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 -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 quant.i.ty of Radium only a certain definitely limited amount of Radium C, or of emanation, or any other of the derived bodies, will be a.s.sociated. Why is this? The answer is because the several successive elements are themselves decaying --_i.e._ changing one into the other. The atomic per-

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centage of each, which decays in a second, is a fixed quant.i.ty which we cannot alter. Now if we picture radium which has been completely deprived of its emanation, again acc.u.mulating by automatic trans.m.u.tation 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 acc.u.mulated emanation has increased to such an extent that the number of emanation atoms trans.m.u.ting 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 quant.i.ty 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.

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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 quant.i.ty 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 trans.m.u.ted 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

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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 Inst.i.tute.[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 Inst.i.tute. 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.

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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 --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 quant.i.ties of

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emanation employed can fit in the finest capillary gla.s.s 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 Inst.i.tute 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.

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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 gla.s.s 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 gla.s.s 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.

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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, is deserving of our careful attention. Let not, then, the t.i.tle 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 gla.s.s and the slipperiness of ice. Here is a slab of polished gla.s.s. I can raise it to any angle I please so that at length this bra.s.s weight of 250 grams just slips down when started with a slight shove. The angle is, as you see, about 12 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 gla.s.s possesses by far the smoother surface although I have rubbed the deeper rugosities out of the ice by smoothing it with a gla.s.s surface. Notwithstanding this, its surface is spotted with small cavities due to bubbles and imperfections. It is certain that if the gla.s.s was equally rough, its angle of friction towards the bra.s.s weight would be higher.

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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, bra.s.s curtain ring. This can be detached. Its ma.s.s is only 6 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 gla.s.s. You see that there is little or no difference in the angle of friction of bra.s.s on gla.s.s when we press the surfaces together with a heavy or with a light weight. The light weight requires the same slope of 12 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

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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 gla.s.s, 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 gla.s.s. 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 gla.s.s 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. A weight placed on the ice can be easily seen through the gla.s.s 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 13, 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 quant.i.ties 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

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