The widespread distribution of radioactive substances is
most
readily appreciated by examination of sections of rocks cut
thin
enough for microscopic investigation. It is, indeed, difficult
to
find, in the older rocks of granitic type, mica which does
not
show haloes, or traces of haloes. Often we find that every one
of
the inclusions in the mica—that is, every one of the
earlier
formed substances—contain radioactive elements, as
indicated by
the presence of darkened borders. As will be seen presently
the
quantities involved are generally vanishingly small. For
example
it was found by direct determination that in one gram of the
halo-rich mica of Co. Carlow there was rather less than
twelve
billionths of a gram of radium, We are
230
entitled to infer that other rare elements are similarly
widely
distributed but remain undetectable because of their more
stable
properties.
It must not be thought that the under-exposed halo is a
recent
creation. By no means. All are old, appallingly old; and in
the
same rock all are, probably, of the same, or neatly the same,
age. The under-exposure is simply due to a lesser quantity of
the
radioactive elements in the nucleus. They are under-exposed,
in
short, not because of lesser duration of exposure, but because
of
insufficient action; as when in taking a photograph the stop
is
not open enough for the time of the exposure.
The halo has, so far, told us that the additive law is obeyed
in
solid media, and that the increased ionisation attending the
slowing down of the ray obtaining in gases, also obtains in
solids; for, otherwise, the halo would not commence its
development as a spherical shell or envelope. But here we
learn
that there is probably a certain difference in the course of
events attending the immediate passage of the ray in the gas
and
in the solid. In the former, initial recombination may
obscure
the intense ionisation near the end of the range. We can only
detect the true end-effects by artificially separating the
ions
by a strong electric force. If this recombination happened in
the
mineral we should not have the concentric spheres so well
defined
as we see them to be. What, then, hinders the initial
recombination in the solid? The answer probably is that the
newly
formed
231
ion is instantly used up in a fresh chemical combination. Nor
is
it free to change its place as in the gas. There is simply a
new
equilibrium brought about by its sudden production. In this
manner the conditions in the complex molecule of biotite,
tourmaline, etc., may be quite as effective in preventing
initial
recombination as the most effective electric force we could
apply. The final result is that we find the Bragg curve
reproduced most accurately in the delicate shading of the
rings
making up the perfectly exposed halo.
That the shading of the rings reproduces the form of the
Bragg
curve, projected, as it were, upon the line of advance of the
ray
and reproduced in depth of shading, shows that in yet another
particular the alpha ray behaves much the same in the solid as
in
the gas. A careful examination of the outer edge of the
circles
always reveals a steep but not abrupt cessation of the action
of
the ray. Now Geiger has investigated and proved the existence
of
scattering of the alpha ray by solids. We may, therefore,
suppose
with much probability that there is the same scattering
within
the mineral near the end of the range. The heavy iron atom of
the
biotite is, doubtless, chiefly responsible for this in
biotite
haloes. I may observe that this shading of the outer bounding
surface of the sphere of action is found however minute the
central nucleus. In the case of a nucleus of considerable
size
another effect comes in which tends to produce an enhanced
shading. This will
232
result if rays proceed from different depths in the nucleus.
If
the nucleus were of the same density and atomic weight as the
surrounding mica, there would be little effect. But its
density
and molecular weight are generally greater, hence the
retardation
is greater, and rays proceeding from deep in the nucleus
experience more retardation than those which proceed from
points
near to the surface. The distances reached by the rays in the
mica will vary accordingly, and so there will be a gradual
cessation of the effects of the rays.
The result of our study of the halo may be summed up in
the
statement that in nearly every particular we have the
phenomena,
which have been measured and observed in the gas, reproduced on
a
minute scale in the halo. Initial recombination seems,
however,
to be absent or diminished in effectiveness; probably because
of
the new stability instantly assumed by the ionised atoms.
One of the most interesting points about the halo remains to
be
referred to. The halo is always uniformly darkened all round
its
circumference and is perfectly spherical. Sections, whether
taken
in the plane of cleavage of the mica or across it, show the
same
exactly circular form, and the same radius. Of course, if
there
was any appreciable increase of range along or across the
cleavage the form of the halo on the section across the
cleavage
should be elliptical. The fact that there is no measurable
ellipticity is, I think, one which on first consideration
would
not be expected.
233
For what are the conditions attending the passage of the ray
in a
medium such as mica? According to crystallographic conceptions
we
have here an orderly arrangement of molecules, the units
composing the crystal being alike in mass, geometrically
spaced,
and polarised as regards the attractions they exert one upon
another. Mica, more especially, has the cleavage phenomenon
developed to a degree which transcends its development in any
other known substance. We can cleave it and again cleave it
till
its flakes float in the air, and we may yet go on cleaving it
by
special means till the flakes no longer reflect visible
light.
And not less remarkable is the uniplanar nature of its
cleavage.
There is little cleavage in any plane but the one, although it
is
easy to show that the molecules in the plane of the flake are
in
orderly arrangement and are more easily parted in some
directions
than in others. In such a medium beyond all others we must
look
with surprise upon the perfect sphere struck out by the alpha
rays, because it seems certain that the cleavage is due to
lesser
attraction, and, probably, further spacing of the molecules, in
a
direction perpendicular to the cleavage.
It may turn out that the spacing of the molecules will
influence
but little the average number per unit distance encountered
by
rays moving in divergent paths. If this is so, we seem left
to
conclude that, in spite of its unequal and polarised
attractions,
there is equal retardation and equal ionisation in the
molecule
in whatever
234
direction it is approached. Or, again, if the encounters
indeed
differ in number, then some compensating effect must exist
whereby a direction of lesser linear density involves greater
stopping power in the molecule encountered, and vice versa.
The nature of the change produced by the alpha rays is
unknown.
But the formation of the halo is not, at least in its earlier
stages, attended by destruction of the crystallographic and
optical properties of the medium. The optical properties are
unaltered in nature but are increased in intensity. This
applies
till the halo has become so darkened that light is no longer
transmitted under the conditions of thickness obtaining in
rock
sections. It is well known that there is in biotite a maximum
absorption of a plane-polarised light ray, when the plane of
vibration coincides with the plane of cleavage. A section
across
the cleavage then shows a maximum amount of absorption. A
halo
seen on this section simply produces this effect in a more
intense degree. This is well shown in Plate XXIII (lower
figure),
on a portion of the halo-sphere. The descriptive name
"Pleochroic
Halo" has originated from this fact. We must conclude that
the
effect of the ionisation due to the alpha ray has not been to
alter fundamentally the conditions which give rise to the
optical
properties of the medium. The increased absorption is
probably
associated with some change in the chemical state of the iron
present. Haloes are, I believe, not found in minerals from
which
this
235
element is absent. One thing is quite certain. The colouration
is
not due to an accumulation of helium atoms, _i.e._ of spent
alpha
rays. The evidence for this is conclusive. If helium was
responsible we should have haloes produced in all sorts of
colourless minerals. Now we sometimes see zircons in felspars
and
in quartz, etc., but in no such case is a halo produced. And
halo-spheres formed within and sufficiently close to the edge
of
a crystal of mica are abruptly truncated by neighbouring areas
of
fclspar or quartz, although we know that the rays must pass
freely across the boundary. Again it is easy to show that even
in
the oldest haloes the quantity of helium involved is so small
that one might say the halo-sphere was a tolerably good vacuum
as
regards helium. There is, finally, no reason to suppose that
the
imprisoned helium would exhibit such a colouration, or,
indeed,
any at all.
I have already referred to the great age of the halo. Haloes
are
not found in the younger igneous rocks. It is probable that a
halo less than a million years old has never been seen. This,
primâ facie, indicates an extremely slow rate of formation.
And
our calculations quite support the conclusions that the growth
of
a halo, if this has been uniform, proceeds at a rate of
almost
unimaginable slowness.
Let us calculate the number of alpha rays which may have gone
to
form a halo in the Devonian granite of Leinster.
236
It is common to find haloes developed perfectly in this
granite,
and having a nucleus of zircon less than 5 x 10-4 cms.
in
diameter. The volume of zircon is 65 x 10-12 c.cs. and
the mass
3 x 10-10 grm.; and if there was in this zircon
10-8 grm. radium
per gram (a quantity about five times the greatest amount
measured by Strutt), the mass of radium involved is 3 x
10-18
grm. From this and from the fact ascertained by Rutherford
that
the number of alpha rays expelled by a gram of radium in one
second is 3.4 x 1010, we find that three rays are shot
from the
nucleus in a year. If, now, geological time since the Devonian
is
50 millions of years, then 150 millions of rays built up the
halo. If geological time since the Devonian is 400 millions
of
years, then 1,200 millions of alpha rays are concerned in its
genesis. The number of ions involved, of course, greatly
exceeds
these numbers. A single alpha ray fired from radium C will
produce 2.37 x 105 ions in air.
But haloes may be found quite clearly defined and fairly dark
out
to the range of the emanation ray and derived from much less
quantities of radioactive materials. Thus a zircon nucleus with
a
diameter of but 3.4 x 10-4 cms. formed a halo strongly
darkened
within, and showing radium A and radium C as clear smoky
rings.
Such a nucleus, on the assumption made above as to its radium
content, expels one ray in a year. But, again, haloes are
observed with less blackened pupils and with faint ring due
to
radium C, formed round nuclei
237
of rather less than 2 x 10-4 cms. diameter. Such
nuclei would
expel one ray in five years. And even lesser nuclei will
generate
in these old rocks haloes with their earlier characteristic
features clearly developed. In the case of the most minute
nuclei, if my assumption as to the uranium content is correct,
an
alpha ray is expelled, probably, no oftener than once in a
century; and possibly at still longer intervals.
The equilibrium amount of radium contained in some nuclei
may
amount to only a few atoms. Even in the case of the larger
nuclei
and more perfectly developed haloes the quantity of radium
involved is many millions of times less than the least amount
we
can recognise by any other means. But the delicacy of the
observation is not adequately set forth in this statement. We
can
not only tell the nature of the radioactive family with which
we
are dealing; but we can recognise the presence of some of its
constituent members. I may say that it is not probable the
zircons are richer in radium than I have assumed. My
assumption
involves about 3 per cent. of uranium. I know of no analyses
ascribing so great an amount of uranium to zircon. The
variety
cyrtolite has been found to contain half this amount, about.
But
even if we doubled our estimate of radium content, the
remarkable
nature of our conclusions is hardly lessened.
It may appear strange that the ever-interesting question of
the
Earth's age should find elucidation from the
238
study of haloes. Nevertheless the subjects are closely
connected.
The circumstances are as follows. Geologists have estimated
the
age of the Earth since denudation began, by measurements of
the
integral effects of denudation. These methods agree in showing
an
age of about rob years. On the other hand, measurements have
been
made of the accumulation in minerals of radioactive
_débris_—the
helium and lead—and results obtained which, although they
do not
agree very well among themselves, are concordant in assigning
a
very much greater age to the rocks. If the radioactive
estimate
is correct, then we are now living in a time when the
denudative
forces of the Earth are about eight or nine times as active
as
they have been on the average over the past. Such a state of
things is absolutely unaccountable. And all the more
unaccountable because from all we know we would expect a
somewhat
_lesser_ rate of solvent denudation as the world gets older and
the
land gets more and more loaded with the washed-out materials
of
the rocks.
Both the methods referred to of finding the age assume the
principle of uniformity. The geologist contends for
uniformity
throughout the past physical history of the Earth. The
physicist
claims the like for the change-rates of the radioactive
elements.
Now the study of the rocks enables us to infer something as
to
the past history of our Globe. Nothing is, on the other hand,
known respecting the origin of uranium or thorium—the
parent
radioactive bodies. And while not questioning the law
239
and regularity which undoubtedly prevail in the periods of
the
members of the radioactive families, it appears to me that it
is
allowable to ask if the change rate of uranium has been
always
what we now believe it to be. This comes to much the same
thing
as supposing that atoms possessing a faster change rate once
were
associated with it which were capable of yielding both helium
and
lead to the rocks. Such atoms might have been collateral in
origin with uranium from some antecedent element. Like
helium,
lead may be a derivative from more than one sequence of
radioactive changes. In the present state of our knowledge
the
possibilities are many. The rate of change is known to be
connected with the range of the alpha ray expelled by the
transforming element; and the conformity of the halo with our
existing knowledge of the ranges is reason for assuming that,
whatever the origin of the more active associate of uranium,
this
passed through similar elemental changes in the progress of
its
disintegration. There may, however, have been differences in
the
ranges which the halo would not reveal. It is remarkable that
uranium at the present time is apparently responsible for two
alpha rays of very different ranges. If these proceed from
different elements, one should be faster in its change rate
than
the other. Some guidance may yet be forthcoming from the study
of
the more obscure problems of radioactivity.
Now it is not improbable that the halo may contribute directly
to
this discussion. We can evidently attack
240
the biotite with a known number of alpha rays and determine
how
many are required to produce a certain intensity of
darkening,
corresponding to that of a halo with a nucleus of measurable
dimensions. On certain assumptions, which are correct within
defined limits, we can calculate, as I have done above, the
number of rays concerned in forming the halo. In doing so we
assume some value for the age of the halo. Let us take the
maximum radioactive value. A halo originating in Devonian
times
may attain a certain central blackening from the effects of,
say,
rob rays. But now suppose we find that we cannot produce the
same
degree of blackening with this number of rays applied in the
laboratory. What are we to conclude? I think there is only
the
one conclusion open to us; that some other source of alpha
rays,
or a faster rate of supply, existed in the past. And this
conclusion would explain the absence of haloes from the
younger
rocks; which, in view of the vast range of effects possible
in
the development of haloes, is, otherwise, not easy to account
for. It is apparent that the experiment on the biotite has a
direct bearing on the validity of the radioactive method of
estimating the age of the rocks. It is now being carried out
by
Professor Rutherford under reliable conditions.
Finally, there is one very certain and valuable fact to be
learned from the halo. The halo has established the extreme
rarity of radioactivity as an atomic phenomenon. One and all
of
the speculations as to
241
the slow breakdown of the commoner elements may be dismissed.
The
halo shows that the mica of the rocks is radioactively
sensitive.
The fundamental criterion of radioactive change is the
expulsion
of the alpha ray. The molecular system of the mica and of
many
other minerals is unstable in presence of these rays, just as
a
photographic plate is unstable in presence of light.
Moreover,
the mineral integrates the radioactive effects in the same way
as
a photographic salt integrates the effects of light. In both
cases the feeblest activities become ultimately apparent to
our
inspection. We have seen that one ray in each year since the
Devonian period will build the fully formed halo: an object
unlike any other appearance in the rocks. And we have been
able
to allocate all the haloes so far investigated to one or the
other of the known radioactive families. We are evidently
justified in the belief that had other elements been
radioactive
we must either find characteristic haloes produced by them,
or
else find a complete darkening of the mica. The feeblest
alpha
rays emitted by the relatively enormous quantities of the
prevailing elements, acting over the whole duration of
geological
time—and it must be remembered that the haloes we have
been
studying are comparatively young—must have registered
their
effects on the sensitive minerals. And thus we are safe in
concluding that the common elements, and, indeed, many which
would be called rare, are possessed of a degree of stability
which has preserved them un
242
changed since the beginning of geological time. Each
unaffected
flake of mica is, thus, unassailable proof of a fact which
but
for the halo would, probably, have been for ever beyond our
cognisance.
THE USE OF RADIUM IN MEDICINE [1]
IT has been unfortunate for the progress of the
radioactive
treatment of disease that its methods and claims involve much
of
the marvellous. Up till recently, indeed, a large part of
radioactive therapeutics could only be described as bordering
on
the occult. It is not surprising that when, in addition to
its
occult and marvellous characters, claims were made on its
behalf
which in many cases could not be supported, many medical men
came
to regard it with a certain amount of suspicion.
Today, I believe, we are in a better position. I think it
is
possible to ascribe a rational scientific basis to its
legitimate
claims, and to show, in fact, that in radioactive treatment
we
are pursuing methods which have been already tried
extensively
and found to be of definite value; and that new methods
differ
from the old mainly in their power and availability, and
little,
or not at all, in kind.
Let us briefly review the basis of the science. Radium is
a
metallic element chemically resembling barium. It
[1] A Lecture to Postgraduate Students of Medicine in
connection
with the founding of the Dublin Radium Institute, delivered
in
the School of Physic in Ireland, Trinity College, on October
2nd,
1914
244
possesses, however, a remarkable property which barium does
not.
Its atoms are not equally stable. In a given quantity of radium
a
certain very small percentage of the total number of atoms
present break up per second. By "breaking up" we mean their
transmutation to another element. Radium, which is a solid
element under ordinary conditions, gives rise by transmutation
to
a gaseous element—the emanation of radium. The new element
is a
heavy gas at ordinary temperatures and, like other gases, can
be
liquified by extreme cold. The extraordinary property of
transmutation is entirely automatic. No influence which
chemist
or physicist can apply can affect the rate of transformation.
The emanation inherits the property of instability, but in
its
case the instability is more pronounced. A relatively large
fraction of its atoms transmute per second to a solid element
designated Radium A. In turn this new generation of atoms
breaks
up—even faster than the emanation—becoming yet
another element
with specific chemical properties. And so on for a whole
sequence
of transmutations, till finally a stable substance is formed,
identical with ordinary lead in chemical and physical
properties,
but possessing a slightly lower atomic weight.
The genealogy of the radium series of elements shows that
radium
is not the starting point. It possesses ancestors which have
been
traced back to the element uranium.
Now what bearing has this series of transmutations
245
upon medical science? Radium or emanation, &c., are not in
the
Pharmacopoeia as are, say, arsenic or bismuth. The whole
medicinal value of these elements resides in the very
wonderful
phenomena of their radiations. They radiate in the process of
transmuting.
The changing atom may radiate a part of its own mass. The
"alpha"-ray (a-ray) is such a material ray. It is an
electrified
helium atom cast out of the parent atom with enormous
velocity—such a velocity as would carry it, if not impeded,
all
round the earth in two seconds. All alpha-rays are positively
electrified atoms of the element helium, which thereby is
shown
to be an integral constituent of many elements. The alpha-ray
is
not of much value to medical science, for, in spite of its
great
velocity, it is soon stopped by encounter with other atoms.
It
can penetrate only a minute fraction of a millimetre into
ordinary soft tissues. We shall not further consider it.
Transmuting atoms give out also material rays of another
kind:
the ß-rays. The ß-ray is in mass but a very small
fraction of,
even, a hydrogen atom. Its speed may approach that of light.
As
cast out by radioactive elements it starts with speeds which
vary
with the element, and may be from one-third to nine-tenths
the
velocity of light. The ß-ray is negatively electrified. It
has
long been known to science as the electron. It is also
identical
with the cathode ray of the vacuum tube.
246
Another and quite different kind of radiation is given out
by
many of the transmuting elements:—the y-ray. This is
not
material, it is ethereal. It is known now with certainty that
the
y-ray is in kind identical with light, but of very much
shorter
wave length than even the extreme ultraviolet light of the
solar
spectrum. The y-ray is flashed from the transmuting atom
along
with the ß-ray. It is identical in character with the x-ray
but
of even shorter wave length.
There is a very interesting connection between the y-ray and
the
ß-ray which it is important for the medical man to
understand—as
far as it is practicable on our present knowledge.
When y-rays or x-rays fall on matter they give rise to
ß-rays.
The mechanism involved is not known but it is possibly a
result
of the resonance of the atom, or of parts of it, to the short
light waves. And it is remarkable that the y-rays which, as
we
have seen, are shorter and more penetrating waves than the
x-rays, give rise to ß-rays possessed of greater velocity
and
penetration than ß-rays excited by the x-rays. Indeed the
ß-rays
originated by y-rays may attain a velocity nearly approaching
that of light and as great as that of any ß-rays emitted
by
transmuting atoms. Again there is demonstrable evidence that
ß-rays impinging on matter may give rise to y-rays. The
most
remarkable demonstration of this is seen in the x-ray tube.
Here
the x-rays originate where the stream of ß- or
cathode-rays
247
are arrested on the anode. But the first relation is at
present
of most importance to us—_i.e._ that the y-or x-rays give
rise to
ß-rays.
This relation gives us additional evidence of the identity of
the
physical effects of y-, x-, and light-rays —using the term
light
rays in the usual sense of spectral rays. For it has long
been
known that light waves liberate electrons from atoms. It has
been
found that these electrons possess a certain initial velocity
which is the greater the shorter the wave length of the light
concerned in their liberation. The whole science of
"photo-electricity" centres round this phenomenon. The action
of
light on the photographic plate, as well as many other
physical
and chemical phenomena, find an explanation in this liberation
of
the electron by the light wave.
Here, then, we have spectral light waves liberating
electrons—_i.e._ very minute negatively-charged particles,
and we
find that, as we use shorter light waves, the initial velocity
of
these particles increases. Again, we have x-rays which are
far
smaller in wave length than spectral light, liberating much
faster negatively electrified particles. Finally, we have
y-rays—the shortest nether waves of all-liberating
negative
particles of the highest velocity known. Plainly the whole
series
of phenomena is continuous.
We can now look closer at the actions involved in the
therapeutic
influence of the several rays and in
248
this way, also, see further the correlation between what may
be
called photo-therapeutics and radioactive therapeutics.
The ß-ray, whether we obtain it directly from the
transforming
radioactive atom or whether we obtain it as a result of the
effects of the y- or x-rays upon the atom, is an ionising
agent
of wonderful power. What is meant by this? In its physical
aspect
this means that the atoms through which it passes acquire
free
electric charges; some becoming positive, some negative. This
can
only be due to the loss of an electron by the affected atom.
The
loss of the small negative charge carried in the electron
leaves
the atom positively electrified or creates a positive ion.
The
fixing of the wandering electron to a neutral atom creates a
negative ion. Before further consideration of the importance
of
the phenomenon of ionisation we must fix in our minds that
the
agent, which brings this about, is the ß-ray. There is
little
evidence that the y-ray can directly create ions to any large
extent. But the action of liberating high-speed ß-rays
results in
the creation of many thousands of ions by each ß-ray
liberated.
As an agent in the hands of the medical man we must regard
the
y-ray as a light wave of extremely penetrating character,
which
creates high-speed ß-rays in the tissues which it
penetrates,
these ß-rays being most potent ionising agents. The
ß-rays
directly obtained from radioactive atoms assist in the work
of
ionisation. ß-rays do not
249
penetrate far from their source. The fastest of them would
not
probably penetrate one centimetre in soft tissues.
We must now return to the phenomenon of ionisation. Ionisation
is
revealed to observation most conspicuously when it takes place
in
a gas. The + and - electric charges on the gas particles endow
it
with the properties of a conductor of electricity, the + ions
moving freely in one direction and the - ions in the opposite
direction under an electric potential. But there are effects
brought about by ionisation of more importance to the medical
man
than this. The chemist has long come to recognise that in the
ion
he is concerned with the inner mechanism of a large number of
chemical phenomena. For with the electrification of the atom
attractive and repulsive forces arise. We can directly show
the
chemical effects of the ionising ß-rays. Water exposed to
their
bombardment splits up into hydrogen and oxygen. And, again,
the
separated atoms may be in part recombined under the influence
of
the radiation. Ammonia splits up into hydrogen and nitrogen.
Carbon dioxide forms carbon, carbon monoxide, and oxygen;
hydrochloric acid forms chlorine and hydrogen. In these
cases,
also, recombination can be partially effected by the rays.
We can be quite sure that within the complex structure of
the
living cell the ionising effects which everywhere accompany
the
ß-rays must exert a profound influence. The sequence of
chemical
events which as yet seem
250
beyond the ken of science and which are involved in
metabolism
cannot fail to be affected. Any, it is not surprising that as
the
result of eaperinient it is found that the radiations are
agents
which may be used either for the stimulation of the natural
events of growth or used for the actual destruction of the
cell.
It is easy to see that the feeble radiation should produce
the
one effect, the strong the other. In a similar way by a
moderate
light stimulus we create the latent image in the photographic
plate; by an intense light we again destroy this image. The
inner
mechanism in this last case can be logically stated.[1]
_There is plainly a true physical basis here for the efficacy
of
radioactive treatment and, what is more, we find when we
examine
it, that it is in kind not different from that underlying
treatment by spectral radiations. But in degree it is very
different and here is the reason for the special importance
of
radioactivity as a therapeutic agent._ The Finsen light is
capable
of influencing the soft tissues to a short depth only. The
reason
is that the wave length of the light used is too great to
pass
without rapid absorption through the tissues; and, further,
the
electrons it gives rise to—_i.e._ the ß-rays it
liberates—are too
slow-moving to be very efficient ionisers. X-rays penetrate
in
some cases quite freely and give rise to much faster and more
powerful ß-rays
[1] See _The Latent Image_, p. 202.
251
than can the Finsen light. But far more penetrating than
x-rays
are the y-rays emitted in certain of the radioactive changes.
These give rise to ß-rays having a velocity approximate to
that
of light.
The y-rays are, therefore, very penetrating and powerfully
ionising light waves; light waves which are quite invisible
to
the eye and can beam right through the tissues of the body.
To
the mind's eye only are they visible. And a very wonderful
picture they make. We see the transmuting atom flashing out
this
light for an inconceivably short instant as it throws off the
ß-ray. And "so far this little candle throws his beams" in
the
complex system of the cells, so far atoms shaken by the rays
send
out ß-rays; these in turn are hurled against other
atomic
systems; fresh separations of electrons arise and new
attractions
and repulsions spring up and the most important chemical
changes
are brought about. Our mental picture can claim to be no more
than diagrammatic of the reality. Still we are here dealing
with
recognised physical and chemical phenomena, and their
description
as "occult" in the derogatory sense is certainly not
justifiable.
Having now briefly reviewed the nature of the rays arising
in
radioactive substances and the rationale of their influence,
we
must turn to more especially practical considerations.
The Table given opposite shows that radium itself is
responsible
for a- and ß-rays only. It happens that
252
Period in whioh ½ element is transformed.
URANIUM 1 & 2 { a 6 } x 109 years.
URANIUM X { a ß } 24.6 days.
IONIUM { a 8 } x 104 years.
RADIUM { a ß } 2 x 102 years.
EMANATION { a } 8.85 days.
RADIUM A { a 8 } minutes.
RADIUM B { ß y } 26.7 minutes.
RADIUM C { a ß y } 13.5 minutes.
RADIUM D { ß } 15 years.
RADIUM E { ß y } 4.8 days.
RADIUM (Polonium) F { a } 140 days.
Table showing the successive generations of the elements of
the
Uranium-radium family, the character of their radiations and
their longevity.
253
the ß-rays emitted by radium are very
"soft"—_i.e._ slow and
easily absorbed. The a-ray is in no case available for more
than
mere surface application. Hence we see that, contrary to what
is
generally believed, radium itself is of little direct
therapeutic
value. Nor is the next body in succession—the emanation,
for it
gives only a-rays. In fact, to be brief, it is not till we
come
to Radium B that ß-rays of a relatively high penetrative
quality
are reached; and it is not till we come to Radium C that
highly
penetrative y-rays are obtained.
It is around this element, Radium C, that the chief
medical
importance of radioactive treatment by this family of
radioactive
bodies centres. Not only are ß-rays of Radium C very
penetrating,
but the y-rays are perhaps the most energetic rays of the,
kind
known. Further in the list there is no very special medical
interest.
Now, how can we get a supply of this valuable element Radium
C?
We can obtain it from radium itself. For even if radium has
been
deprived of its emanation (which is easily done by heating it
or
bringing it into solution) in a few weeks we get back the
Radium
C. One thing here we must be clear about. With a given
quantity
of Radium only a certain definitely limited amount of Radium
C,
or of emanation, or any other of the derived bodies, will be
associated. Why is this? The answer is because the several
successive elements are themselves decaying —_i.e._
changing one
into the other. The atomic per-
254
centage of each, which decays in a second, is a fixed
quantity
which we cannot alter. Now if we picture radium which has
been
completely deprived of its emanation, again accumulating by
automatic transmutation a fresh store of this element, we have
to
remember:— (i) That the rate of creation of emanation by
the
radium is practically constant; and (2) that the absolute
amount
of the emanation decaying per second increases as the stock
of
emanation increases. Finally, when the amount of accumulated
emanation has increased to such an extent that the number of
emanation atoms transmuting per second becomes exactly equal
to
the number being generated per second, the amount of
emanation
present cannot increase. This is called the equilibrium
amount.
If fifteen members are elected steadily each year into a
newly-founded society the number of members will increase for
the
first few years; finally, when the losses by death of the
members
equal about fifteen per annum the society can get no bigger.
It
has attained the equilibrium number of members.
This applies to every one of the successive elements. It
takes
twenty-one days for the equilibrium quantity of emanation to
be
formed in radium which has been completely de-emanated; and
it
takes 3.8 days for half the equilibrium amount to be formed.
Again, if we start with a stock of emanation it takes just
three
hours for the equilibrium amount of Radium C to be formed.
255
We can evidently grow Radium C either from radium itself or
from
the emanation of radium. If we use a tube of radium we have
an
almost perfectly constant quantity of Radium C present, for
as
fast as the Radium C and intervening elements decay the
Radium,
which only diminishes very slowly in amount, makes up the
loss.
But, if we start off with a tube of emanation, we do not
possess
a constant supply of Radium C, because the emanation is
decaying
fairly rapidly and there is no radium to make good its loss.
In
3.8 days about one half the emanation is transmuted and the
Radium C decreases proportionately and, of course, with the
Radium C the valuable radiations also decrease. In another
3.8
days—that is in about a week from the start—the
radioactive value
of the tube has fallen to one-fourth of its original value.
But in spite of the inconstant character of the emanation
tube
there are many reasons for preferring its use to the use of
the
radium tube. Chief of these is the fact that we can keep the
precious radium safely locked up in the laboratory and not
exposed to the thousand-and-one risks of the hospital. Then,
secondly, the emanation, being a gas, is very convenient for
subdivision into a large number of very small tubes according
to
the dosage required.
In fact the volume of the emanation is exceedingly minute.
The
amount of emanation in equilibrium with one gramme of radium
is
called the curie, and with one
256
milligramme the millicurie. Now, the volume of the curie is
only
a little more than one half a cubic millimetre. Hence in
dealing
with emanation from twenty or forty milligrammes of radium we
are
dealing with very small volumes.
How may the emanation be obtained? The process is an easy one
in
skilled and practised hands. The salt of radium—generally
the
bromide or chloride—is brought into acid solution. This
causes
the emanation to be freely given off as fast as it is formed.
At
intervals we pump it off with a mercury pump.
Let us see how many millicuries we will in future be able to
turn
out in the week in our new Dublin Radium Institute.[1] We
shall
have about 130 milligrammes of radium. In 3.8 days we get 65
millicuries from this—_i.e._ half the equilibrium amount of
130
millicuries. Hence in the week, we shall have about 130
millicuries.
This is not much. Many experts consider this little enough
for
one tube. But here in Dublin we have been using the emanation
in
a more economical and effective manner than is the usage
elsewhere; according to a method which has been worked out
and
developed in our own Radium Institute. The economy is obtained
by
the very simple expedient of minutely subdividing the' dose.
The
system in vogue, generally, is to treat the tumour by
inserting
into it one or two very active
[1] Then recently established by the Royal Dublin Society.
257
tubes, containing, perhaps, up to 200 millicuries, or even
more,
per tube. Now these very heavily charged tubes give a
radiation
so intense at points close to the tube, due to the greater
density of the rays near the tube, and, also, to the action
of
the softer and more easily absorbable rays, that it has been
found necessary to stop these softer rays—both the y and
ß—by
wrapping lead or platinum round the tube. In this lead or
platinum some thirty per cent. or more of the rays is
absorbed
and, of course, wasted. But in the absence of the screen there
is
extensive necrosis of the tissues near the tubes.
If, however, in place of one or two such tubes we use ten
or
twenty, each containing one-tenth or one-twentieth of the
dose,
we can avail ourselves of the softer rays around each tube
with
benefit. Thus a wasteful loss is avoided. Moreover a more
uniform
"illumination" of the tissues results, just as we can
illuminate
a hall more uniformly by the use of many lesser centres of
light
than by the use of one intense centre of radiation. Also we
get
what is called "cross-radiation,"which is found to be
beneficial.
The surgeon knows far better what he is doing by this method.
Thus it may be arranged for the effects to go on with
approximate
uniformity throughout the tumour instead of varying rapidly
around a central point or—and this may be very
important— the
effects may be readily concentrated locally.
Finally, not the least of the benefit arises in the easy
technique of this new method. The quantities of
258
emanation employed can fit in the finest capillary glass
tubing
and the hairlike tubes can in turn be placed in fine
exploring
needles. There is comparatively little inconvenience to the
patient in inserting these needles, and there is the most
perfect
control of the dosage in the number and strength of these
tubes
and the duration of exposure.[1]
The first Radium Institute in Ireland has already done good
work
for the relief of human suffering. It will have, I hope, a
great
future before it, for I venture, with diffidence, to hold the
opinion, that with increased study the applications and claims
of
radioactive treatment will increase.
[1] For particulars of the new technique and of some of the
work
already accomplished, see papers, by Dr. Walter C. Stevenson,
_British Medical Journal_, July 4th, 1914, and March 20th,
1915.
259
SKATING [1]
IT is now many years ago since, as a student, I was present at
a
college lecture delivered by a certain learned professor on
the
subject of friction. At this lecture a discussion arose out of
a
question addressed to our teacher: "How is it we can skate on
ice
and on no other substance?"
The answer came back without hesitation: "Because the ice is
so
smooth."
It was at once objected: "But you can skate on ice which is
not
smooth."
This put the professor in a difficulty. Obviously it is not
on
account of the smoothness of the ice. A piece of polished
plate
glass is far smoother than a surface of ice after the latter
is
cut up by a day's skating. Nevertheless, on the scratched and
torn ice-surface skating is still quite possible; on the
smooth
plate glass we know we could not skate.
Some little time after this discussion, the connection
between
skating and a somewhat abstruse fact in physical science
occurred
to me. As the fact itself is one which has played a part in
the
geological history of the earth,
[1] A lecture delivered before the Royal Dublin Society in 1905.
260
and a part of no little importance, the subject of
skating,
whereby it is perhaps best brought home to every one, is
deserving of our careful attention. Let not, then, the title
of
this lecture mislead the reader as to the importance of its
subject matter.
Before going on to the explanation of the wonderful freedom
of
the skater's movements, I wish to verify what I have inferred
as
to the great difference in the slipperiness of glass and the
slipperiness of ice. Here is a slab of polished glass. I can
raise it to any angle I please so that at length this brass
weight of 250 grams just slips down when started with a
slight
shove. The angle is, as you see, about 12½ degrees. I
now
transfer the weight on to this large slab of ice which I
first
rapidly dry with soft linen. Observe that the weight slips
down
the surface of ice at a much lower angle. It is a very low
angle
indeed: I read it as between 4 and 5 degrees. We see by this
experiment that there is a great difference between the
slipperiness of the two surfaces as measured by what is
called
"the angle of friction." In this experiment, too, the glass
possesses by far the smoother surface although I have rubbed
the
deeper rugosities out of the ice by smoothing it with a glass
surface. Notwithstanding this, its surface is spotted with
small
cavities due to bubbles and imperfections. It is certain that
if
the glass was equally rough, its angle of friction towards
the
brass weight would be higher.
261
We have, however, another comparative experiment to carry out.
I
made as you saw a determination of the angle at which this
weight
of 250 grams just slipped on the ice. The lower surface of
the
weight, the part which presses on the ice, consists of a
light,
brass curtain ring. This can be detached. Its mass is only
6½
grams, the curtain ring being, in fact, hollow and made of
very
thin metal. We have, therefore, in it a very small weight
which
presents exactly the same surface beneath as did the weight
of
250 grams. You see, now, that this light weight will not slip
on
ice at 5 or 6 degrees of slope, but first does so at about io
degrees.
This is a very important experiment as regards our present
inquiry. Ice appears to possess more than one angle of
friction
according as a heavy or a light weight is used to press upon
it.
We will make the same experiment with the plate of glass. You
see
that there is little or no difference in the angle of friction
of
brass on glass when we press the surfaces together with a
heavy
or with a light weight. The light weight requires the same
slope
of 12½ degrees to make it slip.
This last result is in accordance with the laws of friction.
We
say that when solid presses on solid, for each pair of
substances
pressed together there is a constant ratio between the force
required to keep one in motion over the other, and the force
pressing the solids together. This ratio is called"the
coefficient of friction."The coefficient is, in fact, constant
or
approximately
262
so. I can determine the coefficient of friction from the angle
of
friction by taking the tangent of the angle. The tangent of
the
angle of friction is the coefficient of friction. If, then,
the
coefficient is constant, so, of course, must the angle of
friction be constant. We have seen that it is so in the case
of
metal on glass, but not so in the case of metal on ice. This
curious result shows that there is something abnormal about
the
slipperiness of ice.
The experiments we have hitherto made are open to the
reproach
that the surface of the ice is probably damp owing to the
warmth
of the air in contact with it. I have here a means of dealing
with a surface of cold, dry ice. This shallow copper tank
about
18 inches (45 cms.) long, and 4 inches (10 cms.) wide, is
filled
with a freezing 'mixture circulated through it from a larger
vessel containing ice melting in hydrochloric acid at a
temperature of about -18° C. This keeps the tank below
the
melting point of ice. The upper surface of the tank is
provided
with raised edges so that it can be flooded with water. The
water
is now frozen and its temperature is below 0° C. It is
about
10° C. I can place over the ice a roof-shaped cover made of
two
inclined slabs of thick plate glass. This acts to keep out
warm
air, and to do away with any possibility of the surface of
the
ice being wet with water thawed from the ice. The whole tank
along with its roof of glass can be adjusted to any angle, and
a,
scale at the
263
raised end of the tank gives the angle of slope in degrees.
A
weight placed on the ice can be easily seen through the glass
cover.
The weight we shall use consists of a very light ring of
aluminium wire which is rendered plainly visible by a
ping-pong
ball attached above it. The weight rests now on a copper
plate
provided for the purpose at the upper end of the tank. The
plate
being in direct contact beneath with the freezing mixture we
are
sure that the aluminium ring is no hotter than the ice. A
light
jerk suffices to shake the weight on to the surface of the
ice.
We find that this ring loaded with only the ping-pong ball,
and
weighing a total of 2.55 grams does not slip at the low angles.
I
have the surface of the ice at an angle of rather over
13½, and
only by continuous tapping of the apparatus can it be induced
to
slip down. This is a coefficient of 0.24, and compares with
the
coefficient of hard and smooth solids on one another. I now
replace the empty ping-pong ball by a similar ball filled
with
lead shot. The total weight is now 155 grams. You see the
angle
of slipping has fallen to 7°.
Every one who has made friction experiments knows how
unsatisfactory and inconsistent they often are. We can only
discuss notable quantities and broad results, unless the most
conscientious care be taken to eliminate errors. The net
result
here is that ice at about -10° C. when pressed on by a very
light
weight possesses a
264
coefficient of friction comparable with the usual coefficients
of
solids on solids, but when the pressure is increased, the
coefficient falls to about half this value.
The following table embodies some results obtained on the
friction of ice and glass, using the methods I have shown you.
I
add some of the more carefully determined coefficients of
other
observers.
Wt. in On Plate On Ice On
Ice
Grams. Glass. at 0° C. at
10° C.
Angle. Coeff. Angle. Coeff. Angle.
Coeff
Aluminium 2.55 12½° 0.22 12°
0.21 13½° 0.24
Same 155 12½° 0.22 6° 0.11
7° 0.12
Brass 6.5 12½° 0.22 10°
0.17 10½° 0.18
Same 107 12½° 0.22 5° 0.09
6° 0.10
Steel on steel (Morin) - - - - 0.14
Brass on cast iron (Morin) - - 0.19
Steel on cast iron (Morin) - - 0.20
Skate on ice (J. Müller) - - - 0.016—0.032
Best-greased surfaces (Perry) - 0.03—0.036
You perceive from the table that while the friction of brass
or
aluminium on glass is quite independent of the weight used,
that
of brass or aluminium on ice depends in some way upon the
weight,
and falls in a very marked degree when the weight is heavy.
Now,
I think that if we had been on the look out for any
abnormality
in the friction of hard substances on ice, we would have
rather
anticipated a variation in the
265
other direction. We would have, perhaps, expected that a
heavy
weight would have given rise to the greater friction. I now
turn
to the explanation of this extraordinary result.
You are aware that it requires an expenditure of heat merely
to
convert ice to water, the water produced being at the
temperature
of the ice, _i.e._ at 0° C., from which it is derived. The
heat
required to change the ice from the solid to the liquid state
is
the latent heat of water. We take the unit quantity of heat to
be
that which is required to heat 1 kilogram of water 1° C. Then
if
we melt 1 kilogram of ice, we must supply it with 80 such
units
of heat. While melting is going on, there is no change of
temperature if the experiment is carefully conducted. The
melting
ice and the water coming from it remain at 0° C. throughout
the
operation, and neither the thermometer nor your own
sensations
would tell you of the amount of heat which was flowing in.
The
heat is latent or hidden in the liquid produced, and has gone
to
do molecular work in the substance. Observe that if we supply
only 40 thermal units, we get only one-half the ice melted.
If
only 10 units are supplied, then we get only one eighth of a
kilogram of water, and no more nor less.
I have ventured to recall to you these commonplaces of
science
before considering a mode of melting ice which is less
generally
known, and which involves no supply of heat on your part.
This
method involves for its
266
understanding a careful consideration of the thermal
properties
of water in the solid state.
It must have been observed a very long time ago that water
expands when it freezes. Otherwise ice would not float on
water;
and, what is perhaps more important in your eyes, your water
pipes would not burst in winter when the water freezes
therein.
But although the important fact of the expansion of water on
freezing was so long presented to the observation of mankind,
it
was not till almost exactly the middle of the last century
that
James Thomson, a gifted Irishman, predicted many important
consequences arising from the fact of the expansion of water
on
becoming solid. The principles lie enunciated are perfectly
general, and apply in every case of change of volume
attending
change of state. We are here only concerned with the case of
water and ice.
James Thomson, following a train of thought which we cannot
here
pursue, predicted that owing to the fact of the expansion of
water on becoming solid, pressure will lower the melting point
of
ice or the freezing point of water. Normally, as you are
aware,
the temperature is 0° C. or 32° F. Thomson said that this
would
be found to be the freezing point only at atmospheric
pressure.
He calculated how much it would change with change of
pressure.
He predicted that the freezing point would fall 0.0075 of a
degree Centigrade for each additional atmosphere of pressure
applied to the water. Suppose,
267
for instance, our earth possessed an atmosphere so heavy to
as
exert a thousand times the pressure of the existing
atmosphere,
then water would not freeze at 0° C., but at -7.5° C. or
about
18° F. Again, in vacuo, that is when the pressure has
been
reduced to the relatively small vapour pressure of the water,
the
freezing point is above 0° C., _i.e._ at 0.0075° C. In
parts of
the ocean depths the pressure is much over a thousand
atmospheres. Fresh water would remain liquid there at
temperatures much below 0° C.
It will be evident enough, even to those not possessed of
the
scientific insight of James Thomson, that some such fact is to
be
anticipated. It is, however, easy to be wise after the event.
It
appeals to us in a general way that as water expands on
freezing,
pressure will tend to resist the turning of it to ice. The
water
will try to remain liquid in obedience to the pressure. It
will,
therefore, require a lower temperature to induce it to become
ice.
James Thomson left his thesis as a prediction. But he
predicted
exactly what his distinguished brother, Sir William
Thomson—later
Lord Kelvin—found to happen when the matter was put to the
test
of experiment. We must consider the experiment made by Lord
Kelvin.
According to Thomson's views, if a quantity of ice and water
are
compressed, there must be _a fall of temperature_. The nature
of
his argument is as follows:
268
Let the ice and water be exactly at 0° C. to start with.
Then
suppose we apply, say, one thousand atmospheres pressure. The
melting point of the ice is lowered to -7.5° C. That is, it
will
require a temperature so low as -7.5° C. to keep it solid.
It
will therefore at once set about melting, for as we have
seen,
its actual temperature is not -7.5° C., but a higher
temperature,
_i.e._ 0° C. In other words, it is 7.5° above its melting
point.
But as soon as it begins melting it also begins to absorb heat
to
supply the 80 thermal units which, as we know, are required
to
turn each kilogram of the ice to water. Where can it get this
heat? We assume that we give it none. It has only two
sources,
the ice can take heat from itself, and it can take heat from
the
water. It does both in this case, and both ice and water drop
in
temperature. They fall in temperature till -7.5° is reached.
Then
the ice has got to its melting point under the pressure of
one
thousand atmospheres, or, as we may put it, the water has
reached
its freezing point. There can be no more melting. The whole
mass
is down to -7.5° C., and will stay there if we keep heat
from
flowing either into or out of the vessel. There is now more
water
and less ice in the vessel than when we started, and the
temperature has fallen to -7.5° C. The fall of temperature to
the
amount predicted by the theory was verified by Lord Kelvin.
Suppose we now suddenly remove the pressure; what will happen?
We
have water and ice at -7.5° C.
269
and at the normal pressure. Water at -7.5° and at the
normal
pressure of course turns to ice. The water will, therefore,
instantly freeze in the vessel, and the whole process will be
reversed. In freezing, the water will give up its latent
heat,
and this will warm up the whole mass till once again 0° C.
is
attained. Then there will be no more freezing, for again the
ice
is at its melting point. This is the remarkable series of
events
which James Thomson predicted. And these are the events which
Lord Kelvin by a delicate series of experiments, verified in
every respect.
Suppose we had nothing but solid ice in the vessel at
starting,
would the experiment result in the same way? Yes, it
assuredly
would. The ice under the increased pressure would melt a
little
everywhere throughout its mass, taking the requisite latent
heat
from itself at the expense of its sensible heat, and the
temperature of the ice would fall to the new melting point.
Could we melt the whole of the ice in this manner? Again
the
answer is "yes." But the pressure must be very great. If we
assume that all the heat is obtained at the expense of the
sensible heat of the ice, the cooling must be such as to
supply
the latent heat of the whole mass of water produced. However,
the
latent heat diminishes as the melting point is lowered, and at
a
rate which would reduce it to nothing at about 18,000
atmospheres. Mousson, operating on ice enclosed in a
conducting
cylinder and cooled to -18° at starting
270
appears to have obtained very complete liquefaction. Mousson
must
have attained a pressure of at least an amount adequate to
lower
the melting point below -18°. The degree of liquefaction
actually
attained may have been due in part to the passage of heat
through
the walls of the vessel. He proved the more or less complete
liquefaction of the ice within the vessel by the fall of a
copper
index from the top to the bottom of the vessel while the
pressure
was on.
I have here a simple way of demonstrating to you the fall
of
temperature attending the compression of ice. In this mould,
which is strongly made of steel, lined with boxwood to
diminish
the passage of conducted heat, is a quantity of ice which I
compress when I force in this plunger. In the ice is a
thermoelectric junction, the wires leading to which are in
communication with a reflecting galvanometer. The thermocouple
is
of copper and nickel, and is of such sensitiveness as to show
by
motion of the spot of light on the screen even a small
fraction
of a degree. On applying the pressure, you see the spot of
light
is displaced, and in such a direction as to indicate cooling.
The
balancing thermocouple is all the time imbedded in a block of
ice
so that its temperature remains unaltered. On taking off the
pressure, the spot of light returns to its first position. I
can
move the spot of light backwards and forwards on the screen
by
taking off and putting on the pressure. The effects are quite
instantaneous.
271
The fact last referred to is very important. The ice, in fact,
is
as it were automatically turned to water. It is not a matter
of
the conduction of heat from point to point in the ice. Its
own
sensible heat is immediately absorbed throughout the mass.
This
would be the theoretical result, but it is probable that owing
to
imperfections throughout the ice and failure in uniformity in
the
distribution of the stress, the melting would not take place
quite uniformly or homogeneously.
Before applying our new ideas to skating, I want you to notice
a
fact which I have inferentially stated, but not specifically
mentioned. Pressure will only lead to the melting of ice if
the
new melting point, _i.e._ that due to the pressure, is below
the
prevailing temperature. Let us take figures. The ice to start
with is, say, at -3° C. Suppose we apply such a pressure to
this
ice as will confer a melting point of -2° C. on it.
Obviously,
there will be no melting. For why should ice which is at -3°
C.
melt when its melting point is -2° C.? The ice is, in
fact,
colder than its melting point. Hence, you note this fact: The
pressure must be sufficiently intense to bring the melting
point
below the prevailing temperature, or there will be no
melting;
and the further we reduce the melting point by pressure below
the
prevailing temperature, the more ice will be melted.
We come at length to the object of our remarks I don't know
who
invented skating or skates. It is said that in the thirteenth
century the inhabitants of
272
England used to amuse themselves by fastening the bones of
an
animal beneath their feet, and pushing themselves about on
the
ice by means of a stick pointed with iron. With such skates,
any
performance either on inside or outside edge was impossible.
We
are a conservative people. This exhilarating amusement appears
to
have served the people of England for three centuries. Not
till
1660 were wooden skates shod with iron introduced from the
Netherlands. It is certain that skating was a fashionable
amusement in Pepys' time. He writes in 1662 to the effect:
"It
being a great frost, did see people sliding with their
skates,
which is a very pretty art." It is remarkable that it was the
German poet Klopstock who made skating fashionable in
Germany.
Until his time, the art was considered a pastime, only fit
for
very young or silly people.
I wish now to dwell upon that beautiful contrivance the
modern
skate. It is a remarkable example of how an appliance can
develop
towards perfection in the absence of a really intelligent
understanding of the principles underlying its development.
For
what are the principles underlying the proper construction of
the
skate? After what I have said, I think you will readily
understand. The object is to produce such a pressure under
the
blade that the ice will melt. We wish to establish such a
pressure under the skate that even on a day when the ice is
below
zero, its melting
273
point is so reduced just under the edge of the skate that the
ice
turns to water.
It is this melting of the ice under the skate which secures
the
condition essential to skating. In the first place, the skate
no
longer rests on a solid. It rests on a liquid. You are aware
how
in cases where we want to reduce friction—say at the
bearing of a
wheel or under a pivot—we introduce a liquid. Look at
the
bearings of a steam engine. A continuous stream of oil is fed
in
to interpose itself between the solid surfaces. I need not
illustrate so well-known a principle by experiment. Solid
friction disappears when the liquid intervenes. In its place
we
substitute the lesser difficulty of shearing one layer of the
liquid over the other; and if we keep up the supply of oil
the
work required to do this is not very different, no matter how
great we make the pressure upon the bearings. Compared with
the
resistance of solid friction, the resistance of fluid friction
is
trifling. Here under the skate the lubrication is perhaps the
most perfect which it is possible to conceive. J. Müller
has
determined the coefficient by towing a skater holding on by a
spring balance. The coefficient is between 0.016 and 0.032.
In
other words, the skater would run down an incline so little as
1
or 2 degrees; an inclination not perceivable by the eye. Now
observe that the larger of these coefficients is almost
exactly
the same as that which Perry found in the case of
well-greased
surfaces. But evidently no
274
artificial system of lubrication could hope to equal that
which
exists between the skate and the ice. For the lubrication
here
is, as it were, automatic. In the machine if the lubricant
gets
squeezed out there instantly ensues solid friction. Under the
skate this cannot happen for the squeezing out of the
lubricant
is instantly followed by the formation of another film of
water.
The conditions of pressure which may lead to solid friction
in
the machine here automatically call the lubricant into
existence.
Just under the edge of the skate the pressure is enormous.
Consider that the whole weight of the skater is born upon a
mere
knife edge. The skater alternately throws his whole weight
upon
the edge of each skate. But not only is the weight thus
concentrated upon one edge, further concentration is secured
in
the best skates by making the skate hollow-ground, _i.e._
increasing the keenness of the edge by making it less than a
right angle. Still greater pressure is obtained by
diminishing
the length of that part of the blade which is in contact with
the
ice. This is done by putting curvature on the blade or making
it
what is called "hog-backed." You see that everything is done
to
diminish the area in contact with the ice, and thus to
increase
the pressure. The result is a very great compression of the
ice
beneath the edge of the skate. Even in the very coldest
weather
melting must take place to some extent.
As we observed before, the melting is instantaneous,
275
Heat has not to travel from one point of the ice to
another;
immediately the pressure comes on the ice it turns to water.
It
takes the requisite heat from itself in order that the change
of
state may be accomplished. So soon as the skate passes on,
the
water resumes the solid state. It is probable that there is
an
instantaneous escape, and re-freezing of some of the water
from
beneath the skate, the skate instantly taking a fresh bearing
and
melting more ice. The temperature of the water escaping from
beneath the skate, or left behind by it, immediately becomes
what
it was before the skate pressed upon it.
Thus, a most wonderful and complex series of molecular
events
takes place beneath the skate. Swift as it passes, the whole
sequence of events which James Thomson predicted has to take
place beneath the blade Compression; lowering of the melting
point below the temperature of the surrounding ice; melting;
absorption of heat; and cooling to the new melting point,
_i.e._
to that proper to the pressure beneath the blade. The skate
now
passes on. Then follow: Relief of pressure; re-solidification
of
the water; restoration of the borrowed heat from the
congealing
water and reversion of the ice to the original temperature.
If we reflect for a moment on all this, we see that we do
not
skate on ice but on water. We could not skate on ice any more
than we could skate on glass. We saw that with light weights
and
when the pressure
276
{Diagram}
Diagram showing successive states obtaining in ice,
before,
during, and after the passage of the skate. The temperatures
and
pressures selected for illustration are such as might occur
under
ordinary conditions. The edge of the skate is shown in
magnified
cross-section.
277
Was not sufficient to melt the ice, the friction was much
the
same as that of metal on glass. Ice is not slippery. It is an
error to say that it is. The learned professor was very much
astray when he said that you could skate on ice because it is
so
smooth. The smoothness of the ice has nothing to do with the
matter. In short, owing to the action of gravity upon your
body,
you escape the normal resistance of solid on solid, and glide
about with feet winged like the messenger of the Gods; but on
water.
A second condition essential to the art of skating is also
involved in the melting of the ice. The sinking of the skate
gives the skater "bite." This it is which enables him to urge
himself forward. So long as skates consisted of the rounded
bones
of animals, the skater had to use a pointed staff to propel
himself. In creating bite, the skater again unconsciously
appeals
to the peculiar physical properties of ice. The pressure
required
for the propulsion of the skater is spread all along the
length
of the groove he has cut in the ice, and obliquely downwards.
The
skate will not slip away laterally, for the horizontal
component
of the pressure is not enough to melt the ice. He thus gets
the
resistance he requires.
You see what a very perfect contrivance the skate is; and what
a
similitude of intelligence there is in its evolution. Blind
intelligence, because it is certain the true physics of
skating
was never held in view by
278
the makers of skates. The evolution of the skate has been
truly
organic. The skater selected the fittest skate, and hence the
fit
skate survived.
In a word, the possibility of skating depends on the
dynamical
melting of ice under pressure. And observe the whole matter
turns
upon the apparently unrelated fact that the freezing of water
results in a solid more bulky than the water which gives rise
to
it. If ice was less bulky than the water from which it was
derived, pressure would not melt it; it would be all the more
solid for the pressure, as it were. The melting point would
rise
instead of falling. Most substances behave in this manner,
and
hence we cannot skate upon them. Only quite a few substances
expand on freezing, and it happens that their particular
melting
temperatures or other properties render them unsuitable to
skating. The most abundant fluid substance on the earth, and
the
most abundant substance of any one kind on its surface, thus
possesses the ideally correct and suitable properties for the
art
of skating.