profitable to all: as bearing upon special functions, its value,
though not so great, is still more tangible. Why, for example, should
Members of Parliament be ignorant of the subjects concerning which
they are called upon to legislate? In this land of practical physics,
why should they be unable to form an independent opinion upon a
physical question? Why should the member of a parliamentary committee
be left at the mercy of interested disputants when a scientific
question is discussed, until he deems the nap a blessing which rescues
him from the bewilderments of the committee-room? The education which
does not supply the want here referred to, fails in its duty to
England. With regard to our working people, in the ordinary sense of
the term working, the study of Physics would, I imagine, be
profitable, not only as a means of intellectual culture, but also as a
moral influence to woo them from pursuits which now degrade them. A
man's reformation oftener depends upon the indirect, than upon the
direct action of the will. The will must be exerted in the choice of
employment which shall break the force of temptation by erecting a
barrier against it. The drunkard, for example, is in a perilous
condition if he content himself merely with saying, or swearing, that
he will avoid strong drink. His thoughts, if not attracted by another
force, will revert to the public-house, and to rescue him permanently
from this, you must give him an equivalent.
By investing the objects of hourly intercourse with an interest which
prompts reflection, new enjoyments would be opened to the working man,
and every one of these would be a point of force to protect him
against temptation. Besides this, our factories and our foundries
present an extensive field of observation, and were those who work in
them rendered capable, by previous culture, of _observing_ what they
see, the results might be incalculable. Who can say what intellectual
Samsons are at the present moment toiling with closed eyes in the
mills and forges of Manchester and Birmingham? Grant these Samsons
sight, and you multiply the chances of discovery, and with them the
prospects of national advancement. In our multitudinous technical
operations we are constantly playing with forces our ignorance of
which is often the cause of our destruction. There are agencies at
work in a locomotive of which the maker of it probably never dreamed,
but which nevertheless may be sufficient to convert it into an engine
of death. When we reflect on the intellectual condition of the people
who work in our coal mines, those terrific explosions which occur from
time to time need not astonish us. If these men possessed sufficient
physical knowledge, from the operatives themselves would probably
emanate a system by which these shocking accidents might be avoided.
Possessed of the knowledge, their personal interests would furnish the
necessary stimulus to its practical application, and thus two ends
would be served at the same time the elevation of the men and the
diminution of the calamity.
Before the present Course of Lectures was publicly announced, I had
many misgivings as to the propriety of my taking a part in them,
thinking that my place might be better filled by an older and more
experienced man. To my experience, however, such as it was, I
resolved to adhere, and I have therefore described things as they
revealed themselves to my own eyes, and have been enacted in my own
limited practice. There is one mind common to us all; and the true
expression of this mind, even in small particulars, will attest itself
by the response which it calls forth in the convictions of my hearers.
I ask your permission to proceed a little further in this fashion, and
to refer to a fact or two in addition to those already cited, which
presented themselves to my notice during my brief career as a teacher
in the college already alluded to. The facts, though extremely
humble, and deviating in some slight degree from the strict subject of
the present discourse, may yet serve to illustrate an educational
principle.
One of the duties which fell to my share was the instruction of a
class in mathematics, and I usually found that Euclid and the ancient
geometry generally, when properly and sympathetically addressed to the
understanding, formed a most attractive study for youth. But it was
my habitual practice to withdraw the boys from the routine of the
book, and to appeal to their self-power in the treatment of questions
not comprehended in that routine. At first, the change from the
beaten track usually excited aversion: the youth felt like a child
amid strangers; but in no single instance did this feeling continue.
When utterly disheartened, I have encouraged the boy by the anecdote
of Newton, where he attributes the difference between him and other
men, mainly to his own patience; or of Mirabeau, when he ordered his
servant, who had stated something to be impossible, never again to use
that blockhead of a word. Thus cheered, the boy has returned to his
task with a smile, which perhaps had something of doubt in it, but
which, nevertheless, evinced a resolution to try again. I have seen
his eye brighten, and, at length, with a pleasure of which the ecstasy
of Archimedes was but a simple expansion, heard him exclaim, 'I have
it, sir.' The consciousness of self-power, thus awakened, was of
immense value; and, animated by it, the progress of the class was
astonishing. It was often my custom to give the boys the choice of
pursuing their propositions in the book, or of trying their strength
at others not to be found there. Never in a single instance was the
book chosen. I was ever ready to assist when help was needful, but my
offers of assistance were habitually declined. The boys had tasted
the sweets of intellectual conquest and demanded victories of their
own. Their diagrams were scratched on the walls, cut into the beams
upon the playground, and numberless other illustrations were afforded
of the living interest they took in the subject. For my own part, as
far as experience in teaching goes, I was a mere fledgling--knowing
nothing of the rules of pedagogics, as the Germans name it; but
adhering to the spirit indicated at the commencement of this
discourse, and endeavouring to make geometry a means rather than a
branch of education. The experiment was successful, and some of the
most delightful hours of my existence have been spent in marking the
vigorous and cheerful expansion of mental power, when appealed to in
the manner here described.
Our pleasure was enhanced when we applied our mathematical knowledge
to the solution of physical problems. Many objects of hourly contact
had thus a new interest and significance imparted to them. The swing,
the see-saw, the tension of the giant-stride ropes, the fall and
rebound of the football, the advantage of a small boy over a large one
when turning short, particularly in slippy weather; all became
subjects of investigation. A lady stands before a looking-glass, of
her own height; it was required to know how much of the glass was
really useful to her? We learned with pleasure the economic fact that
she might dispense with the lower half and see her whole figure
notwithstanding. It was also pleasant to prove by mathematics, and
verify by experiment, that the angular velocity of a reflected beam is
twice that of the mirror which reflects it. From the hum of a bee we
were able to determine the number of times the insect flaps its wings
in a second. Following up our researches upon the pendulum, we
learned how Colonel Sabine had made it the means of determining the
figure of the earth; and we were also startled by the inference which
the pendulum enabled us to draw, that if the diurnal velocity of the
earth were seventeen times its present amount, the centrifugal force
at the equator would be precisely equal to the force of gravitation,
so that an inhabitant of those regions would then have the same
tendency to fall upwards as downwards. All these things were sources
of wonder and delight to us: and when we remembered that we were
gifted with the powers which had reached such results, and that the
same great field was ours to work in, our hopes arose that at some
future day we might possibly push the subject a little further, and
add our own victories to the conquests already won.
I ought to apologise to you for dwelling so long upon this subject;
but the days spent among these young philosophers made a deep
impression on me. I learned among them something of myself and of
human nature, and obtained some notion of a teacher's vocation. If
there be one profession in England of paramount importance, I believe
it to be that of the schoolmaster; and if there be a position where
selfishness and incompetence do most serious mischief, by lowering the
moral tone and exciting irreverence and cunning where reverence and
noble truthfulness ought to be the feelings evoked, it is that of the
principal of a school. When a man of enlarged heart and mind comes
among boys, when he allows his spirit to stream through them, and
observes the operation of his own character evidenced in the elevation
of theirs,--it would be idle to talk of the position of such a man
being honourable. It is a blessed position. The man is a blessing to
himself and to all around him. Such men, I believe, are to be found
in England, and it behoves those who busy themselves with the
mechanics of education at the present day, to seek them out. For no
matter what means of culture may be chosen, whether physical or
philological, success must ever mainly depend upon the amount of life,
love, and earnestness, which the teacher himself brings with him to
his vocation.
Let me again, and finally, remind you that the claims of that science
which finds in me to-day its unripened advocate, are those of the
logic of Nature upon the reason of her child--that its disciplines, as
an agent of culture, are based upon the natural relations subsisting
between Man and the universe of which he forms a part. On the one
side, we have the apparently lawless shifting of phenomena; on the
other side, mind, which requires law for its equilibrium, and through
its own indestructible instincts, as well as through the teachings of
experience, knows that these phenomena are reducible to law. To
chasten this apparent chaos is a problem which man has set before him.
The world was built in order: and to us are trusted the will and power
to discern its harmonies, and to make them the lessons of our lives.
From the cradle to the grave we are surrounded with objects which
provoke inquiry. Descending for a moment from this high plea to
considerations which lie closer to us as a nation--as a land of gas
and furnaces, of steam and electricity: as a land which science,
practically applied, has made great in peace and mighty in war: I ask
you whether this 'land of old and just renown' has not a right to
expect from her institutions a culture more in accordance with her
present needs than that supplied by declension and conjugation? And
if the tendency should be to lower the estimate of science, by
regarding it exclusively as the instrument of material prosperity, let
it be the high mission of our universities to furnish the proper
counterpoise by pointing out its nobler uses--lifting the national
mind to the contemplation of it as the last development of that
'increasing purpose' which runs through the ages and widens the
thoughts of men.
********************
XII. ON CRYSTALLINE AND SLATY CLEAVAGE.
[Footnote: From a discourse delivered in the Royal Institution of
Great Britain, June 6, 1856.]
WHEN the student of physical science has to investigate the character
of any natural force, his first care must be to purify it from the
mixture of other forces, and thus study its simple action. If, for
example, he wishes to know how a mass of liquid would shape itself if
at liberty to follow the bent of its own molecular forces, he must see
that these forces have free and undisturbed exercise. We might
perhaps refer him to the dewdrop for a solution of the question; but
here we have to do, not only with the action of the molecules of the
liquid upon each other, but also with the action of gravity upon the
mass, which pulls the drop downwards and elongates it. If he would
examine the problem in its purity, he must do as Plateau has done,
detach the liquid mass from the action of gravity; he would then find
the shape to be a perfect sphere. Natural processes come to us in a
mixed manner, and to the uninstructed mind are a mass of
unintelligible confusion. Suppose half-a-dozen of the best musical
performers to be placed in the same room, each playing his own
instrument to perfection, but no two playing the same tune; though
each individual instrument might be a source of perfect music, still
the mixture of all would produce mere noise.
Thus it is with the processes of nature, where mechanical and
molecular laws intermingle and create apparent confusion. Their
mixture constitutes what may be called the _noise_ of natural laws, and
it is the vocation of the man of science to resolve this noise into
its components, and thus to detect the underlying music.
The necessity of this detachment of one force from all other forces is
nowhere more strikingly exhibited than in the phenomena of
crystallisation. Here, for example, is a solution of common sulphate
of soda or Glauber salt. Looking into it mentally, we see the
molecules of that liquid, like disciplined squadrons under a governing
eye, arranging themselves into battalions, gathering round distinct
centres, and forming themselves into solid masses, which after a time
assume the visible shape of the crystal now held in my hand. I may,
like an ignorant meddler wishing to hasten matters, introduce
confusion into this order. This may be done by plunging a glass rod
into the vessel; the consequent action is not the pure expression of
the crystalline forces; the molecules rush together with the confusion
of an unorganised mob, and not with the steady accuracy of a
disciplined host. In this mass of bismuth also we have an example of
confused crystallisation; but in the crucible behind me a slower
process is going on: here there is an architect at work 'who makes no
chips, no din,' and who is now building the particles into crystals,
similar in shape and structure to those beautiful masses which we see
upon the table. By permitting alum to crystallise in this slow way,
we obtain these perfect octahedrons; by allowing carbonate of lime to
crystallise, nature produces these beautiful rhomboids; when silica
crystallises, we have formed these hexagonal prisms capped at the ends
by pyramids; by allowing saltpetre to crystallise we have these
prismatic masses, and when carbon crystallises, we have the diamond.
If we wish to obtain a perfect crystal we must allow the molecular
forces free play; if the crystallising mass be permitted to rest upon
a surface it will be flattened, and to prevent this a small crystal
must be so suspended as to be surrounded on all sides by the liquid,
or, if it rest upon the surface, it must be turned daily so as to
present all its faces in succession to the working builder.
In building up crystals these little atomic bricks often arrange
themselves into layers which are perfectly parallel to each other, and
which can be separated by mechanical means; this is called the
cleavage of the crystal. The crystal of sugar I hold in my hand has
thus far escaped the solvent and abrading forces which sooner or later
determine the fate of sugar-candy. I readily discover that it cleaves
with peculiar facility in one direction. Again I lay my knife upon
this piece of rocksalt, and with a blow cleave it in one direction.
Laying the knife at right angles to its former position, the crystal
cleaves again; and finally placing the knife at right angles to the
two former positions, we find a third cleavage. Rocksalt cleaves in
three directions, and the resulting solid is this perfect cube, which
may be broken up into any number of smaller cubes. Iceland spar also
cleaves in three directions, not at right angles, but oblique to each
other, the resulting solid being a rhomboid. In each of these cases
the mass cleaves with equal facility in all three directions. For the
sake of completeness I may say that many crystals cleave with unequal
facility in different directions: heavy spar presents an example of
this kind of cleavage.
Turn we now to the consideration of some other phenomena to which the
term cleavage may be applied. Beech, deal, and other woods cleave
with facility along the fibre, and this cleavage is most perfect when
the edge of the axe is laid across the rings which mark the growth of
the tree. If you look at this bundle of hay severed from a rick, you
will see a sort of cleavage in it also; the stalks lie in horizontal
planes, and only a small force is required to separate them laterally.
But we cannot regard the cleavage of the tree as the same in character
as that of the hayrick. In the one case it is the molecules arranging
themselves according to organic laws which produce a cleavable
structure, in the other case the easy separation in one direction is
due to the mechanical arrangement of the coarse sensible stalks of
hay.
This sandstone rock was once a powder held in mechanical suspension by
water. The powder was composed of two distinct parts, fine grains of
sand and small plates of mica. Imagine a wide strand covered by a
tide, or an estuary with water which holds such powder in suspension:
how will it sink? The rounded grains of sand will reach the bottom
first, because they encounter least resistance, the mica afterwards,
and when the tide recedes we have the little plates shining like
spangles upon the surface of the sand. Each successive tide brings
its charge of mixed powder, deposits its duplex layer day after day,
and finally masses of immense thickness are piled up, which by
preserving the alternations of sand and mica tell the tale of their
formation. Take the sand and mica, mix them together in water, and
allow them to subside; they will arrange themselves in the manner
indicated, and by repeating the process you can actually build up a
mass which shall be the exact counterpart of that presented by nature.
Now this structure cleaves with readiness along the planes in which
the particles of mica are strewn. Specimens of such a rock sent to me
from Halifax, and other masses from the quarries of Over Darwen in
Lancashire, are here before you. With a hammer and chisel I can
cleave them into flags; indeed these flags are employed for roofing
purposes in the districts from which the specimens have come, and
receive the name of 'slatestone.' But you will discern without a word
from me, that this cleavage is not a crystalline cleavage any more
than that of a hayrick is. It is molar, not molecular.
This, so far as I am aware of, has never been imagined, and it has
been agreed among geologists not to call such splitting as this
cleavage at all, but to restrict the term to a phenomenon of a totally
different character.
Those who have visited the slate quarries of Cumberland and North
Wales will have witnessed the phenomenon to which I refer. We have
long drawn our supply of roofing-slates from such quarries;
school-boys ciphered on these slates, they were used for tombstones in
churchyards, and for billiard-tables in the metropolis; but not until
a comparatively late period did men begin to enquire how their
wonderful structure was produced. What is the agency which enables us
to split Honister Crag, or the cliffs of Snowdon, into laminae from
crown to base? This question is at the present moment one of the
great difficulties of geologists, and occupies their attention perhaps
more than any other. You may wonder at this. Looking into the quarry
of Penrhyn, you may be disposed to offer the explanation I heard given
two years ago. 'These planes of cleavage,' said a friend who stood
beside me on the quarry's edge, 'are the planes of stratification
which have been lifted by some convulsion into an almost vertical
position.' But this was a mistake, and indeed here lies the grand
difficulty of the problem. The planes of cleavage stand in most cases
at a high angle to the bedding. Thanks to Sir Roderick Murchison, I
am able to place the proof of this before you. Here is a specimen of
slate in which both the planes of cleavage and of bedding are
distinctly marked, one of them making a large angle with the other.
This is common. The cleavage of slates then is not a question of
stratification; what then is its cause?
In an able and elaborate essay published in 1835, Prof. Sedgwick
proposed the theory that cleavage is due to the action of crystalline
or polar forces subsequent to the consolidation of the rock. 'We may
affirm,' he says, 'that no retreat of the parts, no contraction of
dimensions in passing to a solid state, can explain such phenomena.
They appear to me only resolvable on the supposition that crystalline
or polar forces acted upon the whole mass simultaneously in one
direction and with adequate force.' And again, in another place:
'Crystalline forces have re-arranged whole mountain masses, producing
a beautiful crystalline cleavage, passing alike through all the
strata.' [Footnote: Transactions of the Geological Society, ser. ii,
vol. iii. p. 477.]
The utterance of such a man struck deep, as it ought to do, into the
minds of geologists, and at the present day there are few who do not
entertain this view either in whole or in part. [Footnote: In a letter
to Sir Charles Lyell, dated from the Cape of Good Hope February 20,
1836, Sir John Herschel writes as follows: 'If rocks have been so
heated as to allow of a commencement of crystallisation, that is to
say, if they have been heated to a point at which the particles can
begin to move amongst themselves, or at least on their own axes, some
general law must then determine the position in which these particles
will rest on cooling. Probably that position will have some relation
to the direction in which the heat escapes. Now when all or a
majority of particles of the same nature have a general tendency to
one position, that must of course determine a cleavage plane.'] The
boldness of the theory, indeed, has, in some cases, caused speculation
to run riot, and we have books published on the action of polar forces
and geologic magnetism, which rather astonish those who know something
about the subject. According to this theory whole districts of North
Wales and Cumberland, mountains included, are neither more nor less
than the parts of a gigantic crystal. These masses of slate were
originally fine mud, composed of the broken and abraded particles of
older rocks. They contain silica, alumina, potash, soda, and mica
mixed mechanically together. In the course of ages the mixture became
consolidated, and the theory before us assumes that a process of
crystallisation afterwards rearranged the particles and developed in
it a single plane of cleavage. Though a bold, and I think
inadmissible, stretch of analogies, this hypothesis has done good
service. Right or wrong, a thoughtfully uttered theory has a dynamic
power which operates against intellectual stagnation; and even by
provoking opposition is eventually of service to the cause of truth.
It would, however, have been remarkable if, among the ranks of
geologists themselves, men were not found to seek an explanation of
slate-cleavage involving a less hardy assumption.
The first step in an enquiry of this kind is to seek facts. This has
been done, and the labours of Daniel Sharpe (the late President of the
Geological Society, who, to the loss of science and the sorrow of all
who knew him, has so suddenly been taken away from us), Mr. Henry
Clifton Sorby, and others, have furnished us with a body of facts
associated with slaty cleavage, and having a most important bearing
upon the question.
Fossil shells are found in these slate-rocks. I have here several
specimens of such shells in the actual rock, and occupying various
positions in regard to the cleavage planes. They are squeezed,
distorted, and crushed; in all cases the distortion leads to the
inference that the rock which contains these shells has been subjected
to enormous pressure in a direction at right angles to the planes of
cleavage. The shells are all flattened and spread out in these
planes. Compare this fossil trilobite of normal proportions with
these others which have suffered distortion. Some have lain across,
some along, and some oblique to the cleavage of the slate in which
they are found; but in all cases the distortion is such, as required
for its production a compressing force acting, at right angles to the
planes of cleavage. As the trilobites lay in the mud, the jaws of a
gigantic vice appear to have closed upon them and squeezed them into
the shapes you see.