XLIV. On the Emission of Electrons by Metals under the Influence of Alpha Rays. By H. A. Bumstead and A. G. McGougan, Yale University [Communicated by the Authors.]. Introduction. IN a previous paper under the same title by one of the present authors [citation redacted], an account was given of some experiments upon the so-called [delta]-rays which are emitted by [header] 463 metals when struck by [alpha]-rays. The emission is known to consist of electrons moving with comparatively small velocities. Maximum estimates of their velocity, based upon the potential difference necessary to cause saturation of the current carried through a high vacuum by these electrons, cm give about 3 x 10 8 : . corresponding to a potential difference of about 25 volts ; minimum estimates, obtained by measuring the positive potential which a source of [delta]-rays will attain if insulated in a high vacuum, give velocities corresponding to 1 to 3 volts. Campbell [citation redacted] has recently brought forward some evidence for believing that the electrons have considerably smaller velocities even than this, if indeed they have any measurable velocity at all. The experiments to be described in § 3 of this paper, however, render this conclusion improbable. In the previous paper it was shown that there was a close analogy between the emission of [delta]-electrons by a metal and the ionization of a gas by [alpha]-rays. The number of electrons emitted by the metal varies with the speed of the [alpha]-particles in the same manner as the number of ions produced in a gas ; so that, by interposing various thicknesses of aluminium foil between the source of [alpha]-rays and the metal, one can plot a curve entirely similar to the ionization curves first obtained by Bragg. The number of electrons emitted by the metal increases with the number of foils interposed until their combined thickness is nearly equal to the range of the [alpha]-rays in aluminium, after which the emission of electrons falls off rapidly. The increase in the number of electrons with diminishing speed of the [alpha]-rays, however, is not so great as the increase in the number of ions in a gas [The increase in the emission as the speed of the [alpha]-particles decreases has also been observed by Campbell, Phil. Mag-, xxi. p. 276 (1911).]. The ionization curve of the metal lies within, or to the left of, the corresponding curve for gaseous ionization and has a less pronounced maximum or " knee " just before the end of the range is reached. This result was anticipated before the experiments were undertaken, for reasons given in the previous paper. The same arguments which led to this conclusion also gave reason to believe that the curve for a metal of high atomic weight, such as gold, would lie within that of a metal of lower atomic weight such as aluminium, just as the latter would lie within the curve of gaseous ionization. This expectation, however, was not fulfilled by the results of the experiments. The curves for gold and for aluminium 464 [header] coincided within the limits of accuracy of the somewhat rough method which was used for determining them. Quite apart from the theoretical reasons discussed in the former paper, it was somewhat surprising to find that two metals which differ so much as aluminium and gold gave, nevertheless, the same ionization curves. For the ionization curves of gases and vapours differ considerably among themselves, not only in the area enclosed (total ionization) but also in their shape [citation redacted]. The close similarity between the curves for aluminium and gold gave rise to the suspicion that the electrons which had been producing the effects observed came not from the metals, but perhaps from a layer of adsorbed gas which was the same in both cases. In order to test this possibility the following experiment was made. § 1. Attempt to remove Adsorbed Gases by Heating. A strip of thin platinum foil, 6 cm. long, 3'7 cm. wide, and 2*4 X 10 -4 cm. thick, was stretched horizontally between two heavy brass clamps ; the clamps were carried each on a vertical copper rod which passed through the cover-plate of the evacuated chamber in which the [delta]-ray effects took place ; the rods were insulated from the plate by ebonite, an earthed guard-tube, and amber, and the joints made tight with sealing-wax. The platinum foil was arranged so that it could be exposed to a pencil of [alpha]-rays from polonium deposited on the end of a copper plug 4 mm. in diameter. Between the polonium and the platinum, one could interpose aluminium foils, without interfering with the vacuum, in the manner described in the former paper. Two, three, four, five, or six layers of foil could be interposed, each 3*2 x 10~ 4 cm. thick. The case was exhausted to about *0001 mm. with the help of charcoal and liquid air ; one of the insulated copper rods which carried the platinum foil was connected with a quadrant electrometer, the case surrounding the exhausted chamber was charged positively, and measurements of the negative current leaving the platinum were taken in the usual manner. After an "ionization curve " had been determined in this way, the platinum strip could be heated by a current sent through it and the two copper rods, and the curve could be again determined when the liberated gas had been removed. Even before the platinum strip was heated its behaviour gave evidence that the occluded gases had some effect upon the phenomena, if only a temporary one. With the metals [header] 465 used previously, the saturation value of the current had been obtained with 4- 40 volts on the case. With the platinum, an hour after the liquid air had been applied to the charcoal, it required -f 160 volts to cause saturation, and the current at this potential was 20 per cent, greater than at 40 volts. Four hours later 120 volts was sufficient to cause saturation, and the current was only 12 per cent, greater than at 40 volts. After an interval of 24 hours, saturation was reached at 80 volts with a 5 per cent, increase over 40 volts. During the same time the magnitude of the current (taken under similar conditions) fell off about 30 per cent. But the shape of the ionization curve, obtained by using a saturating potential and interposing aluminium foils, changed very little, if at all, while these very considerable changes were going on in the conditions of saturation and in the actual magnitude of the current. The results are given in Table I. The first line of the table gives the time after the liquid air was applied to the charcoal bulb, the second line gives the value of the currents (with two toils interposed) corresponding to these times ; the last five lines of the table give the values of the current when different numbers of foil are interposed, the current with two foils being taken as 100 in each case, to facilitate comparison. Table I. [table redacted] It will be seen that the relative values for 2, 3, and 4 foils show no progressive change with the time ; the differences between them are of the order of magnitude of the experimental errors. The values for 5 and 6 foils, however, appear to increase with the time ; these values are on the decreasing portion of the ionization curve, where a small change in the range v of the [alpha]-rays makes a large difference in the current. The observed increase can be explained by supposing that the progressive removal of occluded gas from the platinum 466 [header] foil slightly diminishes its stopping power for [alpha]-rays, and thus the [delta]-radiation from the 'emergence side is increased. After making the measurements which are recorded in the last column of Table I., a current of 12 amperes was passed through the platinum foil. With this current a bright red heat was obtained in the middle of the foil, fading away gradually to the ends which were cooled by conduction through the clamps and copper rods *. The current was continued for 10 minutes, during which time the pressure rose from less than '0001 mm. to '004 mm. The charcoal bulb did not absorb the gas, although the liquid air was left on over-night ; this is doubtless due to the fact that the gas emitted by the platinum contained considerable hydrogen which is not readily absorbed by the charcoal. The liquid air was then removed, and the Toepler pump was operated, while the charcoal was re-heated to aid in sweeping out the hydrogen. When a pressure of about '001 mm. had been reached the liquid air was again applied, and the pressure soon fell to less than '0001 mm. After two hours the value of G 2 was 134, and the variation for the different foils interposed did not differ appreciably from the last column of Table I. This test, however, was not very satisfactory, on account of the failure of the charcoal to remove promptly the gas emitted by the heated platinum. Accordingly the charcoal bulb was removed and a Gaede pump substituted for the Toepler pump. When a vacuum of *0001 mm. had been maintained for an hour, measurements were taken as before. Then the strip was heated five times, for ten minutes at a time, with intervals of fifteen minutes between, to avoid too great heating of che clamps and copper rods ; the pump was kept running continuously. Measurements of the [delta]-ray current were then made as before. The results are given in Table II. Table IT. Foils Before After [table redacted] [header] 467 Here there does appear to be a slight alteration in the form of the ionization curve, and in the direction expected. But the differences are so slight that no great confidence can be placed in the result. Further experience with the method did not give any reason for hoping that the question as to the effect o£ adsorbed gases could be definitely settled in this way. The results of this experiment are susceptible of two quite different interpretations. We may say that, since the heating of the platinum strip did not alter the shape of its ionization curve, we may conclude that this shape is due to the properties of the metal itself and not to adsorbed or occluded gases. On the other hand, we may put the emphasis on the fact that, under certain conditions, at least 30 per cent, of the [delta]-ray effect is due to such gases, and that when these are removed there is no change in the shape of the curve. If the residual effect is really due to the metal, we must suppose that platinum and the adsorbed gases have ionization curves of very nearly the same shape, which is not altogether probable considering the variations which are met with in the curves of gaseous ionization. From tins point of view, therefore, it seems more probable that the [delta]-ray emission (slow electrons) is mainly due to such a layer of gas, which may be reduced but not entirely removed by the methods which we have employed [Since the present investigation was completed a paper has appeared [citation redacted] in which the effect of occluded, gases upon the magnitude of the [delta]-radiation is clearly brought out.]. § 2. Determination of the Ionization Curves of Various Metals. In the determination of the ionization curve of platinum in the preceding section and of those of gold and aluminium in the previous paper, the metals were so thin that the [alpha]-rays passed through them, except when they were near the end of their range. This has the advantage that, at least until the top of the curve is reached, no correction for the charge of the [alpha]-rays is necessary, and one need not apply a magnetic field in order to determine this charge. On the other hand, a difficulty results if one wishes to make a careful comparison of different metals. It is impossible to obtain foils of different metals which have the same retarding effect on the [alpha]-rays ; and hence the emergence [delta]-radiation from the different metals corresponds to different speeds of the [alpha]-rays even when the same number of aluminium foils are interposed. This is 468 [header] plainly shown by a comparison of the results for platinum with those for gold and aluminium given in the previous paper. The platinum foil is so much thicker than the others that the entire form of the curve is distorted. Moreover, in the foregoing experiments, very few points on the curve were taken, so that indeed it is only by courtesy that it could be called a curve at all. For these reasons a much more careful determination was undertaken by means of the apparatus shown in fiV. 1. [figure redacted] A copper plug, P, 4 mm. in diameter, whose lower surface is covered with polonium, is surrounded by a brass cylinder, C, which limits the cone of the rays so that they fall completely within the brass ring, E, which supports the sheet of [header] 468 metal under investigation. In order to obtain more points upon the ionization curves, two disks, D L and D 2 , are used instead of the one which was used in the previous experiments. In order to make the drawing clearer, the rod supporting E is shown in the same plane with the axes of the disks ; in the actual apparatus it is in the plane perpendicular to this. The disks are divided into eight equal sectors. D 1 has a hole 1*5 cm. in diameter cut in each sector. One hole is left open and the others are covered with 1, 2, 3, 4, 5, 6, and 7 layers of aluminium foil of thickness 3*2 x 10~ 4 cm., having a retarding effect upon the [alpha]-rays, according to Taylor's results, equivalent to that of 0*58 cm. of air (air equivalent). The disk D 2 has one sector without a hole so that the [alpha]-rays can be stopped completely; the other sectors have holes, one of which is left open, others being covered with 1, 2, 3, and 4 layers of thinner aluminium foil, 0'64xl0~ 4 cm. thick. Thus five of the thin foils are equivalent to one of the thicker. The dials, Si and S 2 , outside the evacuated chamber enable one to set the disks Di and D 2 so that any combination of the thick and thin foils may be interposed in the path of the [alpha]-rays, or the brass sector may stop them entirely, or the two holes allow them an uninterrupted passage to the electrode. The metal plate attached to the ring E was in every case chosen of sufficient thickness to absorb completely the [alpha]-rays, so that the [delta]-electrons were emitted only from the side on which the [alpha]-rays were incident. The electrode is insulated from the case by ebonite earthed guard-tube and amber, and is connected to a sensitive gold-leaf electroscope of the Hankel type [citation redacted]. A key is connected to a potentiometer arrangement so that the leaf can be insulated, grounded, or charged to any desired potential ; the volt-sensitiveness was thus taken after each reading. In the following measurements, the sensitiveness was adjusted to give a deflexion of about 25 divisions on the scale of the microscope for 0*2 volt. The tube T is connected to pump, gauge, and charcoal bulb. When the [alpha]-rays fall on the electrode E, they carry over to it their positive charges; the [delta]-rays which they excite are negatively charged and these, leaving the electrode, add to its positive charge. In order to insure the removal of all the emitted electrons from the electrode, and to prevent the [delta]-rays emitted by other parts of the apparatus from reaching it, a positive potential of 40 volts is applied to the case. If a sufficient magnetic field is applied, with its lines of force parallel to the electrode, the electrons emitted will be turned [footer] 470 [header] back to the electrode, and in this way the charge due to the [alpha]-rays alone may be determined. For this purpose an electromagnet was constructed of Swedish iron, 2 inches square in section. It was forged into the shape of a rectangle 30 cm. by 25 cm., and a gap left in one side 15*2 cm. long which was just sufficient to embrace the exhausted chamber. It was wound with about 1000 turns of No. 14 cotton insulated, paraffined wire. The field at various points between the poles was measured with a Grassot flux-meter ; a current of 3 amperes produced a field, midway between the poles, of 95 gausses. It was found that, with the case earthed, this field reduced the current received by the electrode to a minimum ; no further diminution occurred when the current through the magnet-coil was increased to 9 amperes. On account of the large air-gap the field was very nearly proportional to the current. The results obtained when the electrode was a sheet of aluminium are shown in fig. 2, in which the ordinates represent the number of aluminium foils between the polonium [figure redacted] and the electrode, and the abscissae are the currents measured by the electroscope. Curve I. a gives the results with no magnetic field, and thus represents the total effect due to both [alpha]- and [delta]-rays. Curve II. shows the currents observed when the magnetic field was on, due to the charge carried by the [alpha]-rays alone. Curve I. b is obtained by subtracting the [header] 471 abscissæ o£ II. from La and represents the [delta]-ray effect, or "ionization" of the metal. It will be observed from an inspection of Curve II. that the number of [alpha]-particles which reach the electrode apparently decreases as more foils are interposed. Up to five thick foils this decrease is approximately linear, and amounts to about 20 per cent, of the total. This is too great a falling off to be attributed to the scattering of the [alpha]-rays according to the results obtained by Geiger*. It is possible that an explanation of this effect may be found in the phenomena to be discussed in the following section. Beyond five thick foils, the number of [alpha]-particles diminishes rapidly ; this is doubtless due to their absorption in the aluminium foils, the more oblique rays being the first to be stopped. By dividing the abscissæ of I.b by those of II., a curve could be obtained which would represent the ionization or [delta]-ray effect produced by a fixed number of [alpha]-particles, which is, strictly speaking, what should be given by an ionization curve. Nevertheless it does not seem advisable to use results thus obtained in the present investigation ; the [alpha]-ray currents are small and the errors introduced by using them as factors might be considerable. Moreover, our purpose is primarily to compare the effects with different metals. The ionization curves of gases and vapours have also usually been obtained without allowance for the decrease in the number of [alpha]-particles, so that a more direct comparison with them is possible by using the curve l.b. An estimate of the number of [delta]-electrons due to one [alpha]-particle may be obtained, however, by dividing the abscissæ of I.b by those of II. Allowing for the fact that the charge on an [alpha]-particle is twice the electronic charge, we find that the number of [delta]-electrons per [alpha]-particle emitted by an aluminium plate from the incidence side only varies from 7 to 17 as the speed of the [alpha]-rays is gradually reduced. One very striking result appeared in the course of these experiments which was quite unexpected from anything previously known as to the effects of [alpha]- rays. As the number of aluminium foils is decreased, the ionization follows a perfectly regular Bragg curve until only one thin foil is left. When, however, this is removed so that there is no obstacle between the polonium and the electrode, a very large increase is observed in the [delta]-ray current. Thus in the series represented by fig. 2, the [delta]-ray current for one thin foil is 7*82 while for no foils it is 16*27, an increase of 107 per cent. It has been shown that this is due to a very absorbable radiation [footer] 472 [header] consisting partly of electrons moving with considerably higher velocities than the hitherto recognized [delta]-rays. An investigation of this absorbable radiation will be described in the next section. Experiments similar to those which have been described at length in the case of aluminium were made also with copper, gold, lead, and platinum. In all cases the surfaces of the metals were made clean and bright by fine sandpaper. The magnitude of the [delta]-ray currents obtained from the various metals under similar conditions were not very different from each other, when correction was made for the decay of the polonium in the intervals between the experiments. The main purpose of the present investigation was to ascertain the variations in the form of the ionization curves for different metals and not their absolute magnitudes; for this reason no attempt was made to get an accurate determination as to the latter point. It is rendered difficult by the fact, discussed in § 1, that the [delta]-ray current falls off with the lapse of time after the liquid air has been applied to the charcoal. This effect was observed in all the metals studied, but it was not quite so marked as in the case of the thin platinum foil described in § 1. However, the diminution in the current sometimes amounted to as much as 20 per cent, and continued to be noticeable for two or three days [* Our observations in regard to the variations in the magnitude of the [delta]-ray current with different metals is in substantial agreement with those of Campbell, Phil. Mag\ xxi. p. 298 (1011 ).]. As in the case of the platinum foil, the relative values at different points of the range of the [alpha]-particles were not affected by this variation, the ratio of the ionizations at any two points remaining practically constant. The results for the different metals are given in Table III. and plotted in fig. 3. The values used are the currents due to the [delta]-electrons alone, corresponding to Curve 1.5 in fig. 2. In order to make the comparison easier they have been reduced to the same scale by making the current for one thick foil the same for all the metals ; the other currents are then altered in the same ratio. The points for the different metals lie so closely together that only one curve has been drawn. Anyone who has had experience with such measurements will recognize that the differences observed are too small to have any significance. Even in the case of aluminium, which appears to differ somewhat from the others, the differences are not at most more than 2 or 3 per cent. ; and differences of this order, which are obviously accidental, occur in all the curves. We are [header] 473 Table III. Al. Foils Thick. Thin. [table redacted] [figure redacted] forced to conclude, therefore, that the ionization curves as observed, for all metals, have the same form. This is in agreement with the results of the less accurate experiments upon gold and aluminium described in the previous paper. 474 [header] Whether or not the curves so obtained really represent the ionization of the metals is by no means certain. As has been said, the fact that there is no change in the form of the curve when its magnitude is considerably decreased by the removal of a surface-film of gas from the metal, makes it not improbable that the whole effect may be due to such a film. The probability of this explanation is increased by the fact that the ionization curves of gases and vapours do vary considerably ; and it seems therefore unlikely that metals, so different in all their properties as those used above, should show such complete similarity in this respect. § 3. Investigation of an Absorbable Radiation accompanying Alpha Rays. When the last thin aluminium foil is removed from the path of the [alpha]-rays, the number of electrons leaving the metal plate is greatly increased ; this is shown by the first line of Table III. § 2. There appears to be, therefore, a very absorbable or " soft '' radiation emitted by the polonium, which is completely stopped by 0*64 X 10 -4 cm. of aluminium. To obtain an idea of the nature of this radiation, some experiments were made, in which we used the apparatus described in the previous paper [citation redacted]. It is substantially the same as that shown in figure 1 of the last section, except for slight differences in dimensions and the fact that there is only one disk to carry the aluminium foils, instead of two. A much stronger preparation of polonium, which we owe to the kindness of Professor Boltwood, permitted the use of an electrometer instead of an electroscope. A brass plate was used as the source of [delta]-rays, and the negative current from it was measured, with one thin foil interposed and with none, when various positive potentials were applied to the case ranging from 40 to 1000 volts. The results of these measurements are shown in fig. 4, where the abscissas are the potentials applied to the case and the ordinates of Curves I. and III. are, respectively, the currents observed with one foil, and with no foils, interposed. The difference between the ordinates of the two curves shows the effect of the assumed soft radiation. This effect is greatly diminished as higher positive potentials are applied to the case, so that at 1000 volts it is reduced to about one-fourth of its value at 40 volts. This indicates that the radiation consists of electrons with much higher velocities than those attributed to the [delta]-rays, and with a wide range of velocities. As the positive potential [header] 475 on the case is increased, more and more of these electrons are withheld from reaching the brass plate. The fact that this radiation communicates a positive charge to the plate is not an obstacle to the hypothesis that it consists of electrons. [figure redacted] Since the early experiments of Lenard it has been known that electrons, moving with velocities corresponding to several hundred volts, when they fall upon a metal, cause the latter to emit secondary electrons, which may carry a larger 476 [header] negative charge away from the metal than it receives from the incident stream [* See also Gehrts, Ann. d. Phys. xxxvi. p. 1001 (1911), where it is shown that, when electrons with a velocity corresponding- to 200 volts fall upon a copper plate, the secondary electrons carry away from the plate more than twice the charge brought to it by the incident electrons.]. It seemed possible that the diminution in the current with an increasing field might be due to an effect upon the electrons emitted by the plate, rather than upon the radiation itself — for example, by increasing the reflexion, or the number of secondary electrons from the case. In order to test this possibility, the brass plate (corresponding to E in fig. 1) was enclosed in a tin box, whose top was made of wire gauze in order to permit the [alpha]-rays and the new radiation to reach the plate. It was insulated from the case and could be charged by means of an external electrode. The box was kept charged to 40 volts while positive potentials up to 1000 volts were applied to the case ; in this way the field in the vicinity of the plate, E, remained practically constant while the soft radiation had to pass through a variable field. The results were not essentially different from those shown in fig. 4. In order to determine whether or not this soft radiation was peculiar to polonium, experiments were made in which the active deposit of thorium (obtained from a preparation of meso-thorium) was used. It was much less active than the polonium and more time was necessary for each reading; on account of the decay of the activity it was not practicable to wait until the changes due to the removal of the gas layer had ceased before beginning the readings. It was thus impossible to obtain as satisfactory numerical results as with the polonium, but there could be no doubt about the existence of the soft radiation. It produced a greater effect in proportion to that due to the [alpha]-rays than in the case of polonium; the ratio was about twice as great. On the other hand, the diminution produced by an opposing electrical field was not as great as with the polonium ; with 940 volts on the case, the effect of the soft radiation was about one-half as great as with 80 volts. A similar change of potential with the polonium reduced the effect to one-third. Returning to fig. 4, it will be observed that Curve I., which was supposed to be due to the [alpha]-rays alone, shows a diminution of the current as the potential on the case is increased, which is similar to that of Carve III. but much less in amount. This was at first difficult to explain ; it is quite evident that [header] 477 the fields used were too small to accelerate the [alpha]-rays sufficiently to cause an appreciable decrease in the [delta]-ray current. The fact that the soft radiation accompanied the [alpha]-rays in the thorium deposit as well as in polonium suggested that it might be a secondary effect ; if this were so, then the currents plotted in Curve I. (fig. 4) would be due not to the [alpha]-rays alone, but there would be a small admixture of the assumed secondary rays from the lower side of the aluminium foil on the disk [At this stage of our experiments, the very interesting paper of Wertenstein, Le Radium, ix. p. 6 (1912), came to hand. By measuring the ionization due to RaC in gases at low pressures, he has demonstrated the existence of two soft radiations ; one is secondary, and deviable in a magnetic field, and doubtless consists of electrons, while the other is not appreciably deflected in a magnetic field of 1100 units. The remainder of our work was done with a knowledge of Wertenstein's results and the next experiment was directly suggested by his paper.]. A small circle of the thicker aluminium foil, of the same diameter as the opening in the brass cylinder C (fig. 1) was pushed up against the polonium. in this way any soft radiation coming directly from the polonium would be stopped ; but a secondary radiation due to the impact of the [alpha]-particles on the inner walls of the brass cylinder C would not be stopped unless a foil were interposed below the cylinder by means of the wheel. The experiment was made as before, by applying various positive potentials to the case and taking- alternate readings with and without the foil below the cylinder. The results are shown in Curve IT. of fig. 4. The sensitiveness of the electrometer had changed by about 5 per cent, since the experiments with the uncovered polonium ; the values of all the currents were reduced in the same ratio so that the measurements with the interposed foil should agree. In Curve I. the crosses represent the measurements when the polonium was covered, the circles those obtained when it was not covered, a thin foil being between the cylinder and electrode in both cases. A comparison of Curves III. and II. shows that the direct radiation contains a component which is much less affected by the retarding field than the secondary radiation alone. This agrees with the results of Wertenstein (I. c.) who, however, worked with a magnetic instead of an electric field. If we assume that the soft radiation is made up of two portions, one coming directly from the polonium, and not retarded by the field, while the other is secondary and consists of electrons, we may show by a simple calculation that the experimental results are accounted for in a very satisfactory manner. 478 [header] Let a be the current of [delta]-electrons leaving the electrode due to the pencil of [alpha]-rays which strike it ; this is present in all the curves. Let b be the current due to a soft radiation from the polonium which is unaffected by the field ; this is present in III. but absent in I. and II. Let s be the current due to a secondary radiation (consisting of electrons), when there is no obstacle between the polonium and the electrode (Curve III.) ; this will vary with the electric field. The secondary radiation which produces s is due to nearly all the [alpha]-particles liberated by the polonium, through the complete solid angle 4-77 ; but the secondary rays from the ping which carries the polonium and from the deeper parts of the cylinder are cut down by the limited aperture. When the polonium is covered, the secondary rays are due to the [alpha]-particles which emerge through a solid angle approximately equal to 2[pi]; their effect will be equal to ms where m< 1. (Curve II.). Finally, when the thin foil is interposed below the cylinder, the secondary rays from the lower side of the foil will be due to the [alpha]-rays which get out of the cylinder and pass through the foil ; the solid angle in this case is about 0'14 [pi], but the beam of secondary rays is not limited by any diaphragm. We may write ns (n