basis. Similar numerical relations appear when
we study the formation of chemical compounds. I have already defined a
chemical element as a substance which has never as yet been decomposed,
and all the matter with which man is now acquainted is composed of one
or more of at most seventy elementary substances. When two of these
elements unite together to form a compound body, the proportions in
which they combine are not decided by chance. You cannot unite these
elementary substances in any proportion you The proportion in each case
is determined by an unvarying law, and the amounts required of either
substance are weighed out by nature in her delicate scales with a
nicety which no art can attain. Thus, for Instance, 23 ounces of sodium
will unite with exactly 35.5 ounces of chlorine; and if you use
precisely these proportions of the two elements, the whole of each will
disappear, and become merged in the compound which is our common table
salt. But if, in attempting to make salt, we bring together clumsily
23.5 ounces of sodium and 35.5 ounces of chlorine, Nature will simply
put the extra half-ounce of sodium on one side, and the rest will
unite. This law which governs all chemical combinations is known as
'the law of definite proportions.'
"Tables will be found in
works on chemistry, which give, opposite to the name of each elementary
substance, a numerical value, usually called its atomic weight, and in
all cases where the elements are capable of combining with each other,
they either unite in the exact proportions indicated by these numbers,
or else in some simple multiple of these proportions."
Drummond tells us the laws of nature are, in mathematics at least they
are so, beyond the possibility of intelligent question. No one, that I
am aware, has ever accused them of poetic license, although poetry on
her side does not refuse their alliance. And as we build our
foundations of what we can find most solid, it need be no wonder that
in proportion as we go down to the foundations of the earth, so do we
find mathematics more and more revealing themselves in proportional
numbers and in geometric forms. Chemistry has become in our day
penetrated with arithmetic; and chemistry deals with those elementary
principles, the combination of which gives us the material world.
"Chemistry," says Herschel, is, in a most pre-eminent degree, the
science of quantity; and to enumerate the discoveries which have arisen
for it from the mere determination of weights and measures would be
nearly to give a synopsis of this branch of knowledge."
What
is this but as if you were to go into some ancient structure, as the
pyramids, and find upon the stones the builder's hieroglyph? We have
been only learning to find deeper truth than we were at all aware of in
the prophet's challenge, "Who hath measured the waters in the hollow of
His hand, and meted out heaven with a span, and comprehended the dust
of the earth in a measure, and weighed the mountains in scales, and the
hills in a balance?" (Is. xl. 12.) What science of the day in which
that question was asked knew any thing about such measurement? How many
centuries has it taken to bring man's tardy feet to where the prophet
stood? But we are able now to see that we may take this as true in the
most absolute way, that every bit of the earth's dust is weighed and
measured.
"The law of simple numerical ratios," says Dr.
Cooke, "Is the fundamental law of crystallography, and gives to the
science a mathematical basis. Similar numerical relations appear when
we study the formation of chemical compounds. I have already defined a
chemical element as a substance which has never as yet been decomposed,
and all the matter with which man is now acquainted is composed of one
or more of at most seventy elementary substances. When two of these
elements unite together to form a compound body, the proportions in
which they combine are not decided by chance. You cannot unite these
elementary substances in any proportion you The proportion in each case
is determined by an unvarying law, and the amounts required of either
substance are weighed out by nature in her delicate scales with a
nicety which no art can attain. Thus, for Instance, 23 ounces of sodium
will unite with exactly 35.5 ounces of chlorine; and if you use
precisely these proportions of the two elements, the whole of each will
disappear, and become merged in the compound which is our common table
salt. But if, in attempting to make salt, we bring together clumsily
23.5 ounces of sodium and 35.5 ounces of chlorine, Nature will simply
put the extra half-ounce of sodium on one side, and the rest will
unite. This law which governs all chemical combinations is known as
'the law of definite proportions.'
"Tables will be found in
works on chemistry, which give, opposite to the name of each elementary
substance, a numerical value, usually called its atomic weight, and in
all cases where the elements are capable of combining with each other,
they either unite in the exact proportions indicated by these numbers,
or else in some simple multiple of these proportions."
Thus these elements are themselves manufactured articles, and
are stamped indelibly with the Manufacturer's name. For nothing
addresses itself more to mind as from mind than just such relations as
are discovered here. As another has said, "The most careful structure
of brown stone is not so precise in number, relation, and dimensions of
its blocks as are molecules, the first terms in matter, in their atomic
formation." It should be as easy, then to refer the natural product to
the workmanship of eternal mind, the recent structure to man's hand and
mind. And who would have a doubt as to the latter?
Having got
so far, moreover, ought we not to be able to go further? Ought not
these numbers individually to have a voice for us, and in their
relation to one another also? If all things are full of reason, is it
too much to expect that these proportions have a reason too? Oh, for
some interpreter here, some master mind, lowly and reverent enough to
follow out this clue, and tell us whither it leads! But we must not
expect these elements to speak yet clearly. Pythagoras has given place
to Darwin; and final cause to formal cause; and we must wait for the
wheel to come round again.
As to relations as indicated by the numbers we have just a hint: -
"Attempts
have been made in the same science," say M'Cosh & Dickie, in their
work on "Typical Forms," "to form bodies into groups or congeners. M.
Dumas, in particular, has detected a number of triads, or series of
three bodies, which have analogous properties, and showing a singular
numerical profession in their equivalent weights; the equivalents of
two of these added together, and divided by two, giving approximately
the equivalent of the third, thus: -
Chlorine 35 } Potassium 40 }
Bromine }80 Sodium }24
Iodine 125 } Lithium 7 }
Calcium 20 } Sulphur 16 }
Strontium }44 Selenium }40
Barium 69 } Tellurium 64 }
"
'Regarding,' says Faraday, 'chlorine, bromine, and iodine as one triad,
it will be seen that between the first and the last there is
recognizable a well-marked progression of qualities. Thus chlorine is a
gas, under ordinary temperatures and pressures; bromine, a fluid; and
iodine, a solid; in this manner displaying a progression in the
difference of cohesive force. Again, chlorine is yellow; bromine, red;
iodine, black, or in vapor, a reddish violet.' "
This glimmer
of light seems to have well-nigh gone out. The atomic weight of some of
these has been since doubled, and of others more or less changed. At
the best, it carries us but a little way upon the road we seek. None
the less sure is it that there is a numerical impress upon all nature.
"Indeed,"
says Sir John Herschel again, "it is a character of all the higher laws
of nature to assume the form of a precise quantitative statement."
And Humboldt declares, -
"It may be said that the only
remaining and widely diffused hieroglyphic characters still In our
writing - numbers - appear to us again as powers of the cosmos,
although in a wider sense than that applied to them by the Italian
School."
Much more might be said here, but it needs not to try
more to establish what no science of the day will attempt to dispute.
It is the meaning of admitted facts that we are seeking; and this is
just what is so hard to reach. Save in their testimony to an Author of
nature, they are yet dumb and unspiritual: how shall we spiritualize
them? Is it not possible - yea, rather, may we not expect, that God has
given us somewhere some clue to their interpretation, by which we may
follow on to find ourselves more in the presence of the King? Nature
seems to us as yet dumb, and God, if we own Him there, yet distant;
where shall we find, then, the interpreter we seek, if not in
Revelation?