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TER VERKRIJGING VAN DEN GRAAD VAN
DOCTOR IN DE WIS- EN NATUURKUNDE
AAN DE RIJKS-UNIVERSITEIT TE UTRECHT
OP GEZAG VAN DEN RECTOR MAGNIFICUS
DR. F. H. QUIX, HOOGLEERAAR IN DE FACULTEIT
DER GENEESKUNDE, VOLGENS BESLUIT VAN DEN
SENAAT DER UNIVERSITEIT TEGEN DE BE-
DENKINGEN VAN DE FACULTEIT DER WIS- EN
NATUURKUNDE TE VERDEDIGEN OP MAANDAG
25 SEPTEMBER 1939, DES NAMIDDAGS TE 4 UUR
DOOR

Jegens allen, die gedurende mijn studietijd tot mijn wetenschappelijke
vorming hebben bijgedragen, moge ik hierbij uiting geven aan mijn groote
dankbaarheid.

Tot U, Hooggeleerde ORNSTEIN, Hooggeachte Promotor, wensch ik
mij daarbij in het bijzonder te richten. De ideale sfeer, die Gij op het
UTRBCHTSCHE LABORATORIUM wist te scheppen, hebben mij het
werken, eerst als student en later meer onder Uw directe leiding als assistent,
steeds tot een vreugde gemaakt. Het vertrouwen dat Gij in mij steldet,
toen Gij mij verzocht een onderzoek ter hand te nemen samenhangend met
de voor het Laboratorium nieuwe, kernphysische richting, heb ik steeds op
zeer hoogen prijs gesteld, en het is mij dan ook een groot genoegen de
eerste te kunnen zijn, die in den vorm van een proefschrift getuigenis aflegt
van deze voor het Laboratorium nieuwe richting van physisch onderzoek.

De groote invloed, die Gij, Hooggeleerde UHLENBECK, op mijn weten-
schappelijk denken en physisch inzicht hebt gehad, mede door Uw bemin-
lijke persoonlijkheid en Uw groote didactische gaven, zijn nauwelijks onder
woorden te brengen. De intieme colloquia, waarbij onder Uw leiding recente
experimenteele en theoretische vraagstukken behandeld werden, zullen voor
mij onvergetelijk blijven.

Beste MILATZ, voor de wijze, waarop jij mij steeds in alle moeilijkheden,
zoowel binnen als buiten het Laboratorium tegemoet gekomen bent, zal ik
je steeds dankbaar wezen. Ook aan de totstandkoming van dit proefschrift
heb jij een belangrijk aandeel gehad.

De voortdurende medewerking, die ik van jou, TER HORST, bij alle
technische moeilijkheden heb mogen ondervinden, zal ik dankbaar gedenken.

Beste BRINKMAN, dat ik onder jouw leiding de eerste schreden op
het gladde pad der experimenteele Natuurkunde heb mogen zetten, beschouw
ik als een groot voorrecht.

Beste WALLER, voor je buitengewoon prettige en onvermoeide mede-
werking bij de experimenten ben ik je zeer erkentelijk.

The importance of an exact knowledge of the fi ray spectra
has led to the development of several experimental methods.
It seemed therefore interesting to investigate the possibility
of applying the photographic plate for quantitative measure-
ments. In this thesis a purely photographic method has been
worked out to obtain the true intensity distribution in a ray
spectrum of a radioactive substance.

In order to obtain the intensities from the photographic
densities on the plate, the density curves (relation between
density and intensity at a certain energy) and the sensitivity
curve (relation between the relative photographic activity
and the energy) must be known for the plates used. The
density curves have been measured by varying the strength
of the source. The sensitivity curve for the plate has been
obtained by changing artificially the energy of the [i particles
with the aid of an electric field, enabling to compare the
densities, caused by the same number of particles with and
without the changed energies.

The greater part of this investigation has been performed
with a ThB source, emitting a combined fi ray spectrum of
ThB, ThC and ThCquot;. As a strong y radiation is emitted by
this source, which would disturb some of the intended measure-
ments, a part of the investigation has been performed with
a RaD source (in equilibrium with RaE), emitting no y rays.

No attempt has been made to ehminate the errors influencing
the ray spectrum itself, such as e.g. those caused by stray

radiation, y rays, etc., as the chief aim of this investigation
was to develop the photographic method for fi ray spectroscopy.

Due to technical difficulties in using high tensions the ap-
phcation of the photographic method has been restricted to
a limited region of energy, namely from 20 to 350 keV.

This thesis deals with a method of investigating the /S ray
spectra of radioactive sources. The nature of these rays is
well established, the only problem which still arises and which
seems rather difficult from experimental standpoint is that of
the distribution of the electrons over the energies, which in
analogy with the optical spectra is called the „/? ray spectrumquot;.

The methods for the investigation of the /S ray spectra
will be treated in the following paragraph. Here a short
account of the main features of the spectra will be given.

They generally consist of one or more rays of homogeneous
energy and a more or less continuous spectrum (see e.g. a
reproduction of such a spectrum in fig. 27) whose energy
range extends from zero to about one to two million electron-
volts. For a long time it was assumed that the continuous
spectrum originated from stray radiation and thus had no
essential meaning. Further research, however, has led to
a different interpretation. It could be proved that the fi par-
ticles producing the continuous spectrum come in reality
directly from the nucleus of the radioactive atom, whereas
the electrons which produce the homogeneous „finesquot; are of
secondary origin; the latter are thrown out of the electronic
atomshell by the y rays also produced by the nucleus.
Two experimental arguments for the primary character of
the continuous part of the fi ray spectrum are the following:
a. the energetic upper limit of the continuous spectrum seems

to be connected with the decay period of the radioactive
substances in the same way as is the case with the energy
of the a radiation;

b. the total number of the ray particles constituting
the continuous part of the spectrum equals the number of
decaying atoms of the radioactive source (G u rn e y

These results obtained with the fi ray spectra are, however,
in contradiction with all other known radioactive phenomena.
All energy relations in nuclear physics, namely, are generally
characterised by a pronounced discontinuity, such as is the
case e.g. with all a and y energies. The reason for this dis-
continuity is that every nucleus can merely occupy a discrete
set of energy levels, and that a radioactive process consists in a
transition of one such energy level to another one. But, how
could it be explained that there existed primary particles
emitted from the nucleus possessing a continuous energy range
without supposing either that the theory of radioactivity was
wrong or that the principle of energy conservation was
violated? Fermi f») has indicated another possibiHty: to-
gether with the emission ot a ^ particle from the nucleus
there would be expelled another hypothetical particle, the
so-called „neutrinoquot; which should be electrically neutral and
possessing a mass between zero and that of the electron.
The whole energy hberated should then be distributed according
to statistical laws over the electron and the neutrino.
Fermi (2quot;) could even calculate with this theory the actual
form of the fi ray spectrum. The first experiments have
shown a slight divergence from the theory of Fermi.
Thereupon Konopinski and Uhlenbeck introduced
a slight alteration of the theory which seemed to fit in better
with the experiments, although the latest experiments seem
again to confirm the first theory of Fermi.

The main subject of all researches on /S ray spectra, which
are not only performed on the spectra of the known natural
radioactive elements, but also on many artificially radioactive
elements, is to compare the spectra obtained experimentally

with the theories of Fermi and of Konopinski —
Uhlenbeck. The main criteria of the validity of these
theories lie in the behaviour of these spectra at the lowest
and at the highest energies. But, just these parts offer the
greatest difficulties to exact measurements; the reasons of this
will be explained here below.

As the intensities of the spectra decrease strongly at both
ends sensitive measuring instruments are necessary, not only
in order to find the position of the real limits, but also to
determine the exact shape in these regions.

Two other difficulties exist for all experiments on /3 ray spectra.
Firstly the great distortion of the spectrum caused by all
sorts of secondary rays, which plays an especially prominent
part in the energetically lower parts of the spectrum because
all secondary electrons will have lower energies than the
primary P and 7 rays. Secondly the sensitivity of most
detecting instruments depends on the energies of the electrons
which are detected. Up to now it appeared to be extremely
difficult to determine the way in which the sensitivity depends
on the energy. For a long time the importance of these two
sources of error has not been recognised and so frequently
wrong conclusions have been drawn.

This thesis will especially deal with one of the above
mentioned points, namely the determination of the sensitivity
function for the photographic method. It must, however, be
emphasized that the principle of the method can be applied
also to other cases.

The following paragraph will give a brief survey of the
experimental methods applied at present with the aim of getting
an appreciation of the significance of the photographic method
compared with the other methods of investigation.

of detection with their principal characteristics concerning
their way of operation, the possibilities of their appli-
cation, their sensitivity, their precision and their degree
of selectivity.

This method is the most direct one for obtaining the
number of electrons and is not at all selective. G u r n e y
employed e.g. a Faraday cage in which the electrons are
caught. He intended not only to obtain the intensity distribution
in continuous /? ray spectra, but also to determine the total
number of primary electrons which, as explained in the
preceding paragraph, is important for the knowledge of the
origin of these spectra. The charge is measured by a sensitive
electrometer.

Apart from instrumental difficulties the only drawback is
the relatively low sensitivity of this method. The electro-
meter used by Gurney possessed a sensitivity of 3 X 10-''
volt per division. The capacity of the system being mainly
defined by that of the cage cannot be lowered arbitrarily.
The capacity of the system used by Gurney was 87 cm,
so that one division corresponded to about 18X10^ electrons.
It appears from his reproduced curves that it was possible
to measure the rate of accumulation of charge with an accuracy
of about 1 division per minute (fimited e.g. by natural leak
and secondary effects). This means that about 10^ electrons
per second are necessary to keep the error under IO^/q. The
best electrometers obtainable nowadays are about ten times
more sensitive than that used by Gurney, so that the
minimum current for measurements with 10 quot;/g accuracy can
be accepted to be lO'^ electrons per second. This method cannot
be improved by other methods of measuring the charge,
such as e.g. that using amplifiers.

Recapitulating, the method, sketched above appears to have
the great advantage of being a direct method without selec-

tivity effects, but it is necessary to employ relatively strong
electronic sources.

This method is based on the fact that electrons, passing
through a gas-filled volume, cause an ionisation of the gas
the magnitude of which depends on the electronic energies.
Introducing an electric field in this gas the positive and
negative ions move to the cathode and anode respectively.
The total charge of these ions can be measured either with
an electrometer or amplifier.

This method has frequently been applied in all domains
of nuclear physics, however not for measuring the /? ray spectra.

The main disadvantages are the great selectivity and the
relatively big disturbances, caused by the effect of other
ionizing agents which are of the same order of magnitude
as the electronic effect itself. The main reason, however, that
this method is scarcely used for this purpose, is the existence
of better methods. The ionization chamber has in fact been
applied for (i ray spectra only by Ellis C h a d w i c k
and Madgwick(®®).

Concerning the sensitivity attainable with this method
a high-sensitive ionizationchamber, recently designed by
Barnes may be mentioned, enabfing the measurement
of about one electron per second.

In § 13 an application of the ionizationchamber to the
measurement of the strengths of radioactive sources will be
treated.

The principle of the electric counter was first introduced by
Rutherford and Geiger (®^), further developed by Geiger
to the so called „Spitzenzahlerquot; and finally perfected in
1928 to the „Geiger-MiiHerquot; Counter.

The principle of operation is the following: just as in the
case of the ionization-chamber an electric field is applied

between two electrodes in a gas-filled space. The strength of
this electric field is, however, chosen near the value where
a spontaneous discharge would take place. As soon as an
electron enters the field, it is accelerated and produces secon-
dary ions which in their turn produce again new ions etc.,
so that the primary ionization is automatically amplified many
times. The geometrical and electrical device provides a breaking
off of the discharge after a sufficiently short time. The ad-
vantage of this method will immediately be obvious. The
effect of even one electron being greatly amplified all auxi-
liary apparatus can be very simple. As furthermore the mag-
nitude of the discharge does not depend on the initial cause
any selectivity of the method seems to be absent, provided,
of course, there exists a primary ionization.

The type of Geiger-Müller counter, which at present
is mostly used, consists of a thin wire forming the anode and
of a coaxial cylinder forming the cathode.

According to the above given view the counter would
represent the ideal measuring instrument, with a sensitivity
of counting each entering electron and with a total absence
of selectivity. Unfortunately matters are somewhat different.
The energetic selectivity begins to play a part at higher and
at very low electronic energies. The reason is that the ioni-
zation per unit of length is a function of the energy and
that it diminishes at higher energies, so that the probability
that an electron will not produce one or more pairs of ions
in the counter will increase. The probability can be calculated
(viz. Ornstein, Milatz, ten Kate and Miesowicz
and the calculation has experimentally been verified by the same
authors, Riehl and recently de Vries and Sizoo
have also made researches about this point. The probabiUty
that an electron will or will not be detected, depends not
only on the energy of the entering electron, but also on the
pressure of the gas in the counter and on the geometrical
circumstances.

diminished by the above explained selectivity effects. But
still another cause exists limiting the ideally attainable value
of sensitivity, namely the so-called „zero-effectquot; which is
caused by spurious radioactive and cosmic radiations. Even
when there is no electronic source in the neighbourhood of
the counter, this zero-effect exists depending on the geome-
trical and other conditions of the counter, and which amounts
in general, for the ß counters applied for radioactive purposes,
to about one impulse per three seconds.

Here also it is possible to calculate the minimum intensity
of the electronic source necessary to obtain a certain accu-
racy, e.g. of 10 But because of the fact that this accuracy
is here determined by purely statistical factors, it can be
augmented arbitrarily by increasing the time of observation,
because the relative statistical fluctuation of a number of ob-
servations diminishes inversely proportional to the square
root of this number, contrary to most other sources of errors.
Thus we must fix a certain time of observation. With the
above given value of the zero-effect it is easily verified that
for a time of observation of 1 minute the number must be
at least 200 electrons per minute to have an error less than
10%, whereas for a time of observation of three minutes
the corresponding number is 30 per minute.

The Geiger-Müller counter is by far the most frequently
applied instrument for measurements in the ß ray spectra, so
that it may suffice to mention only the latest publications
referring to investigations on the continuous spectra of Ra D E
and Th B C Cquot;, performed with counters and in which
other literature can be found. These publications are of
Flammersfeld on the continuous spectrum of Ra D E
and of Alichanian and Zavelskij(i) the continuous
spectrum of Th B C Cquot;.

This method is based on the fact that when particles
are falling on screens of phosphorescent zinc sulfide, or some

other substances, the spots which have been hit by such
particles show short flashes of Ught which can be seen by
considering the screen with a microscope. This method has
often been used for a particles, but the effect caused by
electrons is too weak for applying the method in this way
to quantitative measurements in ^ ray spectra. The only cases
in which the scintillation screen is used in quantitative electronic
researches are for the visual estimation of intensities in cathode-
ray tubes, or for amplifying the action of electrons on the
photographic plate (only applicable with electrons of low
energies, viz. v. B o r i e s and Knoll (®)).

This method which was first introduced by Wilson
in 1911, and which is used very much in the whole domain
of nuclear physics is based on the following phenomenon. When
a gas volume which is saturated with water vapour, is suddenly
expanded, so that the gas becomes over-saturated, the water
vapour tends to condensate on charged nuclei. It is possible
to adjust the expansion in such a way that the condensation
will only take place at such spots where charged atoms are
present. This phenomenon furnishes the possibility of studying
the tracks of elementary ionizing particles, the secondary
ions acting as charged nuclei.

The most characteristic feature of this method compared
with all preceding ones, is its possibifity to study, or to register
photographically individual particles and processes, and to
give many-sided informations with each observation ; namely
it gives the exact form of the track in three dimensions, the
nature of the particle and also its energy. However, apart
from all these advantages, there exist also disadvantages, and
one of the most serious ones is, that this method becomes very
laborious when it is necessary to study a great number of
such processes, as is required for statistical purposes, and
also for the study of /S ray spectra. This is probably the
reason that this method is very rarely applied to the /? ray spectra.

Since the whole following chapter deals exclusively with this
method, only some characteristic features will be mentioned
which are of importance for comparison.

The photographic plate has some properties analogous
with those of the expansion method, and others belonging
at the same time to the other methods mentioned above.

It has in common with the Wilson chamber method
that it is also able to fix individual processes, though under
less favourable circumstances. Yet, this function of the photo-
graphic plate has e.g. been used by Blau, Wambacher
Taylor Powell and Fertelip®) for the investigation
of the ranges of different particles, for the study of nuclear
reactions and recently for the determination of neutron
energies resp.

On the other hand the density of the photopraphic plate
enables, after calibration, to determine the number of particles
that have fallen on the plate, so that the plate can also be
used as a counting instrument.

This combination of properties, however makes the photo-
graphic plate so specially suitable for the intended purpose,
as it is possible to obtain with one observation a whole
range of intensities as a function of the position on the plate.

But, apart from the advantages of this combination of possi-
bilities, the photographic plate possesses also some of the
disadvantages of the preceding methods.

In the first place there exists a pronounced energetic
selectivity. The greater part of this paper will deal with the
problems in connection with this point.

Furthermore the magnitude of the sensitivity of the photo-
graphic plate is relatively small. As this point will also be treated
in detail in the following chapters, only some general remarks
will be made. As the photographic plate is an accumulative
instrument and as moreover its sensitivity depends on the
size of the exposed surface, this sensitivity has to be defined

in a specific way ; namely by the number of electrons which
has to fall on a certain surface of the plate (in an arbitrary
time) to enable the measurement of the intensity with an
accuracy of e.g. 10%- So for instance a number of 10^—10®
electrons per mm® with an energy of 100 keV is required
for this purpose. A further discussion of the circumstances
determining the sensitivity will take place in the last chapter.

A short enumeration of the methods, used for this purpose,
will be given enabling to judge the relative significances of
these methods, and to justify the choice made in this paper.

All sorts of radioactive radiations undergo absorption (a
diminution of intensity and energy) in matter, the mechanism
and the rate and kind of absorption of the radiation being
different under different circumstances.

If the radiation is of an energetically homogeneous nature, and
consists of a parallel beam, an exponential dependence between
the transmitted intensity J and the thickness x of the absorbing
material will exist :

Here fj, is called the absorption-coefficient, which depends
on the kind and energy of the radiation and on the
absorbing material. It appears that the absorption-coefficient is
approximately proportional to the density q of the absorber;
it is therefore convenient to introduce the mass-absorption-

It must, however, be emphasized, that the exponential law
holds only for absorbing thicknesses, which are small compared
with the total range, because at greater absorptions a qualitative
alteration of the radiation takes place, as not only the intensity.

but also the energy diminishes and becomes inhomogeneous,
and moreover the spatial distribution becomes more divergent.

In reality the notion of absorption is a many-sided one.
Firstly there must be made a distinction between an energetic
absorption and an absorption in intensity. This latter can
be subdivided in a real absorption (when the radiation is partly
or wholly captured in the atoms of the absorber) and a scattering
and reflection out of the beam.

The application of the absorption method to energy measu-
rements of rays appears to offer serious difficulties, though
it has been applied in the earlier experiments. The reasons
why this method is unsuitable for this purpose are that it is
difBcult to obtain homogeneous and narrow electronic beams
of radioactive origin (only in this case there exists a well
defined dependence of the absorption-coefficient on the energy)
and that relatively large energy losses occur, even at small
absorptions.

This method can be applied in two forms, namely by
determining the deviation of the particle or by determining
the tension, which must be applied to stop it. Its application
is only possible in those cases where the energies of the
particles are not too high, because otherwise high electric
tensions are necessary. As all radioactive radiations are
generally of a rather high energetic nature, this method has
seldom been applied in the cases which are considered here.

The apphcation of a magnetic field has two important
properties causing that this method is by far superior to all
other methods:

1. the action of the magnetic field on a charged particle
alters the shape of the path without changing the energy of
the particle so that the energy remains well defined during
the whole time of a measurement.

2. It is technically rather easy to produce magnetic fields
of the required strengths, and no materials except the ferro-
magnetic ones disturb the field.

The measurement of the energy by this method takes place
generally with transversal field (field perpendicular to the
velocity of the particle). In this case the particles describe
circles, whose radii depend in a simple way on the energy
of the particles. A closer discussion of this point will be
given in § 10.

The radius can be determined, either by using a small
part of the circle and measuring the deviation of the endpoint
of the considered part of the path, or by using one half of
the circle and measuring directly the radius. The first alter-
native is sometimes necessary, when the particles are very
fast and heavy so that it would be difficult to extend the
magnetic field over a sufficiently large area to enclose a
greater part of the circular trajectory within the field.

The second alternative, namely of using half circles, was
first proposed by Danysz (i®). It has also been applied in
this thesis due to several more special advantages regarding
the application to the photographic method. As, namely, the
sensitivity of the photographic plate depends on the size of
the area which is exposed to a certain beam of particles, it
is of special importance to have the possibility of collecting
as much as possible of the beam on a small area of the
plate, but this focussing must not take place at the expense
of the separation of the different energies. The method of
using half circular trajectories meets all these requirements
in a satisfactory way.

In this paragraph a brief survey will be given of the main
known facts concerning the blackening action of various
radiations on the photographic plate.

The photographic plate can be blackened by visible, ultra-
violet and infrared light as well as by Röntgen, y, and a rays.

In fig. 1, the general shape of the density curves (curves
giving the density as a function of the intensity falling on
the plate) for visible light and Röntgen rays are given, and

from this figure the difference in the photographic action of
these two kinds of radiation can be seen. The curves for the
optical radiation always show a superproportional part at low
intensities (one speaks often of the existence of a „thresholdvaluequot;
of the intensity, being the value of the intensity where the
linear part of the curve intersects with the abscissa), whilst the
curves for Röntgen rays show, already from the beginning,
a proportional relation. The y, (i and a rays appear to act
on the plate in the same way as the Röntgen rays. The
exact shape and the factors determining the shape, will, in
the case of the fl radiation, be discussed in the paragraphs
5, 16 and 18.

Another difference of the behaviour between the rays
giving a density curve of the type a (fig. 1) and those giving
a density curve of the type b exists. Only in the last case
the so-called reciprocity law of Bunsen-Roscoe (®) holds,
that is to say that the density, caused by a certain total
intensity of radiation, is independent of the time during
which this intensity has fallen on the plate. In the other
case, e.g. for visible fight, this law generally does not hold.
This point will also be discussed, in the case of the ^
radiation, in more detail in § 5 and § 16.

All further results are of secondary importance and will
be treated subsequently in the following paragraphs, so far
as the P radiation is concerned.

Although it lies beyond the scope of this thesis to give
an account of the modern conceptions concerning the mechanism
of the blackening action, some consequences of the concep-
tions put forward by Webb (''''), Gurney and Mott
may still be given here because they are immediately appli-
cable to the electronic action on the photographic emulsion.

The action of those rays which give rise to density curves
of the type a (fig. 1), appears to be characterised by the
fact that on the average about 100 quanta must be absorbed
by an AgBr grain of an undeveloped emulsion in order to
make this grain developable, whereas for all rays giving a

density curve of the type b, allready one absorbed quantum
may be sufficient for this purpose. These results which are
explained by the conceptions of the above mentioned authors,
allow some conclusions concerning the action of electrons
on the photographic emulsion, assuming that already one
electron can make an AgBr grain developable. This assump-
tion seems justifiable by the great ionizing power of the electrons,
considered here.

From this assumption it follows that the density curve for
the electrons will be of the type b in fig 1, and furthermore
that the reciprocity law will be valid. Another consequence
is that the shape of the density curve is independent of the
electronic energy.

One must, however, be warned against the error of thinking
that it should already be possible to determine once for all
a density curve for electrons being generally valid. As long
as this point has not been checked by extensive experimental
work, it remains necessary to determine the density curve
for each plate and for each electronic energy separately.

The photographic method for quantitative measurement has
some properties which procure a particular position for it
among all other methods. The plate furnishes a measuring
instrument that never fails to work so that the trouble caused
by disturbances of instrumental kind do not occur.

The only disturbances playing a part are caused by the
faults and fluctuations originating at the manufacturing of
the plates. These irregularities necessitate the introduction of
a special technique when using the method: every plate has
to be calibrated separately.

The calibration of a plate is carried out by determining
the relation between the density and the intensity falling on
the plate per unit of area for one or more wavelengths or

energies. If this dependence can only be determined relatively
(i. e. if only the ratios of the intensities are known), the
calibration has to be divided into two parts : a determination
of the relative density-intensity curves for the separate wave-
lengths or energies, and a determination of the relative sensitivity
of the plate for these different wavelengths or energies.

The measurement of the relative density curves offers no
difficulty. The relative intensity falling on the plate can be
varied in a known way: e. g. by variation of distance and
of the strength of the source or by using diaphragms¹).

The determination of the sensitivity of the plate as a
function of the wavelength or the energy is, however, more
difficult. For electronic radiation it has not been carried out
up to now and also in the case of optics it has taken a
longer time to establish a suitable method. In § 6 and § 7
the method for obtaining the sensitivity in the case of /? radiation,
and the comparison with the method used in optics will be
elucidated.

Some attention may be paid to the measurement of the
density. Though the definition and the way of measuring
this quantity is irrelevant, because the same instrument and
definition is used in calibrating and in using the plate, it is,
on the other hand, important for the discussion of the accu-
racy and for the comparison of the results of different authors.

The suitable quantity for expressing the density, is defined
in the following way: if J^ is the intensity of light falUng

1nbsp; Often variation in time of exposure has been used; this is only justified
if the reciprocity law (see § 3) has been tested.

of the apphed photometer, and discrepancies between the
results of different authors may partly originate from this
point (§ 18).

In the experiments described here Moll's microphoto-
meter has been used. For a detailed description see O r n s t e i n
Moll and Burger This photometer renders possible
the measurement and the registration of the density of the
plate even on areas as small as 10-® cm^. For further dis-
cussion of this subject see § 20.

§ 5. Review of the Use of the photographic Plate for
quantitative Measurements of f) Ray Spectra in the
Literature.

Before 1920, the authors who used the photographic plate
for the study of the f^ ray spectrum contented themselves
with visual estimations of the intensities (e.g, of the different
characteristic lines in a /S ray spectrum). In 1921 Geiger
and B o t h e (quot;) calibrated the plate for the first time with
the help of a density curve, obtained by variation of the
distance. In their experiments they used the whole ^ radiation
of RaE, consequently an energetically heterogeneous radiation.
Notwithstanding this fact they obtained some important density
laws, namely the proportionality of the density curve at low
intensities and the validity of the reciprocity law (see § 3).

Further research on this point had not been done until
1927. Ellis and W o o s t e r ('®), who wished to determine
the absolute intensities of the characteristic lines (in order
to get the internal conversion coefficients), for the first time
applied the action of energetically homogeneous rays on the
plate. These rays were obtained by the half-circular focussing
method, explained in § 2 and discussed more thoroughly in
§ 10. They were able to confirm the results obtained by
B o t h e and Geiger in the case of heterogeneous rays,
for that of homogeneous rays. They found in addition that
the shape of the (logarithmic) density curve is independent
of the electronic energy and, within certain limits, of the

Concerning the sensitivity of the photographic plate for
different electronic energies these authors had to assume a
certain dependence of it on the energy without being able
to check this assumption experimentally. They assumed namely,
that the sensitivity would be proportional to the ionization
of the particles in the plate. This ionization was known to
be inversely proportional to the square of the velocity.

In 1928 Ellis and As ton published a comparison
of the photographic results with those of the measurements
of Gurney who had worked with a Faraday-cage on
the same spectra (charge-determination, see § 2), and in this
way they were able to obtain for the first time a sensitivity
curve for the photograpic plate. This curve, which is represented
in fig. 2 by the solid line, shows that the original assumption
of Ellis and Wooster (which is represented by the
dotted curve in fig. 2) was not correct.

As an explanation for the failure of this hypothesis, they
assume that it is caused by the reflection of the electrons in
the emulsion and on the glass. This point will be discussed
more quantitatively in § 19.

In 1932 Ellis published a continuation of the sensi-
tivity curve to lower energies, which was based on the
comparison of some characteristic lines whose intensities were
measured by others. This proposed continuation is represented
by the broken part of the curve in fig. 2. However, the author
admits, that this part is somewhat problematic.

In conclusion a few words may be said about a publication
by Bories and Knoll in 1934. These authors have used
the electrons of a cathode-ray tube, and could attain energies
up to 80 keV. They give a number of absolute density curves,
from which the sensitivity curves can be derived directly. They
find a surprisingly great dependence of the shape of the
density curves on the energy so that their results seem to
be in contradiction with other experiments.

The preceding researches (except the last one), have been
performed in order to investigate the relative intensities of the
characteristic lines in the ray spectra. The photographic
method has, however, never been applied to the continuous
spectrum. In this case, these continuous spectra being the
subject of investigation, it is even more important to know
the sensitivity of the plate. The purely photographic method
applied in this thesis in order to obtain this sensitivity of
the plate will be described in the next paragraph.

§ 6. The Method of changing artificially the electronic
Energies in a /S Ray Spcctrum.

The following problem had to be solved: when the photo-
graphic density on two spots of the plate caused by two
beams of electrons of known energies is given, then the un-
known intensities at these two spots must be found.

If the energies of the electrons in the two beams are equal,
the intensities can be obtained by means of the density curves.

If, however, the two energies are unequal, the following
artifice has been applied: change the electronic energy of
one beam by an electric field in such a way that this energy
becomes equal to that of the second beam. In this way ob-
taining two beams of the same energy, the ratio of the in-
tensities can be determined by means of the „monochromaticquot;
density curve and thus the desired ratio of the first and the
second beam are obtained.

The way in which this principle can be applied to the
^ ray spectum will be explained below.

In fig. 3 a photographic /S ray spectrum (I) is schematically
represented (the density D as a function of the energy). It
is possible to obtain the relative intensities in the points A,
B, C, and D, showing equal distances in energy, by taking
one more spectral photograph (supposing that the density
curves are known). In this second photograph all energies
ought to be changed by an amount AE, corresponding to
the distance in energy between the points A, B, C and D.

This energy-shift can simply be obtained by a corresponding
electric tension, and changing the energy of every electron
in this way by the amount JE. The shifted spectum is
represented in fig. 3 by curve II, and the points, corresponding
with A, B, C and D are A', B', C and D'. The intensities
at A', B', etc. are, however, equal to those at A, B, etc.
respectively.

can immediately be obtained bij means of the density curves,
the energies of the electrons, falling on the plate at the
points A and B', B and C, C and D' respectively, being
equal. In this way the desired ratios are obtained in the
following form

The result therefore is, that with two photographic spectra,
one unshifted and the other one shifted, the real intensities
in a number of points of the spectrum, can be obtained.

It is, however, possible to obtain the intensities not only
in these points, but over the whole spectrum. For this pur-
pose it is necessary to derive the sensitivity curve of the
plate. This is possible with the aid of the same pair of
spectral exposures. The energies corresponding to the points

In order to deduce the value of the sensitivity for the
plate e.g. at the energy E (B), expressed in that of the
energy E (A) (being the ratio of the intensities with energy
E (A) and E (B) resp. giving the same density), it is sufficient
to determine the densities, caused by the same electronic
intensities, but having energies E(A) and E (B) resp. These
densities can directly be read from fig. 3, and are simply
D^ and D^, (the densities in the points A and A'). The
relative sensitivity at the energies E (C) and E (B) is deter-
mined in the same way; the reduction to the first energy
E (A) is accomplished by means of the density curve. In this
way the sensitivity for the energies belonging to the points
A, B, C and D can be derived. In this case, however, the
values at intermediate points can also be obtained owing to
the fact that the sensitivity curve of the photographic plate
is a smooth function, so that it is permitted to interpolate
between these points.

The way in which the real intensities in arbitrary points
of the spectrum can be determined with the aid of the den-
sity- and the sensitivity curves of the plate, is thus evident.

The experimental details and results, obtained with the
principle explained in this paragraph will be the subject of
the following chapters.

Before proceeding to the treatment of the experiments and
their results a comparative survey of the differences and
resemblances between the method, given in the foregoing
paragraphs and that used in optics will be given. The tech-
nique of quantitative spectroscopic measurement has been
developed especially for the purpose of optical research in
the Utrecht laboratory and so it was possible to profit by
the experience acquired.

In the two cases of electronic and optical spectroscopy
the circumstances are nearly the same: in the first case the
deduction of the real intensity from the density is wanted, when
the energy is given, and in the latter case the deduction of the
intensity from the density is wanted at given wavelength.

This analogy can be emphasized bij considering the light
as a stream of photons in the same way as the electronic
radiation consists of a stream of electrons.

In both cases it is necessary to measure the density-intensity
curves of the plates, and the determination of them takes
place essentially in the same way, namely, bij weakening the
intensity of radiation falling on the plate in a known way.

The second alternative, namely variation in the time of
exposure is incorrect except in those cases where the reci-
procity law holds.

Up to the present the circumstances are, however, entirely
different regarding the determination of the sensitivity of the
plate. In optics a calibrated „standard lampquot; is used. The
calibration refers to the relative or absolute intensities emitted
by the lamp as a function of the wavelength, and are car-
ried out with other, absolute measuring instruments (see e.g.
Ornstein, Moll and Burger

The application of a standard source to electronic spectros-
copy could not yet be taken into consideration,because no
reliable calibrated sources were available. But even if a standard
source would exist, several difficulties would still have to be
overcome. In principle, however, the use of a standard source
should be recommended for the future.

In the preceding paragraph a method has been explained
to obtain the sensitivity of the plate in electronic spectroscopy,
without the use of a standard source, and which is based on
the possibility of changing the energies without altering the
intensities. The application of the same method in optics would
require the possibility of changing the wavelength of the light
without changing the intensity, and is therefore not yet possible.

The photographic (i ray spectra were obtained by bending
the beam of electrons, coming from a radioactive source 5,
into half circles with the aid of a homogeneous magnetic
field and intercepting them by a photographic plate P (see fig. 4).

The spectrograph itself consisted of a metal, entirely air-
tight box. It was constructed of aluminium in order to avoid
as much as possible stray electrons and secondary radiations.
Only the plateholder Ph and the air-tight joints ƒ for this
plateholder and for the screen were made of brass.

The dimensions were chosen in such a way that the radii
of the half-circular trajectories of the electrons ranged from
2.5 cm to 5.5 cm, and that the distance of the magnetic pole-
pieces was 4.5 cm.

The radioactive sources consisted of a thin wire or strip,
fixed on an ebonite holder, which could be mounted by two
plugs in a fixed position. The length of the source was
0.8 cm and it was fixed at a distance of 1.6 cm from the
limiting slit which had a width of 0.4 cm. The other sfits E
served for the distribution of the electric tension, as will be
explained in the next paragraph.

The photographic plates were cut to a size of 2 X 7 cm®,
and rested on a brass plateholder Ph. The plate and the

Fig. 4. The magnetic ray spectrograph.
S = radioactive source ; Sh = sourceholder : SI — hmiting sht; E = electrodesystem for energy-change (see § 9); W = walls
of the spectrograph (made of aluminium); P = photographic plate; Ph ~ plateholder: Sc = screen (screening half of the
plate); / = 2 ground joints for plateholder and screen; M— contour of the magnetic pole-pieces; Vq, Vi, Vj, Vg = electric

plateholdcr could easily be removed and re-set with the aid
of an air-tight ground joint J.

In this joint another joint had been constructed permitting
to rotate the screen Sc and to expose alternately half of the
plate without disturbing the vacuum.

The magnetic field was furnished by a large Dubois-
magnet. The pole-pieces had a mutual distance of 4.5 cm
and a diameter of 16 cm. With a current of 1 Amp. a
magnetic fieldstrength of about 600 Gauss was obtained.

As the exposures generally extended over a period of
6 to 10 hours, it was necessary to maintain the magnetic
field fairly constant. This was accomplished by feeding the
magnet with a constant accu-battery B, and in addition by
applying current stabilizing, hydrogen filled iron-filament lamps
L (see fig. 5).

The constancy was supervised by compensating the magnet
current over the resistance W (=0.1 Ü) by the current
from a storage battery .Ac of 2 V and observing the zero-
deflection of the galvanometer G. In this way variations of
less than 1 quot;/qo in the magnet current could easily be observed.

In view of the required long exposures, it was necessary
to make sure that no light could penetrate to the photographic
plate. Special care was therefore taken to protect these plates
from hght.

In order to change the energy of the (i particles, two
possibilities were available, namely, the change could either
be performed in the beginning of the path (near the source),
or at the moment, when they fall on the plate. Both possi-
bihties possessed certain advantages, but technical reasons
confined the choice to the first one.

As already mentioned the change in energy is obtained
by applying an electric field. The choice of this change is
confined, on account of the experimental requirements, between
rather narrow limits: if the change is too small, the effects
which are a function of its magnitude, become too small to
be measured with sufficient accuracy (see § 20) and if it is
too large, other sources of error come to the fore, e. g. large
deformations of the trajectories (regarding this point see the
next paragraph). As a result a change in energy of 25 % of
the original energy appears to be suitable. The measurement
being extended over a range of energies from 20 to 300 keV,
the applied electric tensions had in some cases to be rather
high. The arrangement, used here, permitted an application
of a tension of maximum 32 kV.

The system of electrodes E which has been applied for
this purpose is represented in fig. 4. It consisted of four
flat circular equidistantial electrodes, consisting of aluminium
in order to avoid stray-effects. Each electrode was provided
with a rectangular slit, whose dimensions were chosen in
such a way that no electron is stopped which would be able
to pass through the last, limiting slit SI. The outer edges of
these electrodes are entirely embedded between glass (fixed

on the glass with pitcheine), as can be seen from fig. 4, in
order to be sure that no discharge could take place from
these edges. The electrical connections to the outside also
pass exclusively between glass-walls.

This construction resulted from a great number of trials
necessary to overcome several difficulties. On account of
geometrical considerations (see the next paragraph) it was
advantageous to have the distance over which the field was
applied, as small as possible. On the other hand a definite
limit for this distance existed determined by the fact that a
tension of the given magnitude had to be maintained. By
using the system of electrodes, described above, a well known
artifice has been applied: the electric tension has been divided
in three equal parts by the two intermediate electrodes in
order to reduce the probability of ionization in remaining
rests of the gas (the tension is only applied under high-vacuum
conditions: the pressure being less than 10—® mm mercury).

Yet, even in the case, that the tension seemed to be well
maintained, small discharges appeared to exist and were still
able to blacken the plate, due to the long durations of the
exposures. The construction described here had the same in-
convenience when the source and the electrodes had a positive
potential with respect to the rest of the spectrograph.
However, in all experiments a negative potential could be used.
This means that the electrons have always been retarded ¹).

The high-tension was obtained bij means of a transfomer
of 0.1 kW transforming 125 Volts up to 10.000 Volts. By
rectifying both phases of the secondary output, a continuous
tension of 28 kV is obtained.

The circuit diagram used in these experiments is represented
in fig. 6, and requires no further explanation. A galvanometer

1nbsp; The proper cause of this asymmetry has never been recognised. It
was proved by an exposure without the source, that this asymmetry was
not caused bij the radioactive source.

G again furnishes the possibility of controlling the value of
the tension during the exposures.

From the electrical constants given in the diagram it can
be calculated that the rectified tension is smoothed out to
less than Vs 7o-

The distribution of the tension over the different electrodes
was accomplished by means of a high resistance of 18X 10''
from which the required tensions could be taken.

In order to ensure a sufficiently constant tension stabilizing
lamps L have been applied in the primary circuit of the
transformer. The required constancy is not so high as in the
case of the magnetic field, because the applied electric tension
corresponds only to a fraction of the whole energy. A variation
of 1 % in the tension e.g. corresponds with a variation of
about 2 7oo in the electronic energies.

If the direction of the velocity v of an electron is per-
pendicular to the direction of a homogeneous magnetic field
of strength H, this electron describes a circular path situated
in a plane perpendicular to the magnetic field, and with a
radius given by the formula

where e and m are the charge and the mass of the electron
and c the velocity of light (e is expressed in electrostatic
units).

This formula holds as long as the velocity is small compared
with the velocity of light c. In general a relativistic correction
must be applied, and formula (1) in this case becomes:

where P is written for ~. The expression for the kinetic
energy of the electron is:

A few remarks must be made concerning the way in which
the electronic energy is expressed. The usual unit of energy
is the erg. In atomic and nuclear physics, another unit, namely
the electron-volt is applied:

express the energy in another way, namely by the product
Hq, q being the radius of the circular path described by an
electron in a homogeneous magnetic field of strength H. This
product is a function of the energy. This function can be
obtained by eliminating fi from (2) and (3), and is represented
in fig. 7.

Dotted curve gives the dependance of H Q without
applying the relativistic correction.

The same figure indicates at which energy the relativistic
correction begins to play a part.

If the directions of velocity and magnetic field are not
mutually perpendicular the electron describes a spiral, the
velocity showing a constant angle with the field, whilst the
enveloping cylinder has a radius, given by (2), multiplied by
the sinus of the mentioned angle.

Applying these elementary laws to the case discussed in
the foregoing paragraphs, it is possible to study the realiza-
tion of the photographic fi ray spectrum in more details.

Suppose that a beam of electrons of one given velocity
is emitted by the source 5 (fig. 8) and passes through the
limiting slit SI. The figure shows that the electrons describing
three arbitrary trajectories a, b and c, lying in a plane per-
pendicular to the magnetic field, meet the plate P at nearly
the same spot.

This property of focussing the electrons makes this method
so specially useful. This focussing, however, occurs only in
the direction of the dispersion, and not perpendicular to it.
If, namely, the same number of electrons discribes in one
case circles with radius Qi, in another case circles with radius
then the intensity falling on the plate per unit of area
is in these two cases inversely proportional to the two radii.

The real intensity distribution of such a homogeneous beam
on the plate, however, does not consist of a sharp line, because
the focussing is not exact and also, because the shape of the
source has some influence. Calculations of the real intensity-
distribution on the plate, caused by a homogeneous beam,

as a function of the slitwidth, the distance and the shape of
the source have been performed by Wooster and Li P).

If the source emits a beam of electrons, continuously distri-
buted over the energies, an analogous reasoning can be applied
to this case. Suppose that the distribution of the electrons
over the energies is uniform (in a Hq—scale), then the
intensity falling on the plate decreases proportionally to the
radius of the corresponding trajectories, owing to the divergence
of the beam perpendicular to the dispersion.

The width of the sht, and the position and the shape of
the source only influence the range of the energy falling
on a given spot of the photographic plate. The magnitude
of this range e.g. as a function of the width of the slit
can easily be calculated from geometrical considerations,
namely in this way, that the difference of the radii of two
circles is determined, both passing through the source and
the given spot of the plate, and passing near the boun-
daries of the slit. If the distance of the source to the slit
is a, the slitwidth 2b, the relative range of energy falling on
one point of the plate can be expressed as follows:

With the applied values a — 1,6 cm and b = 0.2 cm this
range is about 1.5 % of the proper energy expressed in Hp.

The indefiniteness of the energy under the influence of
the breadth of the source can approximately be expressed by:

where 2 dis the breadth of the source. For a source of 0.02 cm
breadth this gives a range of 74^0 and for a source of
0.15 cm breadth, which was also used, it would give 2%
variation of the energy at a of 4 cm.

H a r t r e e has calculated the influence of sUght deviations
of the homogeneity of the magnetic field on the spectrum.
This influence could be neglected in the experiments described
here.

A further investigation is necessary in the case that a
homogeneous electric field is combined with the magnetic
field. The electric field in question is only applied in a small
region of the trajectories of the electrons, namely between
the source S and the slit SI (see fig. 9). In a first approximation
the influence of the electric field on the shape of the trajectories
may be neglected. Then the problem can be treated as if
the electrons are coming from the source already with the
changed energy.

In fig. 9 two electronic beams I and II are represented. It
is supposed that they emerge from the source in the same
soUd angle AQ, one with the original energy E, the other one
changed to an energy E'. They constitute a part of a con-
tinuous spectrum. Suppose further as is shown in fig. 9 that
the first beam hits the plate P on a certain area s, the other
one on an area s'. The density of the plate at the spots s and
s' does not only depend on the intensities of the two beams
(which are supposed to be the same, see above) but also on
the areas which they cover.

The size of the two areas can easily be calculated. In part
A of this paragraph it is already shown, that the dimensions
Az and Az' are proportional to the radii, thus

where q and q' are the average radii belonging to I and II,
resp. The dimensions Ax and Ax' depend on the intervals
of energy of the two beams. Approximately the following
expression holds:

where Ag and Ag' are the maximum differences of the
radii in each beam, corresponding to their intervals in energy.
The latter, however, are equal, because every electron of
the first beam undergoes the same change in energy. From
the formulae (2) and (3) the relation follows:

The following table gives some values of this ratio, which
have occurred in the experiments:

The deformation of the circular trajectories by the electric
field has been neglected until now. This neglection should be
justified.

The main possible influence is a change of the solid angle
A Q ot the beams, which would cause a change of their
intensities.

It is possible to find an approximate expression for this
change by calculating the variation of the angle A ^ (see fig. 9)
existing at the source between the tangents of the limiting
trajectories situated in a plane perpendicular to the magnetic
field. In this calculation the equations of motion of an elec-
tron in a combined electric and magnetic field have been

used. The resuh, which is only deduced for low (not relati-
vistic) energies, can simply be written:

Therefore a variaton in energy of 20 quot;/q only causes a
variation in the solid angle of 5 Furthermore the variations
given by the formulae (10) and (11) act just in an opposite
direction, regarding their photographic effects.

Any deformation of the trajectories, caused by slight de-
viations of the homogeneity of the electric field (e.g. on
account of the slits in the electrodes), could be neglected.

The measurements described in this paper have been done
for the greater part with the (i ray emitting substances ThB,
ThC and ThCquot;. Before dealing with the properties of these
radioactive elements, a survey of the way in which they are
obtained from other active substances, and of the relations
existing between the different products, will be given.

Starting from the radioactive element Thorium as mother-
substance a great number of active elements arises in succession,
emitting a, fi or y rays (sometimes a combination of these
radiations). One of these decay products is called Radio-
Thorium (RaTh). A list of the decay products, arising from
RaTh, with their atomic number, the kind of radiation they
emit and their half-hve periods is given below:

The first (i emitting body of this series is ThB, showing
a half-period of 10.6 hours. This substance must therefore
be obtained from a longer living product. Some RaTh was
available for this purpose, possessing a radioactive strength
of about 0.2 mC (see § 13).

The way in which ThB was obtained from RaTh was
the so-called recoiV-method. In order to activate an object
with ThB, it is exposed in a space containing Tn-gas. This

gas escapes continuously from the RaTh, being one of its
decay products. The atoms of the decay product of Tn, ThA,
attach themselves on the object to be activated. As the half-
period of ThA is very short (0.1 sec.), these atoms decay
nearly immediately to the following product ThB.

The vessels, used for obtaining ThB in this way, are re-
presented in fig. 10 and 11. They are constructed of brass,
except the small grooves, which have to be insulated from
the remaining parts of the vessels, and serve for the intro-
duction of the wires, which had to be activated. The first
figure shows a vessel for the preparation of a single ThB-
source, whereas the vessel, represented in the second figure,
has been constructed, in order to obtain two sources at the
same time.

The ThB sources were obtained on thin platinum wires
fixed on ebonite holders. These wires could be inserted in
the small grooves of the described vessels. During exposure
to the Tn-gas emanating from the RaTh, they were as near
as possible to this substance in order to have a greater yield
of activity. During the exposures, the wires always had a
potential of —220 volt with respect to the vessel. Reference
may be made to the investigations of Gabler(®®), regarding
the influence of different circumstances, as volume, tension,
concentration etc., on the obtained activity.

The RaTh itself was available in a so-called high-emana-
ting form, indicated by Hahn(®®), and consisting mainly of
iron-hydroxide, with which the RaTh is mixed. According
to Hahn, it is possible to obtain with these high-emanating
preparations an emanating power of 80 %, but when these
are preserved under dry conditions, a certain ageing sets in,
causing after some years a diminution of this power to
about 35 o/o-

The activity of the exposed wire does not only depend
on the conditions of exposure mentioned above, but also on
the length of exposure. It can be assumed, that the number
of ThA-atoms (which arises directly from the decaying Tn-

atoms), adhering to the wire, will be proportional to the
time of exposure. The number of ThB-atoms originating
from the ThA, will, however, not increase unHmitedly, because
it decays at the same time according to the exponential law

where A is the decay-constant of the active substance, related
with the half-period T by the formula

The ß ray activity of the wire as a function of the time t of
exposure, is proportional to the number of ThB-atoms, being
on the wire. This number can now easily be determined as
a function of the time from the differential equation:

V being the number of ThA-atoms, attaching themselves on
the wire per unit of time. The solution of (3) is:

n^ being the number of ThB-atoms present on the wire
after an infinite time of exposure.

This relation (4) also gives the activity of the source as
a function of the time of exposure. It is represented graphi-
cally in fig. 12.

Among the decay products of ThB, two elements exist
which also emit particles. These are ThC and ThCquot;.
ThC is a branching substance, decaying into two separate
elements ThC and ThCquot;, respectively by and a ray emission.

other 35 % emit a particles. All /? emitting products, men-
tioned above, moreover emit a strong y radiation.

Relative radioactive intensities of ThB, C and Cquot; (in logarithmic scale) as
a function of the time t, assuming that at t = 0 only ThB is present
(with intensity ]o ).

Taking the /? ray spectrum of a ThB source, in reality a
combined spectrum of ThB, ThC and ThCquot; is obtained.
The ThB source can be considered to give a determined
ray spectrum, if the ratio of the radioactive intensities of
the diflFerent decay products does not vary with the time.

This appears to be the case in consequence of the short
half-periods of all these decay products. In fig. 13 these
relative intensities are given as a function of the time under
the extreme condition that at t = 0 ThB should be present
without any of the decay products. Even in this extreme case
this figure shows, that after about three hours already an
equilibrium between the different products exists. As the ThB
sources are obtained by exposing the wire to the Tn during
several times this period, this equiUbrium is already reached
during this exposure.

may be given of the continuous spectra of ThB and ThC Cquot;,
obtained by Gurney with the charge measuring method,
already mentioned. This reproduction shows that in the region
of 0—2000 Hq, the main part of the total radiation originates
from ThB (fig. 14).

The characteristic Hnes are superposed on the continuous
spectra. These lines also originate partly from ThB, partly
from ThC and partly from ThCquot;. In the table, given below,
the main characteristic lines with their nomenclature, their
/fp-values, their approximate, relative intensities and their
origin are inserted, according to Ellis (compare also
the improved values, given by Surugue :

In the reproduction of a photographic (i ray spectrum
obtained with ThB C Cquot; (fig. 27) five of these lines,
namely F, G, H, I. and ƒ can be observed.

For some measurements a Ra D E source has been
used, because no y rays are emitted by these bodies and
because their fi ray spectrum is stronger in certain energetic
regions, which were of importance for the intended experiments.

RaD and RaE are members of the Ra-family, which, in
its turn, comes from the Uranium-family. Uranium itself is
the ultimate mother-substance for this whole sequence. Here

below a list of decay products, starting from Ra, will be given,
with their atomic numbers, their half-life periods and the
kind of radiation emitted by them:

The usual way of obtaining RaD and its decay products
is by using tubes, filled with Rn-gas. The diagram given
above shows, that such a tube contains after some years only
RaD with its decay products RaE, Po and Pb. Erbacher
and P h i 11 i p p have worked out an electrolytical method
for obtaining RaD, RaE and Po in a pure state from these
tubes.

Although some Rn-tubes were available in the laboratory,
their radioactive strength was not sufficient for the intended
experiments. Owing, however, to the kindness of Prof.
E. S t a h e 1 at Brussels, who lent a preparation of the required
strength, it was possible to perform these experiments ¹).

The preparation, received from Prof. S t a h e 1, has been
obtained by him as a cathode-deposit (metallic RaD Pb)
by performing an electrolysis in a HCl- solution.

Here again a few words must be said about the properties
of the radiations emitted by RaD and its decay products. RaD

1nbsp; The writer wishes to express his gratitude to Prof. S t a h e 1 for
lending this preparation.

itself emits a fi radiation of very low energy namely a con-
tinuous one with an energetic upper limit of about 10 keV,
and furthermore five characteristic lines which are given in the
table at the end of this paragraph. The decay product, RaE,
possesses a /S ray spectrum of higher energies being only of
a continuous nature (no characteristic lines of RaE exist).
The upper limit of this continuous spectrum lies at about
1170 keV. Finally RaF must be mentioned, also called Polonium,
emitting only a rays. An important property of all these
products is, as already mentioned, the absence of y radiation.

In the following table the five characteristic lines of the
RaD [i ray spectrum are given with their Hp-values and
their approximate intensities:

This paragraph gives a short account of the calibrations
of the different radioactive sources, carried out in three ways :
by 7-, /S- and a ray measurements.

The measurement of the y radiation, and also in some
cases of the /S radiation, was performed by determining the
ionization current through a condenser, this current being
measured by the rate of decrease of the potential difference
at this condenser by means of a string electrometer (Edel-
man n-type).

In this way only relative measurements referring to a
standard source could be performed. And even using a standard
source certain precautions ought to be taken in consequence
of possible differences in ionizing power of the or /S rays,
even if the sources have the same radioactive strength.

This method has been applied to measure the strength of
the RaTh-source, present in the laboratory, and serving for
the furnishing of the ThB sources. As a standard source a
Radium source of known strength was available. The measure-
ments were performed in each case with V2 cm lead between
the source and the condenser, in order to screen off the very
soft components of the y radiation. The distances of the Ra
and the RaTh sources to the condenser were adjusted in such
a way that the rate of ionization was the same. From the
ratio of the distances, the strength of the RaTh-source could
be deduced and was found to be 0,2 mC (see § 11). It was
necessary to put the RaTh source under an air-tight glass
cover in order to avoid infection of the apparatus by the
escaping Tn-gas.

Also comparative measurements on the ThB sources
themselves were performed. In this case the ß rays as well
as the y rays, emitted from these sources, were measured with
this method at the same time. These measurements were
mainly performed in order to investigate the influence exerted
on the activity of these sources by applying different conditions
of exposure to the Tn-gas.

Absolute measurements have been performed on some of
the ThB sources, in order to obtain the number of emitted
ß particles (necessary for absolute data about the photographic
plate (see § 20)).

Two methods have been applied for these measurements.
Firstly the absolute intensity of the ß rays, and secondly
that of the a rays have been determined.

The ß ray measurements have been performed by means
of an experimental arrangement, described by Ornstein,
Milatz, ten Kate and Miesowicz consisting
essentially of an electromagnet without iron, in which could
be placed the radioactive source and a Geiger-Müller-

counter, enabling the measurement of the fi ray spectra in
the usual way. Because these same authors had investigated
the efficiency of the applied counter as a function of the energy
of the particles falling on this counter, it was possible to
deduce from the counted number of particles the real one.
In order to obtain the whole number of emitted particles it
was necessary to integrate over the whole f) ray spectrum.
For this integration the measurements of G u r n e y have
been used. At two or three energies the numbers of electrons
have been determined in the way mentioned, and combining
these values with the knowledge of the form of the spectrum
given by Gurney (see fig. H), the total number can be
obtained taking account of the soHd angle (determined by
some hmiting slits) and of the dispersion (determined by the
width of the slit in the counter). The ThB-sources being exposed
only during a finite time to the Tn-gas, the value found for
the total number of emitted particles ought to be corrected,
with the help of fig. 12, in order to obtain this value for an
infinite time of exposure. The final result was that the maximum
attainable strength for these ThB-sources, exposed in the
vessel indicated in fig. 11, amounted to

Secondly the absolute measurement of the a radiation was
performed by Mr. C. v. Heerden and Mr. K. J. K e 11 e r
with an experimental arrangement, consisting of an ionization-
chamber with amplifier. The number of particles was determined
by recording the deflections of a galvanometer. In this way
it was even possible to distinguish between the particles,
emitted by ThC, and those emitted by ThC', by their difference
in energy. The result was that the total number of a particles
of a ThB-source, again corrected to an infinite time of exposure
amounted to

2.5 X 10® a particles per second
being equivalent to about 0.07 mC of ThB alone (the number

of a particles emitted by a ThB-source had to be one half
of the number of ^ particles, as can be seen from the represen-
tation of the genetic dependence of the decay products, given
in the beginning of § 11).

Taking into consideration the strength of the RaTh-source
which was found to be 0,2 mC, the preceding results give
an emanating power of about 50 % being in good agreement
with the expected emanating power of this source (see § 11).

When working with ThB sources, it was necessary to
replace the source before every new exposure by one freshly
exposed to the RaTh. The adjustment in the apparatus was
obtained by two pins, which fitted in the sourceholder. The
source had to be connected electrically to the outside to
make possible the application of electric tensions. Working
with RaD the source could be adjusted once for all.

As photographic plates Ilford „Special Rapid, extra sen-
sitive, 400 H amp; Dquot; were appfied, which, compared with
other plates, showed to be most suited for the intended ex-
periments.

The applied plates had to be cut into the required shape.
Special care was taken to avoid any possibility of fogging,
e.g. by pressure or by light, during the cutting. In the room
only a feeble red lamp was present when the plates were
introduced into the spectrograph. The apparatus was then
shielded off from fight by black cloths. It was exhausted by
a mercury diffusion pump to a pressure of less than 10-® mm.
When the vacuum was sufficient, the magnetic field was
switched on and the exposure could begin.

In order to obtain the density curve of a plate, the in-
tensity of the radiation falling on the plate must be varied
in a known way. In the case of the ThB sources the decay

of these sources could be used for this purpose. Exposing
the plate during a certain time to the source, and doing the
same after 10.6 hours with another part of the plate the
ratio of the intensities on these two exposures would just
have been one half. Taking several exposures with constant
periods of exposure, the intensity is always a known fraction
of that of the first exposure.

In the case of the RaD source, the variation in density
has been obtained by varying the length of exposure. In
this case the validity of the reciprocity-law must be assumed.
If now in both cases the density curves are identical, the
validity of this reciprocity law is proved.

In the described way a series of photographic /3 ray spectra
is obtained with different known intensities, from which the
density curves at every desired energy of the spectrum can
be obtained.

As the density curves are obtained from a scries of different
photographs it was necessary to use neighbouring pieces of
the same photographic plate and further all the plates ought
to be developed under identical circumstances.

As is explained in the preceding chapters, the sensitivity
curve of the plate is obtained by taking two photographic
spectra with the same intensity: one in the usual way, the
other by applying a retarding electric potential. These requi-
rements have been fulfilled by alternately switching the tension
on and off, so that the total intensities at the two exposures
are equal.

This procedure is simple in the case of RaD: the lengths
of the exposures with and without the tension have only to
be taken the same. For the ThB-sources, however, the decay
of the source has to be taken into account. With the aid of
a calculated correction curve (fig. 15), one can determine for
each time tj of exposure without tension, the corresponding
time tg of subsequent exposure with tension, giving the
same intensity.

Taking a photographic spectrum with and without changed
energies merely the primary circuit of the transformer must
be switched on and off and, at the same time, the screen
Sc (fig. 4) must be turned, in order to expose the other half
of the plate.

During each exposure the magnetic and electric field were
regularly controlled by observing the deflection of the gal-
vanometer.

taking place during about SVg minutes at room temperature.
Plates which had to be mutually referred to. were fixed
together on one glass plate and then treated as a single
photographic plate.

The densities of the plates have been determined bij Moll's
microphotometer and were compared to an unexposed part
of the plate (which had not even been in the spectrograph).
A special device was constructed enabling to adjust at the same
time the unexposed and the exposed plate in the photometer.

The photograms, obtained with the photometer,
measured out and drawn in a diagram, as indicated in fig. 16.
The corresponding values of the energies are deduced by
comparing the energies of the characteristic lines with those,
given by E 11 i s (1®^) (see §11, resp. § 12). The retarded spectrum
which comes on the plate in a shifted position, is represented
in these diagrams with the original energies as abscissae.
The two spectra are in this way directly comparable. The
further elaboration has already been dealt with in the second
chapter.

In this paragraph a brief enumeration of the causes of
errors of the method under consideration will be given and
the possibilities of eliminating them. As has already been
remarked in the introduction the possible causes of deforma-
tion in the spectra themselves have not been investigated.
A discussion of the accuracy of the results will be found
in § 20.

The accuracy, attainable with the photographic method in
general, is mainly determined by three factors : the individual
fluctuations of the properties of the plates (e.g. caused by
irregular manufacturing), the unevitable variations in the
treatment of the plates e.g. by developing and fixing; and
thirdly the errors of the measurement of the density.

The first two factors have already been dealt with in the
preceding paragraph, the third factor is determined by the
properties of the applied photometer and by the graininess
of the plates (see § 20).

These errors are partly caused by fluctuations in the elec-
tric tensions, partly by geometric conditions. Their main in-
fluence has already been discussed in the third chapter. Only
one possible source of errors might still be emphasized,
namely that of partly shielding-ofF the fi rays by the inter-
mediate slits. This shielding would cause an alteration of the
distribution of the intensity over the spectrum. The electrical
conditions did not allow to choose these slits very wide. In
order to be as free as possible from this error the slits have
been adjusted with special care.

The influence of errors of this type only plays a part,
when the real form of the /S ray spectra is required. It has.

however, no effect on the applicabihty of the method given
here, at least, as long as the intensity of the stray radiation
is small in comparison with that of the radiation to be
measured.

The density curves being automatically taken under the
same circumstances, in which the spectra themselves are
photographed, the true relative numbers of electrons are directly
obtained from the densities.

The determination of the sensitivity curve is also independent
of stray-, or secondary- or y radiation, because it may be
assumed that by taking a spectrum with- and without electric
tension the intensity of these spurious radiations will not be
altered. It is therefore allowed to compare the densities of
the plate in these cases.

These arguments are only true when the intensity of the
investigated electronic radiation is large in comparison with
these effects. For this reason when using ThB sources, the
method could only be applied with the described apparatus
in the energy region between 60 and 200 keV. It was,
however, desirable to extend the measurements by means of
a RaD source giving a much weaker y radiation.

These errors too effect only the spectrum itself. The in-
vestigations of Flammersfeld on the ß ray spectrum of
RaE have shown the great importance of the properties of
the bearer of the source on the value of this type of errors.

In fig. 17 the curves obtained with ThB, C and Cquot; are
reproduced. They are obtained, as has already been remarked,
with one constant period of exposure of about 10 hours.
This figure shows that the shape of the curves is the same
for different energies of the electrons between 90 and 240 keV.

The density curve in fig. 17 has been drawn on a logarithmic
intensity scale. In a numerical scale (see fig 18) the part of

Finally density curves have been obtained with the RaD
source, for energies from 20 to 170 keV (varying the time
of exposure). In fig. 19 the solid line has been copied from
fig. 17, and the open circles indicate the points, belonging
to the density curves of RaD E, which appear again to
be independent of the energies. This figure shows moreover

From the latter fact something can be deduced about the
validity of the reciprocity-law (see § 3). A deviation of the
reciprocity-law is often characterized by a constant p, the
so-called Schwarzschi Id-exponent, assuming that the
density is not a unique function of i • t, but of i • t''.

From fig. 19 a limit for the value of p can be deduced
by calculating the deviation between the density curves of
ThB and RaD for some values of p (in fig. 19 some points
of the curves for p = 1.1 and p = 1.2 are indicated by
black circles). From the position of the measured points (open
circles) it is seen that the value of p lies certainly between
1.0 and 1.1 ¹).

In conclusion a short numerical extract of the density curves,
obtained in the reported experiments is given in the following
table:

1nbsp; Recent experiments performed by Mr. T. T o 1 with a cathode ray
tube, show, when they are compared with those mentioned above, that the
value of p is equal to one with a possible error much less than 10 O/q.

§ 17. Results conccrning the Sensitivity of the Plate at
different Energies gt; the /S Ray Spectrum.

As the method of obtaining the sensitivity curve of the
plate has been explained in the foregoing paragraphs, it may
suffice to give here the experimental results.

In fig. 20 this sensitivity curve is represented. The value
belonging to a certain ordinate at a certain energy E in this
figure indicates the ratio of the intensities J^ (at 100 keV)
and Jz (at the energy E) causing both the same density on
the plate.

The first experiments have been done with ThB-sources,
but as fig. 20 shows, only a relatively small energy interval
could be used (from 60 to 200 keV) because the intensity of
the ThB spectrum decreases rapidly at both sides of this
interval, and, moreover, because the effect of the y radiation
on the plate becomes comparable with that of the electrons
themselves (compare§ 15).Thepoints indicating the measurements
with the ThB source are average values from several experiments,
whose accuracy will be discussed in § 20.

It was possible to extend the sensitivity curve over a larger
interval of energy by means of the RaD source. The results
of these experiments are also represented in fig. 20.

As the apphed tension was limited to 30 kV, the accuracy
of the sensitivity curve diminishes at higher energies (see
§ 10 and § 20). The part of the sensitivity curve, belonging
to this energy region, has therefore been represented by a
broken line.

In the following table, some values of the sensitivity of
the photographic plate are given, taken from fig. 20:

Using the properties of the plate, given in this chapter, the
relative intensity distribution of the spectrum of ThB C Cquot;
has been obtained and is represented in Fig. 21.

the intensity in a certain constant f/gi-interval). This scale is
obtained from the relative intensities on the plate by multi-
plying each intensity by the radius of the corresponding
trajectory (see § 10).

The spectrum of RaD E is not represented because the
source used for the experiments consisted of a rather broad
strip (0.15 cm), and therefore a distortion of the obtained
spectrum was to be feared. On the other hand there is no
objection to use this source for the investigation of the reci-
procity law and of the sensitivity curve.

properties of the plate can be obtained independently of the
measuring of the spectra, so that, e.g. it is possible to use
different spectrographs or different sources for the calibration
of the plate and for the measurement of the spectra, provided
that pieces of the same plate are used.

The main resuhs obtained in § 16 are: the independence
of the shape of the density curves of the energy of the
electrons, the linear relation between density and intensity
for low intensities, and the validity of the reciprocity law
within the experimental accuracy (see figs. 17, 18 and 19).
Analogous results have been obtained by other investigators
(compare § 5). Moreover it appeared that generally the shape
of the density curves obtained in this thesis and that of other
authors are exactly the same, as is shown in fig 22.

In this figure some points of the density curves published
by Ellis and Wooster(i*') fo^ electrons having energies
from 150 to 1000 keV are given, obtained with photographic
X ray Ilford plates. According to these authors the curves
obtained under different conditions of development and at
different energies of the electrons can be represented by the
well known formula, already given by Silberstein(^^) and
Busé(^°):

J being the total intensity, and C and t parameters. The
equality of the shape of the density curves under the men-
tioned conditions implies the constancy of C in this formula.

Reasons exist (compare § 3) to suppose, that not only elec-
trons of different energies, but also other kinds of radiation

will act in the same way. To check this assumption, the
density curve obtained by Bouwersf) for Röntgen rays of

about 1 A with Ilford Special Rapid plates has been compared
with that, obtained in § 16. The data of Bouwers are also
represented in fig 22. Even in the case of Röntgen rays a
perfect similarity between the different density curves exists.

In fig. 22, also some points of a curve obtained by Sal-
bach (1922) for electrons of heterogeneous energies of radio-
active origin are indicated, showing a deviation from the
other curves. The cause of this deviation might be the use
of other types of photographic plates or the different way
of measuring the density [Gallier (quot;)].

In § 5 it has been remarked that the results of the expe-
riments of Bories and Knoll (®) do not agree with those
of others. They find e.g. a strong dependence of the shape
of the density curves on the energy. It has therefore no sense
to compare numerically their curves with those obtained in
this thesis. One may, however, point to the fact that the
density curves obtained by Mr. T. Tol with a cathode ray
tube in this laboratory (serving for electronic diffraction ex-
periments), agree very well with those in fig. 22 (for the
same type of plates), although the periods of exposure are
much shorter, being of the order of Vz sec- (In the experi-
ments of Bories and Knoll, these periods ranged from 10-®
to 10-8 sec.).

To begin with a qualitative interpretation of the shape of
the sensitivity curve, represented in fig. 20, will be given.
This curve consists of an ascending and a descending part.

The ascending part, corresponding with electronic energies
below 100 keV, can be explained by the fact, that their range
is less than the thickness of the photographic emulsion. So
long as the range of the electrons is of the given order the

effect on the plate will increase with increasing energy, the
energy, absorbed by the plate, being equal to the whole
energy of the electrons themselves.

The descending part of the sensitivity curve, corresponding
to the energies of those electrons, which are able to pass
through the photographic emulsion, can be explained by the
fact that the loss of energy of the electrons in the plate

decreases with increasing energy. An approximate expression
for this decrease (already used by Ellis and Wooster(quot;)),
is obtained assuming that the ionization of an electron on a
certain length of its path is inversely proportional to the
square of its velocity. In fig. 23 the sensitivity curve calcu-
lated on this basis is given together with the experimental
one. The calculated curve has only sense, when the electrons
pass through the emulsion, therefore only for the energies
corresponding to the descending part of the experimental curve.

In this connection the measurements of Lenard(®i)
of importance, concerning the determination of the „practical
absorptionquot; of the electrons in thin sheets of material, which
is defined by the apparent decrease of the number of electrons
in passing through matter. In fig. 24 the mass-absorption

Practical mass-absorption coefficient fijg of the electrons as
a function of their energy, measured by Lenard

From this curve, the number of electrons absorbed in the
photographic emulsion can be calculated if the thickness and

the specific weight of the emulsion are known. In this way
the average energy absorbed by the photographic plate per
electron of given primary energy, is obtained. The electronic
energy being E, the absorption coefficient at this energy
being /^(E), and the thickness of the emulsion lt;i, the average
energy F absorbed in the plate per electron amounts to:
(1)nbsp;F(E) = E[\-e-dfMB)^

Using fig. 24, the quantity F can be calculated as a function
of the energy. Assuming that the photographic sensitivity
will be proportional to the absorbed energy, the function F
gives at the same time the sensitivity function. It is repre-
sented in fig. 23 by the dotted curve. The following numerical
data concerning the photographic plate have been used for
this calculation:

The curves show that only a qualitative agreement exists.
This agreement becomes, however, much better if an important
factor is taken into account whose influence was already
surmised by Ellis and Wooster: a considerable part of
the electrons after passing through the emulsion will be
reflected by the glass plate, and thus exert a photographic
action for the second time.

This influence could be estimated using some experiments
of Schonland(^''), concerning the ratio of the electrons,
scattered backwards, and of Wagner concerning the energy
of the scattered electrons. It appeared to be permitted in
first approximation to assume that the number of electrons,
scattered back from the glass plate, amounted to 16% of
the electrons, faUing on the glass, and that their average
energy amounted to 80% of the primary energy (in both
cases these percentages appear to be approximately indepen-
dent of the energies of the electrons). In order to take into
account that the scattered electrons re-penetrate the emulsion
in all possible directions, it was assumed, that they had to

penetrate in this case an emulsion of the double thickness (cor-
responding to a cosine distribution of the scattered electrons).
Moreover, the primary loss in energy of the electrons, pene-
trating the emulsion (which was not taken into account in
the expression (1)) has been assumed to be 5X10® eV/cm
(Lenard(8i)) ¹)

A possible photographic action of secondary Röntgen rays
could completely be neglected.

The result of all these considerations is given by the broken
curve in fig. 23, which is in striking agreement with the
experimental results, at least for the lower energies.

The principal sources of error have been treated in § 15.
In the present paragraph the value of some of the errors,
and of their effect on the accuracy of the method will be given.

The accuracy is mainly determined by that of the photo-
graphic procedure, and regarding the sensitivity curve, also
by some geometrical and constructional factors.

The accuracy of the measurement of the density depends
on the microphotometer and on the „graininessquot; of the plate.
A distinction must be made between the determination of the
„absolutequot; density and of relative differences in the densities.
In the first case, the adjustment of the microphotometer is
the essential cause of error (the image of the illuminated spot
of the plate has to be adjusted on the thermo-element). By
repeating an adjustment several times, it appeared that a
maximum variation of 2 % i« experimental value of the
absolute density can occur. As each point of the density
curves corresponds to separate pieces of a plate and thus to
separate adjustments, an error of the given magnitude can
therefore be expected.

If, however, only differences in densities on the same plate
have to be determined, as is the case in obtaining the sen-

Besides the error, caused by the adjustment of the photo-
meter, the accuracy is determined by the graininess of the
plate. A photogram of a part of a plate obtained with the
microphotometer does not consist of a smooth line, but of a
zigzag line, as is illustrated by fig. 25. This zigzag line is caused
by the fact that the number of developed grains, present at the
spot where the density is measured, shows statistical fluctuations.

Investigations about the graininess of the photographic
plate have been performed by v. Kreveld(^®-®°). This author
defines a quantity AD, the fluctuation of the density, as
follows: if the total area of the fluctuations of the zigzag line,
divided by the length of that fine, is ^(average deviation),
and the density D being

This quantity A D depends on the area O of the image
of the first slit formed by the microphotometer on the plate.
It could be shown by the mentioned author that the quantity

is independent of O. It is called the „absolute graininessquot;.
This quantity has the dimension of a length, and its value
is under the circumstances considered here:

In order to calculate the accuracy in the real intensities,
it is necessary to take into account the density curves. This
is accomplished by the mentioned author by defining a quantity
Ycj (differential gradation):

being the differential quotient of the density to the logarithmic
intensity (e.g. the slope of the curve in an arbitrary point of
fig. 17). Now the expression

gives the relative accuracy corresponding to a given uncer-
tainty in the density. In the same way, the quantity

appears to be useful. This quantity is not only approximately
constant for different areas O of the image in the microphoto-
meter, but also for all densities ranging from 0.2—1.0 {AK
and depend approximately in the same way on the density
in this region). It depends, however, on the type of the plate,
on the conditions of development and on the kind and energy

This formula shows that the accuracy can be augmented
by using a larger image of the slit of the microphotometer
on the plate. The efficient size of this image was limited by
the photometer and by the condition that the plate-density
inside this image ought to be homogeneous.

The absolute number of electrons, necessary to effect a
given density, has been determined with the aid of the ap-
paratus designed by Ornstein, Milatz, ten Kate and
Miesowicz P^), already mentioned in §13. This determina-
tion was possible by the known efficiency of the counter
used, this efficiency having been investigated by the mentioned
authors. The number N of electrons falling on an area of
1 cm^ of the plate, and causing a density of 0.5, was found
to be:¹)

The statistical fluctuation A N in the number N of electrons
is given by the formula:

1nbsp; This result appeared to be in accordance with a determination of this
number by Mr. T. Tol in this laboratory, using a cathode-ray tube.

If an area O of the plate is used for the determination
of the density, the number of electrons, falling on this area is

Comparing (9) and (14), it appears that the fluctuations
in the photograms are not caused exclusively by the photo-
meter or by the photographic errors in general but that they
are for a considerable part of an essential character, connected
with the radiation to be measured. These fluctuations cannot
therefore be eliminated by improving the photometer or the
photographic plate. It would e.g. be possible to use plates
with smaller grains. These plates being necessarily less sen-
sitive, no advantage is reached. This highest accuracy is only
obtained for electrons of the most favourable energies, that
are energies between 70 and 150 keV for t'le Ilford plates
of the type Special Rapid, Extra Sensitive (400 H amp; D).

Continuing the discussion regarding the accuracy of the
sensitivity curve, a remark of a more geometrical kind must
be made. The sensitivity curve for a given range of energies
is generally obtained by a number of steps in energy, as
described in the second chapter. The magnitude of the steps
giving subsequent points of the sensitivity curve, is limited
because the geometrical corrections become of importance
for larger steps (see § 10) and these cannot yet be calculated
exactly. Now the error made with one step influences all
points of the sensitivity curve corresponding to the following
steps, so that the error will augment proportionally to the

number of steps. For a future development of this method
it will therefore be necessary either to find out a method of
obtaining these corrections more exactly, so that the number
of steps can be diminished, or to diminish the error for each
separate step.

The error made for each step is exclusively determined
by the graininess of the plate. This error depends on the
average area O on the plate, suitable for the measurement
of the density at an arbitrary point. The area used in the
experiments, reported here, amounted to 75X10-® cm^. From
formula (9), the relative accuracy in the intensity corresponding
to this area, appears to be

The accuracy of every point in the sensitivity curve can
be calculated, using (15). This accuracy is not yet very high
because the relative intensity differences between two succes-
sive points are generally rather small (see fig. 20), so that
the error in these differences will be larger. Furthermore
the part belonging to the higher energies (indicated by a
broken line in fig. 20) is still less reliable owing to the great
number of steps in this region.

The given accuracy can be augmented by using a larger
area O, necessitating an improvement of the photometer and
of the photographic P ray spectra.

Surveying the results obtained in the preceding chapters
it can be concluded that the photographic method proposed
is practically applicable and moreover appears to be rather
simple. This simplicity is partly due to the fact that the
density curves coincide for all energies investigated.

There exist, however, still some difficulties, partly of a
technical kind (e.g. the application of high tensions) and partly
of a geometrical character (the exact calculation of the de^
formations of the trajectories, etc.). Further investigations
will surely show that it is possible to overcome these difficulties.

For strong preparations the photographic method appears
to be of the same sensitivity as that of a counter. The method
has then, however, the advantage that large parts of a spectrum
can be investigated simultaneously.

For weak preparations, however, the sensitivity of the
photographic plate is rather low which is then a serious
disadvantage of the photographic method. An effect being
easily detectable by a counter (e.g. one electron per second
per cm®) would require a photographic exposure of about
1000 hours.

It may still be pointed out that the application of electric
fields, as used in this thesis, offers some more general prospects.
For instance the investigation of the part of lowest energy
in the P ray spectrum could be performed with more profit
by applying an accelerating tension on the (i particles.

Not only a calibration of the photographic plate, but in
principle the sensitivity of any detecting instrument can be
obtained with the method described in this thesis.

May the given method contribute to the furtherance of
some problems in atomic and nuclear physics.

First a review of existing experimental methods for the
investigation of the /S ray spectrum is given. A photographic
method for the measurement of /S ray spectra is then described.
In this method the density curves are obtained by variation
of the strength of the source and the sensitivity curve by
changing the energy of the § particles. A description of the
experimental arrangeaient and of the properties of the radio-
active sources used is given. The density and sensitivity
curves for the type of plate used are discussed. The density
curves appear to be independent of the energies, and the
Schwarzschild-exponent appears to be equal to one, within
the experimental accuracy. A further discussion showed, that
the density curves show a perfect similarity with those
obtained by other investigators not only for electrons, but
also for Röntgen rays. The shape of the sensitivity curve
can be explained with the aid of the absorption measurements
of Lenard, and the reflection measurements of Schonland
and Wagner. A /S ray spectrum of ThB C Cquot;, ob-
tained with the method described, is reproduced. Finally a
discussion of the accuracy of the method is given.

Reproduction of a photographic /? ray spectrum, obtained with ThB C Cquot;.
The upper spectrum is retarded by a tension of 28 kV, the lower spectrum

Ellis, G. D and G. A. Aston .
Ellis, G. D. and Skinner . . .
Ellis, G. D. and W. A. Wooster
Erbacher, O. and K. Philipp .

10.
11.
12.

13.

14.

15.

16.

17.

18.

19.

20.
21.
22.

23.

24.

25.

26.

27.

28.

29.

30.

31.

Proc. Kon. Ac. Amst. 41, 1051, '38.
Pogg. Ann. 100,81, '57; 117,529, '62.
Physica 3, 64, '22.
Zs. f. Wiss. Phot. 7, '09.
Proc. Cambr. Phil. Soc. 21,274, '22.
CR. 153, 339, 1066, '11.
Proc. Cambr. Phil. Soc. 21, 121,'22.
P.R.S. 138, 318, '32.
P. R. S. 119, 645, '28.
P. R. S. 105, 60, '24.
P. R. S. 114, 266, '27.
Zs. f. Phys. 51, 309, '28.
Zs. f. Phys. 88, 161, '34.
Zs. f. Phys. 112, 727, '39.
Ber. Wien. 129, 201, '20.
Phys. Zs. 14, 1129, '13.
P. R. S. 109, 540, '25; 112, 380, '26.
P.R.S. 164, 151, '38.
Ann. d. Chem. 440, 121, '24.
Proc. Cambr. Phil. Soc. 21, '23.
Phys. Rev. 48, 7, '35.
]. O. S. A. 26, 170, '36.
J. O. S. A. 27, 100, '37.
„Quantitatives über Kathoden-
strahlenquot;.
Proc. Cambr. Phil.Soc.33,164, '39.

Nature, 144, 115, '39.
Zs. f. Phys. 46, 28.
P.R. S. 81, 141, '08.
Phil. Mag. 26, 717, '13.
P.R. S. 108, 187, 25.
Phys. Zs. 30, '29.
Phil. Mag. 45, 1062, '23.
Thèse, Paris, '36.
P. R. S. 150, 390, 'SS.
Physica, 6, 593, '39.
Phys. Rev. 35, 98, '30.
J. O. S. A. 26, 367, '36.
P.R. S. 85, '11.
P. R. S. 114, 729, '27.

§ 3. The blackening Action of various Radiations 23
§ 4. The Use of the photographic Plate for

§ 5. Review of the Use of the photographic
Plate for quantitative Measurements of

electronic Energies in a Ray Spectrum . 29
§ 7 Comparison with the photographic Method

§ 8. The magnetic Ray Spectrograph .... 34
§ 9. The Arrangement for changing the Energy

Bij photografische intensiteitsmetingen aan electronen is
het zinvol, van het bestaan van een „nul-effectquot; bij de photo-
grafische methode te spreken.

Het is gewenscht, dat in wetenschappelijke pubficaties op
het gebied der Natuurwetenschappen, de experimenteele resul-
taten niet alleen in de vorm van grafieken, maar daarnaast
eveneens steeds in de vorm van tabellen weergegeven worden.

Het zou ten zeerste toe te juichen zijn, wanneer de moge-
lijkheid van tijdelijke uitwisseling tusschen Nederlandsche en
buitenlandsche studenten of assistenten van overheidswege
aangemoedigd werd.

Zij fn (x) een oneindige rij van reëele, continue functies
van X met periode 1, die in elk punt gelijkmatig begrensd
is, en zij voorts nog gegeven:

(de streep boven het functie-teeken beteekent de limiet voor
n -gt;■ lt;» van het gemiddelde over de eerste n functies in een
punt x).

Zij verder het „f-gemiddeldequot; van de functie f„ (x) ge-
definieerd door:

dan gelden de volgende benaderde betrekkingen voor het
quadratisch gemiddelde van deze grootheid:

indien ^ 1 en indien \ A (v) \ een langzaam veranderlijke
grootheid is in het gebied O lt; v lt; y.

Nog steeds laat de experimenteele verwezenlijking van de
„Uraanexplosiequot; op zich wachten.

De ingewikkelde meetmethode, die door Joliot en Zlo-
tOwski aangegeven wordt, om de kromming in verschillende
punten van de baan van een elementair deeltje in de Wilson-
kamer te bepalen, kan door een zeer veel eenvoudigere en
ten minste even nauwkeurige methode vervangen worden.

Bij de vergelijking van de vorm van experimenteel ver-
kregen /ö-spectra met de theorie, dient men er rekening mede
te houden, dat de correspondeerende energie overgangen
eventueel verboden kunnen zijn, hetgeen tot nu toe veelal
nagelaten werd.

Door Bethe, Hoyle en Peierlsisde veronderstelling
geopperd, dat de experimenteel verkregen ^-spectra samen-
gesteld zouden zijn uit meerdere enkelvoudige spectra van
verschillende intensiteiten en met verschillende bovenste
grenzen, die elk aan de theorie van F er mi zouden voldoen.
Zij meenen echter, dat deze onderstelling in strijd is met het
feit, dat de spectra beschreven kunnen worden door de theorie
van Konopinsky-Uhlenbeck. Het tegendeel is echter
waar: de goede overeenstemming tusschen de theorie van
K-U en het experiment is een sterke steun voor de onder-
stelling van Bethe, Hoyle en P ei er Is.

* • '
	■




V lt; f	•'.-tsi^ ■ W.Î

Main char. lines	H Q (gauss, cm)	Int.	Origin
A	541.0	3	ThC-^C
B	660.8	2	ThC-^Cquot;
E	1106.8	3	ThB-gt;C
F	1385.8	200	ThB^C
G	1593.8	3.6	ThC''-gt;'D
H	1691.0	6.6	ThB-gt;C
I	1751.0	25.0	ThB-^-C
I	1807.7	6.2	ThB-»C
L	2603.1	1.4	ThCquot;-gt;D
M	2886.6	1.5	ThC'-gt;-D

Hp:	600	606	628	714	738
Int.	50	2	0.5	20	10

Rel. Int.	Density
1	0.10
2	0.17
5	0.32
10	0.50
20	0.72
50	1.13

Energy in keV	Relative phot, action
25	0.30
37	0.56
50	0.84
75	0.99
100	1.00
125	0.98
150	0.91
200	0.71
250	(0.57)
■ 300	(0.47)

-	\ \
	■■.....■■■-. \
/	■••. \ --
in ■1
'•1 - ;//
'•1 - ;//
}/ V 1	1 1 1	1 1	^keV.

1800	- 1
mo	- 1
mo	- 1
mo innn	- \
lUUU 800	- \
600,	-t \
m	\

200	^_____ 1 1 1	—^keV. ■----1-1-