# Rays of Positive Electricity and Their Application to Chemical Analyses/Discussion of the Photographs

The appearance of a typical photograph produced by the Impact of the cathode rays on the plate when the pressure on the camera side of the apparatus Is reduced to about .001 mm. of mercury Is shown in Fig. 15, Plate I. In this and the figures the deflection due to the magnetic field is vertical, while that due to the electrostatic field is horizontal. It will be seen that the curves on the plate are of two different types.
I. A series of separate parabolic arcs, often of considerable length. From the theory given on page 13 it will be seen that each of these parabolas arises from particles having the same value of e/m, and that these particles have retained this charge throughout the whole of the journey through the electric and magnetic fields. As the velocity of a particle is by equation (3), p. 12 proportional to the tangent of the angle which the line joining the origin to the point where the particle hits the screen makes with the horizontal, It follows that there is a considerable range of velocities among the particles having the same value of e/m. In many cases we have velocities among the same kind of particles differing as much as to make the velocity of the slowest ones less than one fifth that of the fastest In some cases the parabolas are of fairly uniform intensity along the whole of their length. In others as In that shown in Fig. 16, Plate I, the head of the parabola (the part least deflected) is considerably brighter than the rest of the curve, while sometimes, as in the case represented in Fig. 17, Plate L, there are several spots of maximum luminosity dotted along the parabolic arc.
With some exceptions (to be considered later) the heads of all the parabolas are in the same vertical line, showing that the minimum electrostatic deflection suffered by the particles which produce these curves is the same for all the different kinds of particles. By equation (2) page 12 the electrostatic deflection is proportional to e/mv$^2$. If the energy of the particles is due to the fall of the charge through a potential difference V
    ${\tfrac {1}{2}}mv^{2}=V\cdot e$
so that
    ${\frac {e}{mv^{2}}}={\frac {1}{2V}}.$
Hence as the minimum electrostatic deflection is the same for all the particles, we conclude that the maximum potential through which the various particles have fallen is the same for all particles. It is natural to conclude that this maximum potential is the difference of potential between the anode and cathode of the discharge tube. It is easy to verify that when the pressure is altered so as to increase this difference of potential)the deflection of the heads of the parabolas diminishes.
2. Besides the parabolas there are on the plate a series of straight lines connecting the parabolas with the origin. These are due, I think, to particles which have been charged during a part only of their passage through the electric and magnetic fields. This might happen in two ways. A particle which had got neutralized before reaching these fields might, while passing through them, come into collison with a corpuscle, get ionized, and acquire a positive charge, and during the rest of its journey be deflected by the electric and magnetic forces. Or again a particle might be positively charged when it entered the fields, attract a corpuscle whilst in them, get neutralized and for the rest of its journey be free from electric and magnetic deflections. This view of the origin of these to me to be proved by the following experiments,.
As on this view these lines are due to particles which are or discharged in the electric and magnetic fields ; their intensity, as compared with that of*the parabolas, ought to diminish If the length of these fields Is reduced. To test this 1 took a photograph with a tube when the lengths of the electric and magnetic fields were reduced to I mm., the in- tensity of the fields being Increased In proportion so as to get deflections comparable with those in the longer fields. With this very short field the straight lines disappeared, and nothing except the parabolas and the undeflected central spot was to be seen on the photographic plate.
Another way of testing this view Is to use magnetic and electric fields, which are not coterminous. Let us suppose for example that the magnetic field stretches beyond the electric, on the camera side. There will be a part of the field where the particles are exposed to magnetic but not to electric forces. If a neutralized particle gets Ionized in this region, it will experience magnetic, i.e. vertical deflection but no electrostatic or horizontal deflection. Thus with a field of this kind we should expect the line due to particles which acquired their charge whilst in the electric field to have the shape shown In Fig. 18. The straight vertical stem near the origin Is due to the particles Ionized beyond the electric field, a piece running up to join the parabola to those ionized Inside this field, the portion close to the parabola being due to particles which get Ionized almost as soon as they enter the fields. Photographs taken with the magnetic field overlapping the electrostatic show this effect very plainly; one of them is reproduced in Fig. 19, Plate L, another In Fig. 25, Plate II.
Let us now consider the case of the charged particles which get neutralized while passing through the field. The part of the line near the origin will be due to particles which get neutralised almost as soon as they enter the field. We have supposed that the magnet was moved towards the camera so that its field overlapped the electric on that side. This will tend to make the electric field overlap the magnetic on the other side, i.e. the side nearest the cathode, so that when a particle first enters the field Its deflection is mainly due to the electrostatic force and is therefore horizontal; thus a particle which gets neutralized at the early stages of Its journey through the fields will have a horizontal displacement abnormally large compared with the vertical; so that the curves produced on the photographic plate by the particles which get neutralized will have a shape something like that shown in Fig. 20. We see that with these overlapping fields we can distinguish between the lines which are due to particles which have gained a charge in their journey and those which have lost one. The concavities of the two curves are in opposite directions. These two sets of lines are very prominent In photographs taken with apparatus in which care has not been taken to make the fields coterminous; an example of this Is shown in Fig. 19, Plate I. If the fields are coterminous and uniform the two curves coincide and are straight lines passing through the origin.
The gain or loss of the charge on the particles in the positive rays is shown very directly by the following experiments:$^1$ The positive rays were produced in a tube made so as to allow room for two electromagnets A and B, Fig. 21, to be inserted between the cathode C and the willemite screen S. The magnets were placed so that the magnetic field due to the one nearest the cathode was horizontal and the deflection due to It therefore vertical, while the field due to the magnet next the screen was vertical and the deflection due to it horizontal.
The deflections due to the two magnets could thus be separated and measured independently. The effects observed when the magnets were applied separately and then In succession are Interesting. A typical case Is represented In Fig. 22.
Fig. 22 (a) represents the appearance of the screen when the electromagnet next the cathode Is the only one in action: a Is the position of the undeflected spot, b that of the deflected. a and b are connected together by a straight band of luminosity; the luminous streak above a Is due to negatively charged particles. Fig. 22 (b) represents the appearance when both magnets are on. If there had been no loss or gain of charge the only effect of the second field would be to remove the spot b horizontally to another place b’, and we should have only two spots visible a and b’. We see that as a matter of fact there are four spots a, a’, b, b’ on the screen, as well as considerable luminosity over the rectangle with these points as corners. Let us consider these spots in succession : b' has experienced the full horizontal as well as the full vertical deflection : it is therefore produced by particles which have retained their charge whilst passing through both magnetic fields. Let us now take b: this spot has the maximum vertical deflection but no horizontal deflection. Thus the particles producing this spot must have been charged all the time they were in the field of the electromagnet A, but have lost their charge before reaching the field of the electromagnet B. This is an example of a particle losing a charge on its way down the tuba Now consider the spot a’: this has not been deflected vertically at all, therefore it must be due to particles which were uncharged when they were passing the first magnet A. On the other hand it has experienced the full horizontal deflection, showing that the particle most have acquired a charge before reaching the second magnet B, This is an example of particle acquiring a charge during its path. The appearance of the luminosity due to the negatively charged particles shows that these, too, gain and lose negative charges in their passage down the tube.
When we reduce the pressure to the lowest value we can reach by the use of charcoal and liquid air, then with the magnet A on alone we have the spots a and b, Fig. 22. There Is no luminosity between them and no luminosity above a, while, when both magnets are on, we have merely the spots a and b’ ; b and a’ have disappeared along with the luminosity inside the rectangle.
We shall call the lines we have just been considering secondary lines, the parabolic arcs primary lines.
It is important to point out that the collision which Ionizes a neutral particle and gives it a positive charge must be a collision with a corpuscle and not with a molecule of the gas through which the positive rays are passing; for the mass of a molecule of the gas is comparable with that of the positive ray particle, hence a collision between the two would result in the particle losing an appreciable fraction of its energy and being deflected through a considerable angle. The appearance and inclination of the secondary lines show that the particles suffer little diminution in velocity in these encounters and no appreciable change in direction, hence we conclude that the system with which the particle collides must have a much smaller mass than the particle, i.e. it must be a corpuscle and not a molecule.
The secondary curves finally join the parabolic arcs produced by the particles which have been charged during the whole of their journey. If the junction occurs at a considerable distance from the head of the primary, care has to be taken in some cases to avoid confusing the secondaries with primaries corresponding to a different value of ejm. Thus, for example, if the shape of the secondary and primary were similar to that shown in Fig. 23a, and the point of junction came off the plate, the appearance on the plate would be that represented in Fig. 23b, and the secondary might be mistaken for a primary with a value of e\m less than the true value. If the magnetic field overlapped the electric field on the camera side of the apparatus, the primary and secondary would resemble Fig. 23a, and if the right hand part were off the plate, the curves would look like Fig. 24b and the secondary might be mistaken for a primary with a value of e/m greater than the true value. This possible confusion of a secondary with a primary line is a point which requires careful attention when the curves produced by the positive rays are used to identify the gases in the discharge tube; for this purpose the primary curves are the only ones that can be relied upon. The tests for a primary line are (1) that it is parabolic, (2) that it shows an abrupt increase in intensity at a point in the same vertical line as the heads of the other parabolas. The first condition is theoretically sufficient, but when only short arcs are available, it is often difficult, unless a very high degree of accuracy is obtained In the measurement of these lines, to tell whether the curve is or Is not a parabola.
A very interesting feature about these secondary lines is that the velocity of the particles which produce them is practically independent of the strength of the electric field in the discharge tube. When, as a result of a change in pressure, the potential difference between the anode and cathode increases, the velocity of the particles which produce the primary curves increases also. The speed of the particles which give rise to the secondary curves on the other hand is little if at all affected. A little consideration will show, however, that this is what we might expect from the theory given on page 28. The secondaries are supposed to be due to particles which have gained or lost a charge whilst passing through the electric and magnetic fields. Let us consider firstly the case of the particles which have gained a charge: they must have done so by coming into collision when moving at a high speed with a corpuscle which, as it is in the space behind the cathode where there is no electric field, will be approximately at rest. The effects of the collision will, however, clearly depend only on the relative motion of the particle and corpuscle, and will be the same as if the particle were at rest and the corpuscle moving with the velocity of the particle. Now in order that a moving corpuscle may ionize an atom or molecule against which It strikes, the velocity of the corpuscle must exceed a certain value which recent researches$^2$ show depends to some extent on the nature of the atom or molecule. Let us call this limiting velocity for a particular kind of atom V; then in order that an uncharged atom of this kind should be ionized when it strikes a corpuscle at rest it must move with a velocity greater than V; hence all the secondary rays of this kind formed by these atoms must have a velocity greater than V. There is thus an inferior limit to the velocity of the secondary rays and this limit depends on the kind of atom which produces these rays. There must, however, be a superior limit to this velocity as well as an inferior one, for these rays are due to particles which move with great velocity and yet can have lost their charge. To have acquired this velocity they must have been positively charged before passing through the cathode or they would not have been acted upon by the electric forces in the discharge tube: and as they are uncharged when they reach the magnetic field they must have got neutralized by combining with a negative corpuscle in the interval. Now a positively electrified particle moving rapidly past a corpuscle could not attract and hold fast the corpuscle if the relative velocity of the particle and corpuscle exceeded a certain value. This velocity is evidently determined by the condition that it is the velocity with which a corpuscle must be moving when it has just sufficient energy to escape from the surface of a positively electrified particle at rest. We should expect the work required to separate a corpuscle from the surface of a positively electrified particle to be of the same order as that required to ionize the particle when neutral, and this work is equal to the kinetic energy of a particle moving with a velocity V. Thus if the velocity of the particle were appreciably greater than V a positively charged particle would not get neutralized, while if the velocity of the neutral particle were appreciably less than V it would not get ionized. Hence the velocity of the secondaries we are considering must be very approximately equal to V, a velocity which depends only on the nature of the particle and not on the potential difference applied to the discharged tube. This accounts for the fact that the velocities of the particles forming the secondary rays are independent of the potential difference between the anode and cathode.
We can by the method described on page 12 measure the velocity of the particles In the secondary rays corresponding to any atom and hence determine V, the smallest velocity which a corpuscle can have if it is to be able to ionize the atom. When this method Is applied to the secondary rays connected with the hydrogen atom we find that V is about 2 x 10$^8$ cm./sec. This velocity would be acquired by a corpuscle if it fell through a potential difference of 11 volts. Hence we may take 11 volts as the measure of the energy required to ionize an atom of hydrogen.
To give to the atom of hydrogen this velocity requires a potential difference of 11 x 1.78 x 10$^7$/10$^4$ volts (taking e/m for the corpuscle to be 1.78 x 10$^7$ and for the atom 10$^4$), this Is about 20,000 volts. If it required the same energy to ionize an atom of oxygen as one of hydrogen, V would be the same for oxygen as for hydrogen. To give an atom of oxygen this velocity would require a potential difference of 16 x 20,000, or 320,000 volts, a much greater potential difference than we usually apply to the discharge tubes. Thus we see that we cannot expect any except the lighter gases such as hydrogen or helium to show secondaries of the type we are considering.
There is, however, another type of secondary—that due to particles which enter the magnetic field in a charged state and lose their charge before emerging from it: this type of secondary, since it arises from the combination of a positively charged particle with a negatively charged corpuscle, might be expected to occur with slowly moving particles more readily than with fast ones; a particle moving faster than a certain speed would not combine with a negative corpuscle, so that there would be a superior limit to the speed of the particles in secondary rays of this kind. There does not, however, seem to be any reason why there should be an inferior limit to the velocity, provided the slow particles have managed to retain their charges up to the beginning of the magnetic field, and as a matter of fact this type of secondary often shows itself, as in Fig. 25, Plate II., as the limit of a patch of fogging on the photographic plate rather than as a sharply defined line. There are, however, cases notable with the mercury lines, when this type of secondary is more sharply defined than we should expect, since there are among the particles which produce the primary parabolas some with a smaller velocity than can be detected In the secondaries of this type.
The question arises whether the corpuscles which produce the secondaries by neutralizing a positively charged particle or ionizing a neutral one are free, or are those bound up in the molecules of the gas through which the positive rays are travelling. There are several reasons for thinking that the latter hypothesis is the more probable one.
For if the corpuscles which neutralize the positive particles are free they should be removed by a strong electric field which ought therefore to dimmish the brightness of the secondaries. I have, however, never been able to detect an effect of this kind.
Again if free corpuscles were those which neutralized the positively charged particles, the distance such a particle would travel before it got neutralized would depend only upon the density of the free corpuscles. Now this density depends upon the amount of ionization produced by the positive rays after they have passed through the cathode; this will vary with the number of these rays as well as with the pressure and nature of the gas through which they travel. Consequently the distance a positive particle has to travel before it gets neutralized will depend upon other things besides the pressure and character of the gas, and will not therefore have a very close connexion with the free path of a molecule of this gas. Wien$^3$ who has made a very complete study of the distance a charged particle travels before it gets neutralized finds that it is of the same order of magnitude as this free path and does not depend upon the number of free corpuscles. This is in favour of the view that the corpuscles which neutralize the positive particles are not free, the process of neutralization seems to be that the positive particles move through the molecules of the gas and pluck out of them the corpuscles required for neutralization.
Again, we conclude for similar reasons that the corpuscles which ionize a neutral particle are not free but bound up in the molecules of the gas through which the positive rays pass. These rays, like the a particles, seern to be able to pass right through molecules, and Königsberger and Kutschewski$^2$ have shown that when moving through a gas they suffer little diminution in velocity until they are nearly at the end of their path. If the corpuscles which neutralize the positive particles are not free but are in the molecules of the gas through which these particles are passing, we can understand why there is a lower as well as an upper limit to the velocity of the particles which give rise to the secondaries due to particles which have been neutralized while passing through the electric and magnetic fields. For on this view the particle before it can be neutralized has to detach a corpuscle from an atom or molecule. To do this requires the expenditure of a definite amount of work which has to be done on the corpuscle by the particle. The energy communicated to the corpuscle depends on the velocity of the particle, and unless this velocity reaches a definite value the corpuscle will not get enough energy to escape from the molecule and will thus be unable to neutralize the particle.
$^1$ J. J. Thomson, "Phil. Mag.," VI, XVIII, p. 824, 1910.
$^2$ Franck and Hertz, " Verhand. d. D. Phys. Ges.," 15, 34, 1913.
$^3$ W. Wien, Berlin, " Sitzraigsberidite," July, 1911.
$^4$ Königsberger and Kutsdiewski, Heidelberg, "Sitzungsberichte," Jan., 1912; "Ann. der Phys.," 38, p. 161.