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entitled to infer that other rare elements are similarly widelydistributed but remain undetectable because of their more stableproperties.
It must not be thought that the under-exposed halo is a recentcreation. By no means. All are old, appallingly old; and in thesame rock all are, probably, of the same, or neatly the same,age. The under-exposure is simply due to a lesser quantity of theradioactive elements in the nucleus. They are under-exposed, inshort, not because of lesser duration of exposure, but because ofinsufficient action; as when in taking a photograph the stop isnot open enough for the time of the exposure.
The halo has, so far, told us that the additive law is obeyed insolid media, and that the increased ionisation attending theslowing down of the ray obtaining in gases, also obtains insolids; for, otherwise, the halo would not commence itsdevelopment as a spherical shell or envelope. But here we learnthat there is probably a certain difference in the course ofevents attending the immediate passage of the ray in the gas andin the solid. In the former, initial recombination may obscurethe intense ionisation near the end of the range. We can onlydetect the true end-effects by artificially separating the ionsby a strong electric force. If this recombination happened in themineral we should not have the concentric spheres so well definedas we see them to be. What, then, hinders the initialrecombination in the solid? The answer probably is that the newlyformed
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ion is instantly used up in a fresh chemical combination. Nor isit free to change its place as in the gas. There is simply a newequilibrium brought about by its sudden production. In thismanner the conditions in the complex molecule of biotite,tourmaline, etc., may be quite as effective in preventing initialrecombination as the most effective electric force we couldapply. The final result is that we find the Bragg curvereproduced most accurately in the delicate shading of the ringsmaking up the perfectly exposed halo.
That the shading of the rings reproduces the form of the Braggcurve, projected, as it were, upon the line of advance of the rayand reproduced in depth of shading, shows that in yet anotherparticular the alpha ray behaves much the same in the solid as inthe gas. A careful examination of the outer edge of the circlesalways reveals a steep but not abrupt cessation of the action ofthe ray. Now Geiger has investigated and proved the existence ofscattering of the alpha ray by solids. We may, therefore, supposewith much probability that there is the same scattering withinthe mineral near the end of the range. The heavy iron atom of thebiotite is, doubtless, chiefly responsible for this in biotitehaloes. I may observe that this shading of the outer boundingsurface of the sphere of action is found however minute thecentral nucleus. In the case of a nucleus of considerable sizeanother effect comes in which tends to produce an enhancedshading. This will
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result if rays proceed from different depths in the nucleus. Ifthe nucleus were of the same density and atomic weight as thesurrounding mica, there would be little effect. But its densityand molecular weight are generally greater, hence the retardationis greater, and rays proceeding from deep in the nucleusexperience more retardation than those which proceed from pointsnear to the surface. The distances reached by the rays in themica will vary accordingly, and so there will be a gradualcessation of the effects of the rays.
The result of our study of the halo may be summed up in thestatement that in nearly every particular we have the phenomena,which have been measured and observed in the gas, reproduced on aminute scale in the halo. Initial recombination seems, however,to be absent or diminished in effectiveness; probably because ofthe new stability instantly assumed by the ionised atoms.
One of the most interesting points about the halo remains to bereferred to. The halo is always uniformly darkened all round itscircumference and is perfectly spherical. Sections, whether takenin the plane of cleavage of the mica or across it, show the sameexactly circular form, and the same radius. Of course, if therewas any appreciable increase of range along or across thecleavage the form of the halo on the section across the cleavageshould be elliptical. The fact that there is no measurableellipticity is, I think, one which on first consideration wouldnot be expected.
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For what are the conditions attending the passage of the ray in amedium such as mica? According to crystallographic conceptions wehave here an orderly arrangement of molecules, the unitscomposing the crystal being alike in mass, geometrically spaced,and polarised as regards the attractions they exert one uponanother. Mica, more especially, has the cleavage phenomenondeveloped to a degree which transcends its development in anyother known substance. We can cleave it and again cleave it tillits flakes float in the air, and we may yet go on cleaving it byspecial 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 iseasy to show that the molecules in the plane of the flake are inorderly arrangement and are more easily parted in some directionsthan in others. In such a medium beyond all others we must lookwith surprise upon the perfect sphere struck out by the alpharays, because it seems certain that the cleavage is due to lesserattraction, and, probably, further spacing of the molecules, in adirection perpendicular to the cleavage.
It may turn out that the spacing of the molecules will influencebut little the average number per unit distance encountered byrays moving in divergent paths. If this is so, we seem left toconclude that, in spite of its unequal and polarised attractions,there is equal retardation and equal ionisation in the moleculein whatever
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direction it is approached. Or, again, if the encounters indeeddiffer in number, then some compensating effect must existwhereby a direction of lesser linear density involves greaterstopping 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 earlierstages, attended by destruction of the crystallographic andoptical properties of the medium. The optical properties areunaltered in nature but are increased in intensity. This appliestill the halo has become so darkened that light is no longertransmitted under the conditions of thickness obtaining in rocksections. It is well known that there is in biotite a maximumabsorption of a plane-polarised light ray, when the plane ofvibration coincides with the plane of cleavage. A section acrossthe cleavage then shows a maximum amount of absorption. A haloseen on this section simply produces this effect in a moreintense degree. This is well shown in Plate XXIII (lower figure),on a portion of the halo-sphere. The descriptive name "PleochroicHalo" has originated from this fact. We must conclude that theeffect of the ionisation due to the alpha ray has not been toalter fundamentally the conditions which give rise to the opticalproperties of the medium. The increased absorption is probablyassociated with some change in the chemical state of the ironpresent. Haloes are, I believe, not found in minerals from whichthis
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element is absent. One thing is quite certain. The colouration isnot due to an accumulation of helium atoms, _i.e._ of spent alpharays. The evidence for this is conclusive. If helium wasresponsible we should have haloes produced in all sorts ofcolourless minerals. Now we sometimes see zircons in felspars andin quartz, etc., but in no such case is a halo produced. Andhalo-spheres formed within and sufficiently close to the edge ofa crystal of mica are abruptly truncated by neighbouring areas offclspar or quartz, although we know that the rays must passfreely across the boundary. Again it is easy to show that even inthe oldest haloes the quantity of helium involved is so smallthat one might say the halo-sphere was a tolerably good vacuum asregards helium. There is, finally, no reason to suppose that theimprisoned helium would exhibit such a colouration, or, indeed,any at all.
I have already referred to the great age of the halo. Haloes arenot found in the younger igneous rocks. It is probable that ahalo less than a million years old has never been seen. This,primâ facie, indicates an extremely slow rate of formation. Andour calculations quite support the conclusions that the growth ofa halo, if this has been uniform, proceeds at a rate of almostunimaginable slowness.
Let us calculate the number of alpha rays which may have gone toform a halo in the Devonian granite of Leinster.
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It is common to find haloes developed perfectly in this granite,and having a nucleus of zircon less than 5 x 10-4cms. indiameter. The volume of zircon is 65 x 10-12c.cs. and the mass3 x 10-10grm.; and if there was in this zircon 10-8grm. radiumper gram (a quantity about five times the greatest amountmeasured by Strutt), the mass of radium involved is 3 x 10-18grm. From this and from the fact ascertained by Rutherford thatthe number of alpha rays expelled by a gram of radium in onesecond is 3.4 x 1010, we find that three rays are shot from thenucleus in a year. If, now, geological time since the Devonian is50 millions of years, then 150 millions of rays built up thehalo. If geological time since the Devonian is 400 millions ofyears, then 1,200 millions of alpha rays are concerned in itsgenesis. The number of ions involved, of course, greatly exceedsthese numbers. A single alpha ray fired from radium C willproduce 2.37 x 105ions in air.
But haloes may be found quite clearly defined and fairly dark outto the range of the emanation ray and derived from much lessquantities of radioactive materials. Thus a zircon nucleus with adiameter of but 3.4 x 10-4cms. formed a halo strongly darkenedwithin, and showing radium A and radium C as clear smoky rings.Such a nucleus, on the assumption made above as to its radiumcontent, expels one ray in a year. But, again, haloes areobserved with less blackened pupils and with faint ring due toradium C, formed round nuclei
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of rather less than 2 x 10-4cms. diameter. Such nuclei wouldexpel one ray in five years. And even lesser nuclei will generatein these old rocks haloes with their earlier characteristicfeatures clearly developed. In the case of the most minutenuclei, if my assumption as to the uranium content is correct, analpha ray is expelled, probably, no oftener than once in acentury; and possibly at still longer intervals.
The equilibrium amount of radium contained in some nuclei mayamount to only a few atoms. Even in the case of the larger nucleiand more perfectly developed haloes the quantity of radiuminvolved is many millions of times less than the least amount wecan recognise by any other means. But the delicacy of theobservation is not adequately set forth in this statement. We cannot only tell the nature of the radioactive family with which weare dealing; but we can recognise the presence of some of itsconstituent members. I may say that it is not probable thezircons are richer in radium than I have assumed. My assumptioninvolves about 3 per cent. of uranium. I know of no analysesascribing so great an amount of uranium to zircon. The varietycyrtolite has been found to contain half this amount, about. Buteven if we doubled our estimate of radium content, the remarkablenature of our conclusions is hardly lessened.
It may appear strange that the ever-interesting question of theEarth's age should find elucidation from the
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study of haloes. Nevertheless the subjects are closely connected.The circumstances are as follows. Geologists have estimated theage of the Earth since denudation began, by measurements of theintegral effects of denudation. These methods agree in showing anage of about rob years. On the other hand, measurements have beenmade of the accumulation in minerals of radioactive _débris_—thehelium and lead—and results obtained which, although they do notagree very well among themselves, are concordant in assigning avery much greater age to the rocks. If the radioactive estimateis correct, then we are now living in a time when the denudativeforces of the Earth are about eight or nine times as active asthey have been on the average over the past. Such a state ofthings is absolutely unaccountable. And all the moreunaccountable because from all we know we would expect a somewhat_lesser_ rate of solvent denudation as the world gets older and theland gets more and more loaded with the washed-out materials ofthe rocks.
Both the methods referred to of finding the age assume theprinciple of uniformity. The geologist contends for uniformitythroughout the past physical history of the Earth. The physicistclaims the like for the change-rates of the radioactive elements.Now the study of the rocks enables us to infer something as tothe past history of our Globe. Nothing is, on the other hand,known respecting the origin of uranium or thorium—the parentradioactive bodies. And while not questioning the law
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and regularity which undoubtedly prevail in the periods of themembers of the radioactive families, it appears to me that it isallowable to ask if the change rate of uranium has been alwayswhat we now believe it to be. This comes to much the same thingas supposing that atoms possessing a faster change rate once wereassociated with it which were capable of yielding both helium andlead to the rocks. Such atoms might have been collateral inorigin with uranium from some antecedent element. Like helium,lead may be a derivative from more than one sequence ofradioactive changes. In the present state of our knowledge thepossibilities are many. The rate of change is known to beconnected with the range of the alpha ray expelled by thetransforming element; and the conformity of the halo with ourexisting knowledge of the ranges is reason for assuming that,whatever the origin of the more active associate of uranium, thispassed through similar elemental changes in the progress of itsdisintegration. There may, however, have been differences in theranges which the halo would not reveal. It is remarkable thaturanium at the present time is apparently responsible for twoalpha rays of very different ranges. If these proceed fromdifferent elements, one should be faster in its change rate thanthe other. Some guidance may yet be forthcoming from the study ofthe more obscure problems of radioactivity.
Now it is not improbable that the halo may contribute directly tothis discussion. We can evidently attack
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the biotite with a known number of alpha rays and determine howmany are required to produce a certain intensity of darkening,corresponding to that of a halo with a nucleus of measurabledimensions. On certain assumptions, which are correct withindefined limits, we can calculate, as I have done above, thenumber of rays concerned in forming the halo. In doing so weassume some value for the age of the halo. Let us take themaximum radioactive value. A halo originating in Devonian timesmay attain a certain central blackening from the effects of, say,rob rays. But now suppose we find that we cannot produce the samedegree of blackening with this number of rays applied in thelaboratory. What are we to conclude? I think there is only theone conclusion open to us; that some other source of alpha rays,or a faster rate of supply, existed in the past. And thisconclusion would explain the absence of haloes from the youngerrocks; which, in view of the vast range of effects possible inthe development of haloes, is, otherwise, not easy to accountfor. It is apparent that the experiment on the biotite has adirect bearing on the validity of the radioactive method ofestimating the age of the rocks. It is now being carried out byProfessor Rutherford under reliable conditions.
Finally, there is one very certain and valuable fact to belearned from the halo. The halo has established the extremerarity of radioactivity as an atomic phenomenon. One and all ofthe speculations as to
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the slow breakdown of the commoner elements may be dismissed. Thehalo shows that the mica of the rocks is radioactively sensitive.The fundamental criterion of radioactive change is the expulsionof the alpha ray. The molecular system of the mica and of manyother minerals is unstable in presence of these rays, just as aphotographic plate is unstable in presence of light. Moreover,the mineral integrates the radioactive effects in the same way asa photographic salt integrates the effects of light. In bothcases the feeblest activities become ultimately apparent to ourinspection. We have seen that one ray in each year since theDevonian period will build the fully formed halo: an objectunlike any other appearance in the rocks. And we have been ableto allocate all the haloes so far investigated to one or theother of the known radioactive families. We are evidentlyjustified in the belief that had other elements been radioactivewe must either find characteristic haloes produced by them, orelse find a complete darkening of the mica. The feeblest alpharays emitted by the relatively enormous quantities of theprevailing elements, acting over the whole duration of geologicaltime—and it must be remembered that the haloes we have beenstudying are comparatively young—must have registered theireffects on the sensitive minerals. And thus we are safe inconcluding that the common elements, and, indeed, many whichwould be called rare, are possessed of a degree of stabilitywhich has preserved them un
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changed since the beginning of geological time. Each unaffectedflake of mica is, thus, unassailable proof of a fact which butfor the halo would, probably, have been for ever beyond ourcognisance.
THE USE OF RADIUM IN MEDICINE[1]
IT has been unfortunate for the progress of the radioactivetreatment of disease that its methods and claims involve much ofthe marvellous. Up till recently, indeed, a large part ofradioactive therapeutics could only be described as bordering onthe occult. It is not surprising that when, in addition to itsoccult and marvellous characters, claims were made on its behalfwhich in many cases could not be supported, many medical men cameto regard it with a certain amount of suspicion.
Today, I believe, we are in a better position. I think it ispossible to ascribe a rational scientific basis to its legitimateclaims, and to show, in fact, that in radioactive treatment weare pursuing methods which have been already tried extensivelyand found to be of definite value; and that new methods differfrom 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 ametallic element chemically resembling barium. It
[1] A Lecture to Postgraduate Students of Medicine in connectionwith the founding of the Dublin Radium Institute, delivered inthe School of Physic in Ireland, Trinity College, on October 2nd,1914
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possesses, however, a remarkable property which barium does not.Its atoms are not equally stable. In a given quantity of radium acertain very small percentage of the total number of atomspresent break up per second. By "breaking up" we mean theirtransmutation to another element. Radium, which is a solidelement under ordinary conditions, gives rise by transmutation toa gaseous element—the emanation of radium. The new element is aheavy gas at ordinary temperatures and, like other gases, can beliquified by extreme cold. The extraordinary property oftransmutation is entirely automatic. No influence which chemistor physicist can apply can affect the rate of transformation.
The emanation inherits the property of instability, but in itscase the instability is more pronounced. A relatively largefraction of its atoms transmute per second to a solid elementdesignated Radium A. In turn this new generation of atoms breaksup—even faster than the emanation—becoming yet another elementwith specific chemical properties. And so on for a whole sequenceof 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 radiumis not the starting point. It possesses ancestors which have beentraced back to the element uranium.
Now what bearing has this series of transmutations
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upon medical science? Radium or emanation, &c., are not in thePharmacopoeia as are, say, arsenic or bismuth. The wholemedicinal value of these elements resides in the very wonderfulphenomena of their radiations. They radiate in the process oftransmuting.
The changing atom may radiate a part of its own mass. The"alpha"-ray (a-ray) is such a material ray. It is an electrifiedhelium atom cast out of the parent atom with enormousvelocity—such a velocity as would carry it, if not impeded, allround the earth in two seconds. All alpha-rays are positivelyelectrified atoms of the element helium, which thereby is shownto be an integral constituent of many elements. The alpha-ray isnot of much value to medical science, for, in spite of its greatvelocity, it is soon stopped by encounter with other atoms. Itcan penetrate only a minute fraction of a millimetre intoordinary 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. Ascast out by radioactive elements it starts with speeds which varywith the element, and may be from one-third to nine-tenths thevelocity of light. The ß-ray is negatively electrified. It haslong been known to science as the electron. It is also identicalwith the cathode ray of the vacuum tube.
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Another and quite different kind of radiation is given out bymany of the transmuting elements:—the y-ray. This is notmaterial, it is ethereal. It is known now with certainty that they-ray is in kind identical with light, but of very much shorterwave length than even the extreme ultraviolet light of the solarspectrum. The y-ray is flashed from the transmuting atom alongwith the ß-ray. It is identical in character with the x-ray butof even shorter wave length.
There is a very interesting connection between the y-ray and theß-ray which it is important for the medical man to understand—asfar 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 resultof the resonance of the atom, or of parts of it, to the shortlight waves. And it is remarkable that the y-rays which, as wehave seen, are shorter and more penetrating waves than thex-rays, give rise to ß-rays possessed of greater velocity andpenetration than ß-rays excited by the x-rays. Indeed the ß-raysoriginated by y-rays may attain a velocity nearly approachingthat of light and as great as that of any ß-rays emitted bytransmuting atoms. Again there is demonstrable evidence thatß-rays impinging on matter may give rise to y-rays. The mostremarkable demonstration of this is seen in the x-ray tube. Herethe x-rays originate where the stream of ß- or cathode-rays
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are arrested on the anode. But the first relation is at presentof most importance to us—_i.e._ that the y-or x-rays give rise toß-rays.
This relation gives us additional evidence of the identity of thephysical effects of y-, x-, and light-rays —using the term lightrays in the usual sense of spectral rays. For it has long beenknown that light waves liberate electrons from atoms. It has beenfound that these electrons possess a certain initial velocitywhich is the greater the shorter the wave length of the lightconcerned in their liberation. The whole science of"photo-electricity" centres round this phenomenon. The action oflight on the photographic plate, as well as many other physicaland chemical phenomena, find an explanation in this liberation ofthe electron by the light wave.
Here, then, we have spectral light waves liberatingelectrons—_i.e._ very minute negatively-charged particles, and wefind that, as we use shorter light waves, the initial velocity ofthese particles increases. Again, we have x-rays which are farsmaller in wave length than spectral light, liberating muchfaster negatively electrified particles. Finally, we havey-rays—the shortest nether waves of all-liberating negativeparticles of the highest velocity known. Plainly the whole seriesof phenomena is continuous.
We can now look closer at the actions involved in the therapeuticinfluence of the several rays and in
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this way, also, see further the correlation between what may becalled photo-therapeutics and radioactive therapeutics.
The ß-ray, whether we obtain it directly from the transformingradioactive atom or whether we obtain it as a result of theeffects of the y- or x-rays upon the atom, is an ionising agentof wonderful power. What is meant by this? In its physical aspectthis means that the atoms through which it passes acquire freeelectric charges; some becoming positive, some negative. This canonly be due to the loss of an electron by the affected atom. Theloss of the small negative charge carried in the electron leavesthe atom positively electrified or creates a positive ion. Thefixing of the wandering electron to a neutral atom creates anegative ion. Before further consideration of the importance ofthe phenomenon of ionisation we must fix in our minds that theagent, which brings this about, is the ß-ray. There is littleevidence that the y-ray can directly create ions to any largeextent. But the action of liberating high-speed ß-rays results inthe creation of many thousands of ions by each ß-ray liberated.As an agent in the hands of the medical man we must regard they-ray as a light wave of extremely penetrating character, whichcreates high-speed ß-rays in the tissues which it penetrates,these ß-rays being most potent ionising agents. The ß-raysdirectly obtained from radioactive atoms assist in the work ofionisation. ß-rays do not
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penetrate far from their source. The fastest of them would notprobably penetrate one centimetre in soft tissues.
We must now return to the phenomenon of ionisation. Ionisation isrevealed to observation most conspicuously when it takes place ina gas. The + and - electric charges on the gas particles endow itwith the properties of a conductor of electricity, the + ionsmoving freely in one direction and the - ions in the oppositedirection under an electric potential. But there are effectsbrought about by ionisation of more importance to the medical manthan this. The chemist has long come to recognise that in the ionhe is concerned with the inner mechanism of a large number ofchemical phenomena. For with the electrification of the atomattractive and repulsive forces arise. We can directly show thechemical effects of the ionising ß-rays. Water exposed to theirbombardment splits up into hydrogen and oxygen. And, again, theseparated atoms may be in part recombined under the influence ofthe 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 theliving cell the ionising effects which everywhere accompany theß-rays must exert a profound influence. The sequence of chemicalevents which as yet seem
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beyond the ken of science and which are involved in metabolismcannot fail to be affected. Any, it is not surprising that as theresult of eaperinient it is found that the radiations are agentswhich may be used either for the stimulation of the naturalevents of growth or used for the actual destruction of the cell.It is easy to see that the feeble radiation should produce theone effect, the strong the other. In a similar way by a moderatelight stimulus we create the latent image in the photographicplate; by an intense light we again destroy this image. The innermechanism in this last case can be logically stated.[1]
_There is plainly a true physical basis here for the efficacy ofradioactive treatment and, what is more, we find when we examineit, that it is in kind not different from that underlyingtreatment by spectral radiations. But in degree it is verydifferent and here is the reason for the special importance ofradioactivity as a therapeutic agent._ The Finsen light is capableof influencing the soft tissues to a short depth only. The reasonis that the wave length of the light used is too great to passwithout rapid absorption through the tissues; and, further, theelectrons it gives rise to—_i.e._ the ß-rays it liberates—are tooslow-moving to be very efficient ionisers. X-rays penetrate insome cases quite freely and give rise to much faster and morepowerful ß-rays
[1] See _The Latent Image_, p. 202.
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than can the Finsen light. But far more penetrating than x-raysare the y-rays emitted in certain of the radioactive changes.These give rise to ß-rays having a velocity approximate to thatof light.
The y-rays are, therefore, very penetrating and powerfullyionising light waves; light waves which are quite invisible tothe eye and can beam right through the tissues of the body. Tothe mind's eye only are they visible. And a very wonderfulpicture they make. We see the transmuting atom flashing out thislight for an inconceivably short instant as it throws off theß-ray. And "so far this little candle throws his beams" in thecomplex system of the cells, so far atoms shaken by the rays sendout ß-rays; these in turn are hurled against other atomicsystems; fresh separations of electrons arise and new attractionsand repulsions spring up and the most important chemical changesare brought about. Our mental picture can claim to be no morethan diagrammatic of the reality. Still we are here dealing withrecognised physical and chemical phenomena, and their descriptionas "occult" in the derogatory sense is certainly notjustifiable.
Having now briefly reviewed the nature of the rays arising inradioactive substances and the rationale of their influence, wemust turn to more especially practical considerations.
The Table given opposite shows that radium itself is responsiblefor a- and ß-rays only. It happens that
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Period in whioh ½ element is transformed.
URANIUM 1 & 2 { a 6 } x 109years.
URANIUM X { a ß } 24.6 days.
IONIUM { a 8 } x 104 years.
RADIUM { a ß } 2 x 102years.
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 theUranium-radium family, the character of their radiations andtheir longevity.
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the ß-rays emitted by radium are very "soft"—_i.e._ slow andeasily absorbed. The a-ray is in no case available for more thanmere surface application. Hence we see that, contrary to what isgenerally believed, radium itself is of little direct therapeuticvalue. Nor is the next body in succession—the emanation, for itgives only a-rays. In fact, to be brief, it is not till we cometo Radium B that ß-rays of a relatively high penetrative qualityare reached; and it is not till we come to Radium C that highlypenetrative y-rays are obtained.
It is around this element, Radium C, that the chief medicalimportance of radioactive treatment by this family of radioactivebodies centres. Not only are ß-rays of Radium C very penetrating,but the y-rays are perhaps the most energetic rays of the, kindknown. Further in the list there is no very special medicalinterest.
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 beendeprived of its emanation (which is easily done by heating it orbringing it into solution) in a few weeks we get back the RadiumC. One thing here we must be clear about. With a given quantityof Radium only a certain definitely limited amount of Radium C,or of emanation, or any other of the derived bodies, will beassociated. Why is this? The answer is because the severalsuccessive elements are themselves decaying —_i.e._ changing oneinto the other. The atomic per-
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centage of each, which decays in a second, is a fixed quantitywhich we cannot alter. Now if we picture radium which has beencompletely deprived of its emanation, again accumulating byautomatic transmutation a fresh store of this element, we have toremember:— (i) That the rate of creation of emanation by theradium is practically constant; and (2) that the absolute amountof the emanation decaying per second increases as the stock ofemanation increases. Finally, when the amount of accumulatedemanation has increased to such an extent that the number ofemanation atoms transmuting per second becomes exactly equal tothe number being generated per second, the amount of emanationpresent cannot increase. This is called the equilibrium amount.If fifteen members are elected steadily each year into anewly-founded society the number of members will increase for thefirst few years; finally, when the losses by death of the membersequal about fifteen per annum the society can get no bigger. Ithas attained the equilibrium number of members.
This applies to every one of the successive elements. It takestwenty-one days for the equilibrium quantity of emanation to beformed in radium which has been completely de-emanated; and ittakes 3.8 days for half the equilibrium amount to be formed.Again, if we start with a stock of emanation it takes just threehours for the equilibrium amount of Radium C to be formed.
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We can evidently grow Radium C either from radium itself or fromthe emanation of radium. If we use a tube of radium we have analmost perfectly constant quantity of Radium C present, for asfast 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 possessa constant supply of Radium C, because the emanation is decayingfairly rapidly and there is no radium to make good its loss. In3.8 days about one half the emanation is transmuted and theRadium C decreases proportionately and, of course, with theRadium C the valuable radiations also decrease. In another 3.8days—that is in about a week from the start—the radioactive valueof the tube has fallen to one-fourth of its original value.
But in spite of the inconstant character of the emanation tubethere are many reasons for preferring its use to the use of theradium tube. Chief of these is the fact that we can keep theprecious radium safely locked up in the laboratory and notexposed to the thousand-and-one risks of the hospital. Then,secondly, the emanation, being a gas, is very convenient forsubdivision into a large number of very small tubes according tothe dosage required.
In fact the volume of the emanation is exceedingly minute. Theamount of emanation in equilibrium with one gramme of radium iscalled the curie, and with one
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milligramme the millicurie. Now, the volume of the curie is onlya little more than one half a cubic millimetre. Hence in dealingwith emanation from twenty or forty milligrammes of radium we aredealing with very small volumes.
How may the emanation be obtained? The process is an easy one inskilled and practised hands. The salt of radium—generally thebromide or chloride—is brought into acid solution. This causesthe emanation to be freely given off as fast as it is formed. Atintervals we pump it off with a mercury pump.
Let us see how many millicuries we will in future be able to turnout in the week in our new Dublin Radium Institute.[1] We shallhave about 130 milligrammes of radium. In 3.8 days we get 65millicuries from this—_i.e._ half the equilibrium amount of 130millicuries. Hence in the week, we shall have about 130millicuries.
This is not much. Many experts consider this little enough forone tube. But here in Dublin we have been using the emanation ina more economical and effective manner than is the usageelsewhere; according to a method which has been worked out anddeveloped in our own Radium Institute. The economy is obtained bythe very simple expedient of minutely subdividing the' dose. Thesystem in vogue, generally, is to treat the tumour by insertinginto it one or two very active
[1] Then recently established by the Royal Dublin Society.
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tubes, containing, perhaps, up to 200 millicuries, or even more,per tube. Now these very heavily charged tubes give a radiationso intense at points close to the tube, due to the greaterdensity of the rays near the tube, and, also, to the action ofthe softer and more easily absorbable rays, that it has beenfound necessary to stop these softer rays—both the y and ß—bywrapping lead or platinum round the tube. In this lead orplatinum some thirty per cent. or more of the rays is absorbedand, of course, wasted. But in the absence of the screen there isextensive necrosis of the tissues near the tubes.
If, however, in place of one or two such tubes we use ten ortwenty, each containing one-tenth or one-twentieth of the dose,we can avail ourselves of the softer rays around each tube withbenefit. Thus a wasteful loss is avoided. Moreover a more uniform"illumination" of the tissues results, just as we can illuminatea hall more uniformly by the use of many lesser centres of lightthan by the use of one intense centre of radiation. Also we getwhat 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 approximateuniformity throughout the tumour instead of varying rapidlyaround a central point or—and this may be very important— theeffects may be readily concentrated locally.
Finally, not the least of the benefit arises in the easytechnique of this new method. The quantities of
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emanation employed can fit in the finest capillary glass tubingand the hairlike tubes can in turn be placed in fine exploringneedles. There is comparatively little inconvenience to thepatient in inserting these needles, and there is the most perfectcontrol of the dosage in the number and strength of these tubesand the duration of exposure.[1]
The first Radium Institute in Ireland has already done good workfor the relief of human suffering. It will have, I hope, a greatfuture before it, for I venture, with diffidence, to hold theopinion, that with increased study the applications and claims ofradioactive treatment will increase.
[1] For particulars of the new technique and of some of the workalready accomplished, see papers, by Dr. Walter C. Stevenson,_British Medical Journal_, July 4th, 1914, and March 20th, 1915.
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SKATING[1]
IT is now many years ago since, as a student, I was present at acollege lecture delivered by a certain learned professor on thesubject of friction. At this lecture a discussion arose out of aquestion addressed to our teacher: "How is it we can skate on iceand on no other substance?"
The answer came back without hesitation: "Because the ice is sosmooth."
It was at once objected: "But you can skate on ice which is notsmooth."
This put the professor in a difficulty. Obviously it is not onaccount of the smoothness of the ice. A piece of polished plateglass is far smoother than a surface of ice after the latter iscut up by a day's skating. Nevertheless, on the scratched andtorn ice-surface skating is still quite possible; on the smoothplate glass we know we could not skate.
Some little time after this discussion, the connection betweenskating and a somewhat abstruse fact in physical science occurredto me. As the fact itself is one which has played a part in thegeological history of the earth,
[1] A lecture delivered before the Royal Dublin Society in 1905.
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and a part of no little importance, the subject of skating,whereby it is perhaps best brought home to every one, isdeserving of our careful attention. Let not, then, the title ofthis lecture mislead the reader as to the importance of itssubject matter.
Before going on to the explanation of the wonderful freedom ofthe skater's movements, I wish to verify what I have inferred asto the great difference in the slipperiness of glass and theslipperiness of ice. Here is a slab of polished glass. I canraise it to any angle I please so that at length this brassweight of 250 grams just slips down when started with a slightshove. The angle is, as you see, about 12½ degrees. I nowtransfer the weight on to this large slab of ice which I firstrapidly dry with soft linen. Observe that the weight slips downthe surface of ice at a much lower angle. It is a very low angleindeed: I read it as between 4 and 5 degrees. We see by thisexperiment that there is a great difference between theslipperiness of the two surfaces as measured by what is called"the angle of friction." In this experiment, too, the glasspossesses by far the smoother surface although I have rubbed thedeeper rugosities out of the ice by smoothing it with a glasssurface. Notwithstanding this, its surface is spotted with smallcavities due to bubbles and imperfections. It is certain that ifthe glass was equally rough, its angle of friction towards thebrass weight would be higher.
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We have, however, another comparative experiment to carry out. Imade as you saw a determination of the angle at which this weightof 250 grams just slipped on the ice. The lower surface of theweight, the part which presses on the ice, consists of a light,brass curtain ring. This can be detached. Its mass is only 6½grams, the curtain ring being, in fact, hollow and made of verythin metal. We have, therefore, in it a very small weight whichpresents exactly the same surface beneath as did the weight of250 grams. You see, now, that this light weight will not slip onice at 5 or 6 degrees of slope, but first does so at about iodegrees.
This is a very important experiment as regards our presentinquiry. Ice appears to possess more than one angle of frictionaccording 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 seethat there is little or no difference in the angle of friction ofbrass on glass when we press the surfaces together with a heavyor with a light weight. The light weight requires the same slopeof 12½ degrees to make it slip.
This last result is in accordance with the laws of friction. Wesay that when solid presses on solid, for each pair of substancespressed together there is a constant ratio between the forcerequired to keep one in motion over the other, and the forcepressing the solids together. This ratio is called"thecoefficient of friction."The coefficient is, in fact, constant orapproximately
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so. I can determine the coefficient of friction from the angle offriction by taking the tangent of the angle. The tangent of theangle of friction is the coefficient of friction. If, then, thecoefficient is constant, so, of course, must the angle offriction be constant. We have seen that it is so in the case ofmetal on glass, but not so in the case of metal on ice. Thiscurious result shows that there is something abnormal about theslipperiness of ice.
The experiments we have hitherto made are open to the reproachthat the surface of the ice is probably damp owing to the warmthof the air in contact with it. I have here a means of dealingwith a surface of cold, dry ice. This shallow copper tank about18 inches (45 cms.) long, and 4 inches (10 cms.) wide, is filledwith a freezing 'mixture circulated through it from a largervessel containing ice melting in hydrochloric acid at atemperature of about -18° C. This keeps the tank below themelting point of ice. The upper surface of the tank is providedwith raised edges so that it can be flooded with water. The wateris now frozen and its temperature is below 0° C. It is about10° C. I can place over the ice a roof-shaped cover made of twoinclined slabs of thick plate glass. This acts to keep out warmair, and to do away with any possibility of the surface of theice being wet with water thawed from the ice. The whole tankalong with its roof of glass can be adjusted to any angle, and a,scale at the
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raised end of the tank gives the angle of slope in degrees. Aweight placed on the ice can be easily seen through the glasscover.
The weight we shall use consists of a very light ring ofaluminium wire which is rendered plainly visible by a ping-pongball attached above it. The weight rests now on a copper plateprovided for the purpose at the upper end of the tank. The platebeing in direct contact beneath with the freezing mixture we aresure that the aluminium ring is no hotter than the ice. A lightjerk suffices to shake the weight on to the surface of the ice.
We find that this ring loaded with only the ping-pong ball, andweighing a total of 2.55 grams does not slip at the low angles. Ihave the surface of the ice at an angle of rather over 13½, andonly by continuous tapping of the apparatus can it be induced toslip down. This is a coefficient of 0.24, and compares with thecoefficient of hard and smooth solids on one another. I nowreplace the empty ping-pong ball by a similar ball filled withlead shot. The total weight is now 155 grams. You see the angleof slipping has fallen to 7°.
Every one who has made friction experiments knows howunsatisfactory and inconsistent they often are. We can onlydiscuss notable quantities and broad results, unless the mostconscientious care be taken to eliminate errors. The net resulthere is that ice at about -10° C. when pressed on by a very lightweight possesses a
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coefficient of friction comparable with the usual coefficients ofsolids on solids, but when the pressure is increased, thecoefficient falls to about half this value.
The following table embodies some results obtained on thefriction of ice and glass, using the methods I have shown you. Iadd some of the more carefully determined coefficients of otherobservers.
Wt. in On Plate On Ice On IceGrams. Glass. at 0° C. at 10° C.
Angle. Coeff. Angle. Coeff. Angle. CoeffAluminium 2.55 12½° 0.22 12° 0.21 13½° 0.24Same 155 12½° 0.22 6° 0.11 7° 0.12Brass 6.5 12½° 0.22 10° 0.17 10½° 0.18Same 107 12½° 0.22 5° 0.09 6° 0.10
Steel on steel (Morin) - - - - 0.14Brass on cast iron (Morin) - - 0.19Steel on cast iron (Morin) - - 0.20Skate on ice (J. Müller) - - - 0.016—0.032Best-greased surfaces (Perry) - 0.03—0.036
You perceive from the table that while the friction of brass oraluminium on glass is quite independent of the weight used, thatof 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 abnormalityin the friction of hard substances on ice, we would have ratheranticipated a variation in the
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other direction. We would have, perhaps, expected that a heavyweight would have given rise to the greater friction. I now turnto the explanation of this extraordinary result.
You are aware that it requires an expenditure of heat merely toconvert ice to water, the water produced being at the temperatureof the ice, _i.e._ at 0° C., from which it is derived. The heatrequired to change the ice from the solid to the liquid state isthe latent heat of water. We take the unit quantity of heat to bethat which is required to heat 1 kilogram of water 1° C. Then ifwe melt 1 kilogram of ice, we must supply it with 80 such unitsof heat. While melting is going on, there is no change oftemperature if the experiment is carefully conducted. The meltingice and the water coming from it remain at 0° C. throughout theoperation, and neither the thermometer nor your own sensationswould tell you of the amount of heat which was flowing in. Theheat is latent or hidden in the liquid produced, and has gone todo molecular work in the substance. Observe that if we supplyonly 40 thermal units, we get only one-half the ice melted. Ifonly 10 units are supplied, then we get only one eighth of akilogram of water, and no more nor less.
I have ventured to recall to you these commonplaces of sciencebefore considering a mode of melting ice which is less generallyknown, and which involves no supply of heat on your part. Thismethod involves for its
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understanding a careful consideration of the thermal propertiesof water in the solid state.
It must have been observed a very long time ago that waterexpands when it freezes. Otherwise ice would not float on water;and, what is perhaps more important in your eyes, your waterpipes would not burst in winter when the water freezes therein.But although the important fact of the expansion of water onfreezing was so long presented to the observation of mankind, itwas not till almost exactly the middle of the last century thatJames Thomson, a gifted Irishman, predicted many importantconsequences arising from the fact of the expansion of water onbecoming solid. The principles lie enunciated are perfectlygeneral, and apply in every case of change of volume attendingchange of state. We are here only concerned with the case ofwater and ice.
James Thomson, following a train of thought which we cannot herepursue, predicted that owing to the fact of the expansion ofwater on becoming solid, pressure will lower the melting point ofice or the freezing point of water. Normally, as you are aware,the temperature is 0° C. or 32° F. Thomson said that this wouldbe 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 adegree Centigrade for each additional atmosphere of pressureapplied to the water. Suppose,
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for instance, our earth possessed an atmosphere so heavy to asexert a thousand times the pressure of the existing atmosphere,then water would not freeze at 0° C., but at -7.5° C. or about18° F. Again, in vacuo, that is when the pressure has beenreduced to the relatively small vapour pressure of the water, thefreezing point is above 0° C., _i.e._ at 0.0075° C. In parts ofthe ocean depths the pressure is much over a thousandatmospheres. Fresh water would remain liquid there attemperatures much below 0° C.
It will be evident enough, even to those not possessed of thescientific insight of James Thomson, that some such fact is to beanticipated. It is, however, easy to be wise after the event. Itappeals to us in a general way that as water expands on freezing,pressure will tend to resist the turning of it to ice. The waterwill try to remain liquid in obedience to the pressure. It will,therefore, require a lower temperature to induce it to becomeice.
James Thomson left his thesis as a prediction. But he predictedexactly what his distinguished brother, Sir William Thomson—laterLord Kelvin—found to happen when the matter was put to the testof experiment. We must consider the experiment made by LordKelvin.
According to Thomson's views, if a quantity of ice and water arecompressed, there must be _a fall of temperature_. The nature ofhis argument is as follows:
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Let the ice and water be exactly at 0° C. to start with. Thensuppose we apply, say, one thousand atmospheres pressure. Themelting point of the ice is lowered to -7.5° C. That is, it willrequire a temperature so low as -7.5° C. to keep it solid. Itwill 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 tosupply the 80 thermal units which, as we know, are required toturn each kilogram of the ice to water. Where can it get thisheat? 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 thewater. It does both in this case, and both ice and water drop intemperature. They fall in temperature till -7.5° is reached. Thenthe ice has got to its melting point under the pressure of onethousand atmospheres, or, as we may put it, the water has reachedits freezing point. There can be no more melting. The whole massis down to -7.5° C., and will stay there if we keep heat fromflowing either into or out of the vessel. There is now more waterand less ice in the vessel than when we started, and thetemperature has fallen to -7.5° C. The fall of temperature to theamount predicted by the theory was verified by Lord Kelvin.
Suppose we now suddenly remove the pressure; what will happen? Wehave water and ice at -7.5° C.
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and at the normal pressure. Water at -7.5° and at the normalpressure of course turns to ice. The water will, therefore,instantly freeze in the vessel, and the whole process will bereversed. In freezing, the water will give up its latent heat,and this will warm up the whole mass till once again 0° C. isattained. Then there will be no more freezing, for again the iceis at its melting point. This is the remarkable series of eventswhich James Thomson predicted. And these are the events whichLord Kelvin by a delicate series of experiments, verified inevery respect.
Suppose we had nothing but solid ice in the vessel at starting,would the experiment result in the same way? Yes, it assuredlywould. The ice under the increased pressure would melt a littleeverywhere throughout its mass, taking the requisite latent heatfrom itself at the expense of its sensible heat, and thetemperature of the ice would fall to the new melting point.
Could we melt the whole of the ice in this manner? Again theanswer is "yes." But the pressure must be very great. If weassume that all the heat is obtained at the expense of thesensible heat of the ice, the cooling must be such as to supplythe latent heat of the whole mass of water produced. However, thelatent heat diminishes as the melting point is lowered, and at arate which would reduce it to nothing at about 18,000atmospheres. Mousson, operating on ice enclosed in a conductingcylinder and cooled to -18° at starting
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appears to have obtained very complete liquefaction. Mousson musthave attained a pressure of at least an amount adequate to lowerthe melting point below -18°. The degree of liquefaction actuallyattained may have been due in part to the passage of heat throughthe walls of the vessel. He proved the more or less completeliquefaction of the ice within the vessel by the fall of a copperindex from the top to the bottom of the vessel while the pressurewas on.
I have here a simple way of demonstrating to you the fall oftemperature attending the compression of ice. In this mould,which is strongly made of steel, lined with boxwood to diminishthe passage of conducted heat, is a quantity of ice which Icompress when I force in this plunger. In the ice is athermoelectric junction, the wires leading to which are incommunication with a reflecting galvanometer. The thermocouple isof copper and nickel, and is of such sensitiveness as to show bymotion of the spot of light on the screen even a small fractionof a degree. On applying the pressure, you see the spot of lightis displaced, and in such a direction as to indicate cooling. Thebalancing thermocouple is all the time imbedded in a block of iceso that its temperature remains unaltered. On taking off thepressure, the spot of light returns to its first position. I canmove the spot of light backwards and forwards on the screen bytaking off and putting on the pressure. The effects are quiteinstantaneous.
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The fact last referred to is very important. The ice, in fact, isas it were automatically turned to water. It is not a matter ofthe conduction of heat from point to point in the ice. Its ownsensible heat is immediately absorbed throughout the mass. Thiswould be the theoretical result, but it is probable that owing toimperfections throughout the ice and failure in uniformity in thedistribution of the stress, the melting would not take placequite uniformly or homogeneously.
Before applying our new ideas to skating, I want you to notice afact which I have inferentially stated, but not specificallymentioned. Pressure will only lead to the melting of ice if thenew melting point, _i.e._ that due to the pressure, is below theprevailing temperature. Let us take figures. The ice to startwith is, say, at -3° C. Suppose we apply such a pressure to thisice 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: Thepressure must be sufficiently intense to bring the melting pointbelow the prevailing temperature, or there will be no melting;and the further we reduce the melting point by pressure below theprevailing temperature, the more ice will be melted.
We come at length to the object of our remarks I don't know whoinvented skating or skates. It is said that in the thirteenthcentury the inhabitants of
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England used to amuse themselves by fastening the bones of ananimal beneath their feet, and pushing themselves about on theice by means of a stick pointed with iron. With such skates, anyperformance either on inside or outside edge was impossible. Weare a conservative people. This exhilarating amusement appears tohave served the people of England for three centuries. Not till1660 were wooden skates shod with iron introduced from theNetherlands. It is certain that skating was a fashionableamusement in Pepys' time. He writes in 1662 to the effect: "Itbeing a great frost, did see people sliding with their skates,which is a very pretty art." It is remarkable that it was theGerman poet Klopstock who made skating fashionable in Germany.Until his time, the art was considered a pastime, only fit forvery young or silly people.
I wish now to dwell upon that beautiful contrivance the modernskate. It is a remarkable example of how an appliance can developtowards perfection in the absence of a really intelligentunderstanding of the principles underlying its development. Forwhat are the principles underlying the proper construction of theskate? After what I have said, I think you will readilyunderstand. The object is to produce such a pressure under theblade that the ice will melt. We wish to establish such apressure under the skate that even on a day when the ice is belowzero, its melting
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point is so reduced just under the edge of the skate that the iceturns to water.
It is this melting of the ice under the skate which secures thecondition essential to skating. In the first place, the skate nolonger rests on a solid. It rests on a liquid. You are aware howin cases where we want to reduce friction—say at the bearing of awheel or under a pivot—we introduce a liquid. Look at thebearings of a steam engine. A continuous stream of oil is fed into interpose itself between the solid surfaces. I need notillustrate so well-known a principle by experiment. Solidfriction disappears when the liquid intervenes. In its place wesubstitute the lesser difficulty of shearing one layer of theliquid over the other; and if we keep up the supply of oil thework required to do this is not very different, no matter howgreat we make the pressure upon the bearings. Compared with theresistance of solid friction, the resistance of fluid friction istrifling. Here under the skate the lubrication is perhaps themost perfect which it is possible to conceive. J. Müller hasdetermined the coefficient by towing a skater holding on by aspring balance. The coefficient is between 0.016 and 0.032. Inother words, the skater would run down an incline so little as 1or 2 degrees; an inclination not perceivable by the eye. Nowobserve that the larger of these coefficients is almost exactlythe same as that which Perry found in the case of well-greasedsurfaces. But evidently no
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artificial system of lubrication could hope to equal that whichexists between the skate and the ice. For the lubrication hereis, as it were, automatic. In the machine if the lubricant getssqueezed out there instantly ensues solid friction. Under theskate this cannot happen for the squeezing out of the lubricantis instantly followed by the formation of another film of water.The conditions of pressure which may lead to solid friction inthe machine here automatically call the lubricant intoexistence.
Just under the edge of the skate the pressure is enormous.Consider that the whole weight of the skater is born upon a mereknife edge. The skater alternately throws his whole weight uponthe edge of each skate. But not only is the weight thusconcentrated upon one edge, further concentration is secured inthe best skates by making the skate hollow-ground, _i.e._increasing the keenness of the edge by making it less than aright angle. Still greater pressure is obtained by diminishingthe length of that part of the blade which is in contact with theice. This is done by putting curvature on the blade or making itwhat is called "hog-backed." You see that everything is done todiminish the area in contact with the ice, and thus to increasethe pressure. The result is a very great compression of the icebeneath the edge of the skate. Even in the very coldest weathermelting must take place to some extent.
As we observed before, the melting is instantaneous,
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Heat has not to travel from one point of the ice to another;immediately the pressure comes on the ice it turns to water. Ittakes the requisite heat from itself in order that the change ofstate may be accomplished. So soon as the skate passes on, thewater resumes the solid state. It is probable that there is aninstantaneous escape, and re-freezing of some of the water frombeneath the skate, the skate instantly taking a fresh bearing andmelting more ice. The temperature of the water escaping frombeneath the skate, or left behind by it, immediately becomes whatit was before the skate pressed upon it.
Thus, a most wonderful and complex series of molecular eventstakes place beneath the skate. Swift as it passes, the wholesequence of events which James Thomson predicted has to takeplace beneath the blade Compression; lowering of the meltingpoint 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 nowpasses on. Then follow: Relief of pressure; re-solidification ofthe water; restoration of the borrowed heat from the congealingwater and reversion of the ice to the original temperature.
If we reflect for a moment on all this, we see that we do notskate on ice but on water. We could not skate on ice any morethan we could skate on glass. We saw that with light weights andwhen the pressure
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{Diagram}
Diagram showing successive states obtaining in ice, before,during, and after the passage of the skate. The temperatures andpressures selected for illustration are such as might occur underordinary conditions. The edge of the skate is shown in magnifiedcross-section.
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Was not sufficient to melt the ice, the friction was much thesame as that of metal on glass. Ice is not slippery. It is anerror to say that it is. The learned professor was very muchastray when he said that you could skate on ice because it is sosmooth. The smoothness of the ice has nothing to do with thematter. In short, owing to the action of gravity upon your body,you escape the normal resistance of solid on solid, and glideabout with feet winged like the messenger of the Gods; but onwater.
A second condition essential to the art of skating is alsoinvolved in the melting of the ice. The sinking of the skategives the skater "bite." This it is which enables him to urgehimself forward. So long as skates consisted of the rounded bonesof animals, the skater had to use a pointed staff to propelhimself. In creating bite, the skater again unconsciously appealsto the peculiar physical properties of ice. The pressure requiredfor the propulsion of the skater is spread all along the lengthof the groove he has cut in the ice, and obliquely downwards. Theskate will not slip away laterally, for the horizontal componentof the pressure is not enough to melt the ice. He thus gets theresistance he requires.
You see what a very perfect contrivance the skate is; and what asimilitude of intelligence there is in its evolution. Blindintelligence, because it is certain the true physics of skatingwas never held in view by
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the makers of skates. The evolution of the skate has been trulyorganic. The skater selected the fittest skate, and hence the fitskate survived.
In a word, the possibility of skating depends on the dynamicalmelting of ice under pressure. And observe the whole matter turnsupon the apparently unrelated fact that the freezing of waterresults in a solid more bulky than the water which gives rise toit. If ice was less bulky than the water from which it wasderived, pressure would not melt it; it would be all the moresolid for the pressure, as it were. The melting point would riseinstead of falling. Most substances behave in this manner, andhence we cannot skate upon them. Only quite a few substancesexpand on freezing, and it happens that their particular meltingtemperatures or other properties render them unsuitable toskating. The most abundant fluid substance on the earth, and themost abundant substance of any one kind on its surface, thuspossesses the ideally correct and suitable properties for the artof skating.
I have pointed out that the pressure must be such as to bring thetemperature of melting below that prevailing in the ice at thetime. We have seen also, that one atmosphere lowers the meltingpoint of ice by the 1/140 of a degree Centigrade; more exactly by0.0075°. Let us now assume that the skate is so far sunken in theice as to bear for a length of two inches, and for a width ofone-hundredth of an inch. The skater weighs,
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