DELAY TIME IN THE MAGNETO-OPTICAL FARADAY EFFECT

V. P. Rusakov, Smolensk

I. Introduction

Recently, in foreign periodical literature, especially American, much space and attention have been devoted to the question of the existence of a delay time in the Faraday effect. The phenomenon itself, as is known, consists in the fact that the plane of polarization of light passing through isotropic bodies undergoes rotation in a strong magnetic field. If the magnetic field is produced by a solenoid, inside which the body under investigation is placed, then the angle of rotation is

\[ \alpha = VHl, \tag{1} \]

or

\[ \alpha = 0.4 \pi niV, \tag{1'} \]

where \(H\) is the magnetic-field strength, \(l\) is the length of the light path, \(n\) is the number of turns of wire per \(1\ \text{cm}\) of the coil, \(i\) is the current strength in amperes, and \(V\) is Verdet’s constant.

F. Ellison[^1], attempting to explain certain results observed by him with various liquids placed in a magnetic field, came to the conclusion that between the application of the magnetic field and the resulting rotation of the plane of polarization there exists, though small, a measurable time. This idea had been expressed long ago, but the results of its verification were negative[^2]. Ellison proposed an original apparatus[^3], which gave him grounds to assert that the delay time really exists, that it is characteristic for each chemical compound, and that this effect gives the investigator an extraordinarily precise and delicate method of analysis, suitable for detecting chemical compounds when their concentration is less than \(10^{-11}\) relative to the solvent. A brief description of his apparatus is given in my previous article[^4]. The works of Ellison and his students[^5] attracted wide attention in scientific circles, since, if the theory and the results of these works were confirmed, the investigator would obtain a method of analysis unequaled in accuracy and simple in execution.

method of analysis of substances. In a number of laboratories experiments were set up to verify Ellison’s conclusions.

The aim pursued in the present article was to give a brief survey of the principal works on this question.

II. Investigations of J. Webb and D. Morey

The most complete analysis of Ellison’s apparatus was given by J. Webb and D. Morey⁶. The apparatus which they used was similar to the preceding one and is shown schematically in Fig. 1.

Fig. 1.

The variable capacitor \(C\), which was usually calibrated to a value close to \(0.0005\ \mathrm{mF}\), was charged from a high-potential source; this source was a 25 kV transformer with a kenotron rectifier. Magnesium electrodes were used to form the spark gap, the distance between them being maintained constant and equal to 4 mm. The number of interruptions per second was 60 and could be varied by means of a rheostat included in the primary circuit of the transformer; a larger number of interruptions made the spark unstable. The coils for producing the magnetic field \(L_1\) and \(L_2\) each consisted of 54 turns of telegraph wire \(1.02\) mm in diameter, wound on glass cylinders \(2.5\) cm in diameter. The high-frequency resistance of each coil was \(0.5\ \Omega\), and the self-inductance was \(30\ \mu\mathrm{H}\). The glass cylinders were filled with the liquids under investigation and closed with transparent glass plates, which were fastened with cement in the case of an organic liquid, or with bakelite when an aqueous solution was used. The coils were connected to the spark gap and capacitor \(C\) by means of a series of wires, along

by which the movable contacts \(T_1\) and \(T_2\) were moved. The position of \(T_1\) was changed only at equal intervals, whereas contact \(T_2\) could be placed anywhere. The purpose of the wire system and of the movable contacts was reduced to a relative change in the time of arrival of the wave at coils \(L_1\) and \(L_2\). \(J_1\) and \(J_2\) are radio-frequency ammeters. The light from the spark discharge at \(S\) passed through a color filter \(F\), which transmitted a narrow band of the centered Mg line \(\lambda = 4481\) Å, then through a Nicol \(N_1\), through cylinders containing the liquids under investigation \(L_1\) and \(L_2\), and, finally, through a Nicol \(N_2\), crossed with respect to \(N_1\), and entered the eye.

1. Grounds for asserting the existence of a delay time. The delay time in the Faraday effect was determined by Ellison in the following way. The same liquid, most often \(\mathrm{CS}_2\), was poured into both tubes \(L_1\) and \(L_2\). With the Nicols of the Lippich polarimeter crossed, the light showed a minimum when the movable contact \(T_2\) was placed at such a point that the wire path from the spark gap to \(L_1\) and \(L_2\) had one and the same length. In this case the electric-current wave arrives at coils \(L_1\) and \(L_2\) simultaneously. The coils were connected so that the magnetic field produced by the current had the opposite direction in each of them; consequently, the resultant direction was zero, and therefore the light was blocked by the Nicol \(N_2\). Owing to the fact that the arrangement of the coils in the circuit is symmetrical, the currents in \(L_1\) and \(L_2\) are identical. When the movable contact \(T_2\) was in a position different from \(T_1\), the wire paths were unequal, and therefore the wave arrived at one of the coils earlier than at the other. During the time in which the wave reached the second coil, the plane of polarization rotated in one of them and did not rotate in the other. Hence a certain amount of light could pass through \(N_2\). If the liquids are identical, the minimum of light should be observed when the wire paths to the coils are identical. With different liquids—say, \(\mathrm{CS}_2\) in tube \(L_1\) and \(\mathrm{NaCl}\) in tube \(L_2\)—the minimum of light was observed when the movable contact \(T_2\) was set in such a place that the wire paths were unequal. In this way it was found that, with \(\mathrm{CS}_2\) in one of the tubes and with a number of salt solutions in the other, the minimum was observed at a position of contact \(T_2\) characteristic for each compound. The explanation that Ellison gives for this phenomenon amounts to the following: for two different solutions, the time that must elapse between the application of the magnetic field and the rotation of the plane of polarization must be different. In order that the rotations in each of the tubes occur at one and the same moment and produce a minimum of light, the wire paths must be different. In that case the magnetic fields in the coils, produced by the arriving waves, will be applied at different times.

The Verdet constant is usually different for different liquids, and therefore the rotations also cannot completely balance one another.

even with equal currents. Differences in Verdet’s constant do not, however, affect the positions of those minima which Ellison observed, and affect only the intensity of these minima.

In Ellison’s experiments, a very small displacement of the movable contact \(T_2\) was required in order to observe a sharp change in the intensity of the light and to establish the minimum. According to Ellison,^7 the positions of the minima in different observations, but with one and the same apparatus, lay within \(3\) mm.

1. Influence of the wave. Let us consider what conditions the current in the coils must satisfy in order to produce those sharp minima which were observed by Ellison and his collaborators. The rise of the current in the coils had to be so rapid that, for a wave arriving at one of the coils, the change in time had to be of the order of \(7 \cdot 10^{-11}\) sec. Indeed, assuming that the velocity of the wave in the circuit is the same as the velocity of light, i.e. \(3 \cdot 10^{10}\) cm sec\(^{-1}\), and increasing the limits of displacement of the movable contact indicated by Ellison from \(3\) mm to \(1\) cm, we arrive at the conclusion that the relative change in the lengths of the circuits is equal to \(2\) cm, while the time interval will be

\[ \frac{2}{3 \cdot 10^{10}} = 7 \cdot 10^{-11}\ \text{sec}. \]

This time should be more than sufficient to cause the necessary change in the current, producing a noticeable rotation of the plane of polarization.

Let us assume that the unavoidable oscillation in the circuit due to the presence of resistance, self-induction, and capacitance may be neglected, and that the initial wave arising at the moment of the spark jump determines the magnitude of the magnetic field and, consequently, the occurrence of the sharp minimum.

The waves must be extremely short and, in their length, comparable with the width of the minimum, i.e. with the length of that part of the wire circuit over which the movable contact \(T_2\) is displaced in order to localize the minimum.

A simple calculation on the basis of the quantities characterizing the oscillatory circuit shows that the length of the waves propagating in it must be of the order of several meters.

Further, in our reasoning it was assumed that the front of the current wave upon its entry into a coil with self-induction is vertical. But this is not quite so: its rise is steep, but not vertical. The character of the change in the strength of the current flowing through a linear conductor and encountering self-induction \(L\) or capacitance \(C\) occurs, as is known, according to the law^8

\[ I_L = \frac{2E}{Z}\left(1 - e^{-\frac{Z}{L}t}\right) \tag{2} \]

and

\[ I_C = \frac{2E}{Z}\cdot e^{-\frac{t}{ZC}}, \tag{3} \]

where \(Z\) is the total resistance. The action of such coils, which were used in the study of the Faraday phenomenon, is a combination

In the two cases indicated above, since here there are inductive resistance and capacitance (distributed). Owing to the influence of the capacitance, the current in the coil can increase only at a rate smaller than that given by equation (2).

From Ellison’s work it follows that a displacement of the contact by 1 cm, or a displacement along the wave front by \(7\cdot 10^{-11}\) sec, produces a noticeable effect on the eye. Let us consider how strongly the current in the coil will change during this time. The quantities that occurred in the apparatus are the following: \(E=6500\ \text{V}\), \(Z=790\ \Omega\), \(L=30\ \mu\text{H}\). Hence, on the basis of equation (2), it follows that \(I_L=0.03\ \text{A}\). Thus the current pulse which will flow through one of the coils, without a compensating current in the other coil, as a result of the displacement of the movable contact \(T_2\) from the position of minimum, increases from zero to the greatest value, equal to \(0.03\ \text{A}\).

The duration of the pulse is about \(10^{-10}\) sec. The concentration of the solution in some cases was less than \(10^{-11}\ \text{g}/\text{cm}^3\), with a path length of the light beam of about 10 cm. It is difficult to suppose that such a small amount of substance could produce any noticeable effect.

In the analytic derivation of the equations characterizing an oscillatory circuit, the inductive resistance is represented as concentrated at one point. In reality, the action of induction is not instantaneous: the current enters the coils by one or two turns before its inductive action is felt. Let us suppose that the spark discharge is instantaneous, that the wave can pass along the circuit without diminution of the perpendicular wave front, that no reflection occurs in the coil, that the coil allows the current to increase instantaneously, and that the whole current flows through the turns (\(I_C=0\)); in other words, let us assume that the wave rises in the coil from zero to the possible maximum of 20 A instantaneously. Under these evidently exaggerated and unrealistic conditions, let us see what optical effect should be observed in the experiment.

From the preceding analysis it follows that, if the light minimum arises as a consequence of the existence of a lag, then under our assumptions a current of 20 A for \(10^{-10}\) sec should produce a noticeable rotation. But the lines of the Mg spark exist with sufficiently strong intensity for at least \(5\cdot 10^{-6}\) sec. The number of pulsations during this time will be

\[ \frac{5\cdot 10^{-6}}{10^{-10}}=5\cdot 10^{4}, \]

and the equivalent current will be

\[ \frac{20}{5\cdot 10^{4}}=4\cdot 10^{-4}\ \text{A}. \]

A very large number of experiments with currents of various magnitudes leads to the conclusion that, in order to obtain the smallest noticeable rotation of the plane of polarization, a current of 1 A is necessary when an Mg spark is used as the light source.

On the basis of the analysis carried out, the conclusion suggests itself: the current wave cannot be the cause of the sharp minimum.

1. Influence of the concentration of the solution. From Verdet’s works it was already concluded that the rotation produced by any solution is proportional to the number of molecules of the dissolved substance in \(1\ \mathrm{cm}^3\) of solution. In addition, Shenrok \(^{10}\) showed that the Verdet constant changes with the concentration of the dissolved substance, and gave an explanation of this phenomenon. Let \(V\), \(V_1\), and \(V_2\) be the Verdet constants for the solution, the solvent, and the dissolved substance. Then

\[ V=\frac{V_1 q_1}{d_1}+\frac{V_2 q_2}{d_2}, \tag{4} \]

where \(d_1\) and \(d_2\) are the densities of the solvent and the dissolved substance, and \(q_1\) and \(q_2\) are their concentrations in \(\mathrm{g}/\mathrm{cm}^3\).

The rotation produced by \(\mathrm{CS}_2\), on the basis of (1), is equal to

\[ \alpha_{\mathrm{CS}_2}=HlV_{\mathrm{CS}_2}. \]

The rotation produced by NaCl is equal to

\[ \alpha_{\mathrm{NaCl}}=Hl\frac{V_2 q_2}{d_2}. \]

When the movable contact is in the position of the minimum, the resultant rotation is

\[ \alpha=Hl\left(V_{\mathrm{CS}_2}-\frac{V_2 q_2}{d_2}\right). \tag{5} \]

It follows from this that the smallest intensity of the transmitted light, when contact \(T_2\) is in the position of the minimum, must depend on the relative magnitude of two rotations, one of which is determined by the quantity \(V_{\mathrm{CS}_2}\), and the other by \(\dfrac{V_2 q_2}{d_2}\). When these quantities are equal, the change in intensity will be greatest. For the wavelength \(\lambda=4481\ \text{\AA}\) it is known that \(V_{\mathrm{CS}_2}=0.0871\) and \(V_{\mathrm{NaCl}}=0.056\). Since under the conditions of the experiment \(q_2=0.3\ \mathrm{g}/\mathrm{cm}^3\), which corresponds to a 25% solution of NaCl, and \(d_2=2.16\), then

\[ \frac{V_2 q_2}{d_2}=\frac{0.056\cdot 0.3}{2.16}=0.0078. \]

Comparing these two quantities, we see that even for a 25% solution of NaCl the rotation caused by the salt will amount to approximately 0.09 of the rotation produced by \(\mathrm{CS}_2\).

The magnitude of the rotation is proportional to the concentration. According to Ellison’s statement, the concentration is sufficient if it reaches the value \(q_2=10^{-10}\ \mathrm{g}/\mathrm{cm}^3\), which for NaCl will give

\[ \frac{V_2 q_2}{d_2}=\frac{0.56\cdot 10^{-10}}{2.16}=0.26\cdot 10^{-11}, \]

or approximately \(3\cdot 10^{-11}\) of the rotation produced by \(\mathrm{CS}_2\). In our calculations the influence of water (the solvent) was excluded, for which the Verdet constant is \(V_1=0.0237\). This influence makes the light effect of NaCl an still smaller fraction in relation to the compared one. The arguments presented remain valid for any solution. In addition, the concentration

must play a substantial role, whereas Ellison^5 asserts that the minimum did not show any noticeable change in brightness at various degrees of concentration within the limits \(10^{-11}\)—\(10^{-12}\).

1. The absolute value of the time lag for \(\mathrm{CS}_2\). In his papers Ellison writes^5 that the time lag for \(\mathrm{TiCl}_4\) is shorter by \(27.65\cdot 10^{-9}\) sec than for \(\mathrm{CS}_2\). For the chlorides of Sn and Re it is shorter by \(32.54\cdot 10^{-9}\). It follows from this that the absolute value of the time lag for \(\mathrm{CS}_2\) must in any case be greater than \(3.25\cdot 10^{-8}\). Abram^11, measuring the time lag for \(\mathrm{CS}_2\), found that, if it exists at all, it must be less than \(10^{-8}\). Ellison remarks in this connection that the time lag varies with the wavelength of the light. But the wavelength used by Abram (blue light) differed little from that used by Ellison (\(\lambda = 4\,481\ \text{Å}\)), and therefore the discrepancy between Abram’s and Ellison’s conclusions cannot be explained by this.

2. Influence of the oscillatory circuit. J. Webb and D. Morey, studying the phenomena occurring in the apparatus described above, found considerable damping at current peaks of about 200 A, i.e., much larger than any of the initial currents. Measurement of the damping decrement showed up to 30 oscillations before the current reached 1% of its maximum value. The wavelengths lay between 500 and 110 m and depended chiefly on the capacitance of the capacitor, and also to a small extent on the position of the movable contact. Besides this fundamental frequency, an oscillation of lower intensity with a wavelength of approximately 70 m was found. The oscillation of the latter type was connected with the position of the contacts, since shifting contact \(T_2\) by 36 divisions changed the wavelength from 65 to 73 m, whereas changing the capacitance of the capacitor had no effect. The position of contact \(T_2\) determines the magnitude of the total resistance of the circuit of each of the coils, and hence a phase difference between the currents in \(L_1\) and \(L_2\) may and must arise. Let us denote the change of current in the circuit of coil \(L_1\) by \(I_0\sin\varphi\), and in the circuit \(L_2\) by \(I_0\sin(\varphi-\alpha)\), where \(\alpha\) is the phase difference caused by the displacement of contact \(T_2\). If by \(\beta\) we denote the quantity characterizing the difference in lag times, then the resultant optical rotation must be proportional to

\[ I_0\{\sin\varphi-\sin(\varphi-\alpha+\beta)\}. \tag{6} \]

Equation (6) attains a maximum when \(\varphi=\frac{1}{2}(\alpha-\beta)\). In that case the greatest optical rotation will be proportional to

\[ 2 I_0 \sin \frac{1}{2}(\alpha-\beta), \tag{6'} \]

or, for small angles, proportional to the expression

\[ I_0(\alpha-\beta). \tag{6''} \]

For the case when the same liquid is poured into both tubes, \(\beta = 0\); consequently, the greatest resultant rotation is proportional to the phase difference \(\alpha\), which, for a constant position of contact \(T_1\), depends on the position of \(T_2\). Experimental observations of the dependence between the position of contact \(T_2\) and the magnitude \(\alpha\), determined from the sharp minimum, are given in Fig. 2. The curves show a smooth and gradual increase, which also confirms the change in light intensity as a function of the displacement of the contact.

Fig. 2

Analysis of the results leads to the conclusion that, even if one admits a delay time in the Faraday phenomenon, then for each case two minima are possible, one of which is produced by the principal wave current, and the other by the oscillating one. Two minima were indeed observed, and they were extremely broad and changed their intensity so slowly that it was not possible to determine them accurately. Often one minimum was superposed on the maximum of the other current, which made their detection still more difficult.

6. The influence of displacement of the movable contact on the current strength. As a result of displacement of the movable contact \(T_2\), the distribution of the total resistance in the coil circuits changes, and hence the strengths of the currents in each of them also change. Experimental results concerning the relation between the position \(T_2\) (abscissa axis) and the current strength in each of the coils (ordinate axis) are given in Fig. 3. It also follows from this that the position \(T_2\) affects the magnitude of rotation of the plane of polarization and, consequently, the position of the minimum as well. In fact, for any two liquids the light minimum must be located at such a point when the rotations are equal, i.e., when

Fig. 3

TIME LAG IN THE MAGNETO-OPTICAL FARADAY PHENOMENON

\[ I_1 V_1 = I_2 V_2, \tag{7} \]

or

\[ \frac{I_1}{I_2}=\frac{V_2}{V_1}. \tag{7′} \]

Suppose that benzene is placed in \(L_1\), and carbon disulfide in \(L_2\). Since carbon disulfide has a Verdet constant greater than that of benzene, in order to make the rotations in \(L_1\) and \(L_2\) the same, the current in \(L_2\) must be reduced, which is achieved by shifting \(T_2\), i.e., by adding resistance to the branch containing \(L_2\). Experiments with xylene in tube \(L_1\) and with benzene, xylene, toluene, water, etc. in tube \(L_2\)

Fig. 4

confirmed these conclusions, as may be seen in Fig. 4. Thus the position of the minima on the scale of the movable contact is linear with respect to the Verdet constant; the displacement of the contact is explained by the different magnitude of the rotation of the plane of polarization. There is as yet no basis for introducing the assumption of a time lag in the Faraday effect. On the basis of all that has been set forth, it may be stated with confidence that the Faraday effect cannot be considered the cause of the results obtained by Ellison, which arise from causes as yet unknown and only with a particular apparatus.

III. Investigations of H. Farwell and J. Hocks

Somewhat later there appeared a paper by H. Farwell and J. Hocks\(^{12}\), whose authors modified Ellison’s apparatus in several important details and found a number of new phenomena capable of causing a change in the intensity of light passing through the magneto-optical system. The arrangement of the apparatus is given in Fig. 5, where \(S\) is a magnesium spark, \(B\) a lens, \(F\) a filter, \(D\) a diaphragm, \(N_1\) a polarizer for the direct ray, \(L_1\) and \(L_2\) tubes for the liquids under test,

$N_2$—analyzer, $T$—a small telescope, $M$—a semitransparent mirror at an angle of 45° to the axis of the system, $P_1$, $P_2$, and $P_3$—rectangular glass prisms, $N_3$—polarizer of the “shunt” part of the beam, parallel to $N_2$, $N_4$—a rotating Nicol, whose angles of rotation are indicated by a scale for the intensities being compared. The shunt part of the beam served for comparison of the observed light fields after its passage through the polarization system. If the light intensity changed identically both for the direct beam and for the shunt beam, then the cause of such a change had to lie outside the magnetic field of coils $L_1$ and $L_2$, and depended on other conditions, such as, for example, the spark gap. Another change consisted in the fact that the movable contact $T_2$ was displaced along the scale by means of a cord and pulleys, since it had been established that touching the contact or the wire contour

Fig. 5.

along which the latter was moved by hand left greasy traces, as a result of which the current strength in the coils changed. In addition, with this method the observer could not establish the relation, in the rotation of the wheel, between the observed minimum and the position of the contact; consequently the reading was free from preconceived expectation. Observations were always carried out by two persons, one of whom determined the intensity minimum in the polarization system, while the other rotated the wheel connected with the contact. The observer who followed the change in field intensity, in order to prepare the eye, remained in darkness for 15 min before the beginning of the reading. In other respects both the setup and the procedure of the experiment were similar to those used by Ellison. We now turn to a brief account of the results of the authors’ three-year work.

After the principal minimum with $\mathrm{CS}_2$ had been established in both tubes, a solution of $\mathrm{HCl}$ was poured into the second tube.

The conclusion obtained in this case was the following: a constant sharp minimum for $\mathrm{HCl}$ at some quite definite position of contact $T_2$ was not observed; the minima had a random, disorderly character. The position of the minimum changed not only from day to day, but also from hour to hour. Observation of the magnesium electrodes showed that they oxidized rapidly, and at different rates at one and the same time. Changes in the spark gap caused instability in the pro-

in the transmitted light. In addition, sometimes the spark remained for a considerable period in one place, and then began to shift within the spark gap, which is apparently explained by the inhomogeneity of the electrodes.

Part of the unstable appearance of the maxima had to be attributed to the heating of the tubes with liquid when current passed through the coils \(L_1\) and \(L_2\). Especially sensitive in this respect is \(\mathrm{CS}_2\), whose refractive index changes strongly as a function of temperature. A water cooler eliminated this series of difficulties.

The second temperature factor proved to be connected with evaporation from the opening through which the liquid was poured into the tube. Strong evaporation from the opening caused convection of the liquid, and hence distortion of the path of the ray.

The influence of this factor on the course of the experiment was eliminated by sealing the tubes. It should be noted that, in addition to visual observations, a photometric comparison of two rays—the direct and the shunt ray—was carried out, and, besides the spark light source, a constant point source was used.

All the conclusions obtained may be formulated as follows:

1. Observations with a spark gap are unreliable because of the various changes in the discharge that occur here.

2. The results of observations are undoubtedly affected by the physiological and psychological characteristics of the observer.

3. The temperature effect may distort the results of observations to a considerable degree.

4. When all extraneous influences are taken into account, the intensity of the ray passing through the polarization system is in full agreement with calculations obtained on the basis of the Verdet constant of the liquid being tested, and the dimensions and electrical properties of the circuit.

IV. Other investigations of the delay time in the Faraday phenomenon

1. The Faraday effect at high frequency

An attempt to observe the Faraday effect at high current frequency was made by H. Tarnuelle, V. Blikne, Vorhis, and J. Cooper \({}^{13}\). For this purpose they constructed an apparatus analogous to Ellison’s apparatus. As the source of continuous oscillation, a high-frequency tube with a number of amplifiers was introduced into the circuit. The light source used was constant, usually Hg 5 461. At an oscillation frequency of 7.5 megacycles no change in the intensity of the light was observed when the ray passed through one tube with \(\mathrm{CS}_2\) between crossed Nicols. When the constants of the circuit were changed so that the frequency reached 1.7 megacycles,

clearing of the field was observed with each tube separately. When both tubes were in their places, however, the field remained dark. When the movable contact \(T_2\) was shifted within limits of up to \(5\ \text{m}\), no change in intensity was observed.

2. Observation of vitamins

An interesting application of the phenomenon under consideration was made by Wissink and Wouters[^14]. They also constructed an Ellison apparatus and investigated fish oil, spinach juice, orange juice, tomato juice, a solution of egg yolk, and irradiated carrot juice. These substances contain vitamin A. In all cases a minimum of light was observed. When strongly irradiated fish oil, pure carrot juice, Chinese-nut oil, and Wesson oil were used as the liquid under test, no minimum was noticed. In observing fish oil after air had been blown through it, the minimum was much smaller.

Since all the shortcomings in Ellison’s apparatus were also present in this case, the results of the experiments must arouse doubt.

3. Later investigations

a) G. Slack and J. Phipps[^15] attempted to establish the time of delay and to carry out a chemical analysis of a number of substances, using an apparatus similar to that employed by Farwell and Hox[^12]. Minima were observed. But no constant correspondence between the position of the movable contact and the observed minimum could be established. The change in intensity for both the direct and the “shunt” beam was the same. The authors believe that the existence of the minimum should be ascribed to psychological and physiological effects.

b) MacPherson[^16], on the basis of a large series of observations, came to the conclusion that the appearance of minima is of an entirely accidental character in such random groupings. In those cases where stable minima appeared, their causes were always connected either with the contact system or with the oscillatory circuit. Most often such a cause was greasy or sticky spots on the movable contact, deposited by the hand when it was being moved. When the contact was moved by means of a motor, there were no stable minima at all. The influence of spark fluctuations was excluded by comparing the direct and the “shunt” beam. In addition, besides visual observations, a photographic method was also used[^17]. A test of the eye showed that the author could not detect changes in intensity of less than \(30\%\). In complete agreement with this, individual series of observations, after calculation of the mean results, did not reveal any minima within \(3\%\). No minima characteristic

for various chemical substances actually does not exist—such is the brief conclusion of the authors.

c) M. Jevons and R. Ball[^18] applied a new method of testing Ellison’s method. More than 4,000 readings were made by a large number of observers completely unfamiliar with the apparatus. Each of them followed the change in the field intensity for only a short interval of time and knew neither where the minimum was supposed to appear nor how many of them (minima) there were supposed to be. A second observer controlled the displacement of the contact, and a third made the reading. The latter did not know what reading was to be correct. The zero of the scale was shifted several times, thereby eliminating the possibility of “adjusting” the minimum to a definite reading. When the results were calculated and plotted, with the position of the contact at which the minimum appeared laid off along the abscissa axis, and along the ordinate axis the number of readings corresponding to this position, the curves showed a series of peaks. If one assumes that all positions of the minimum are equally probable and are not determined by the chemical nature of the solution, then all peaks that are random in character must lie within the range

\[ np = 3 (npq)^{\frac{1}{2}}, \tag{8} \]

where \(n\) is the total number of readings, \(p\) is the probability that particular readings will be made, and \(q\) is the probability that they will not be made. Of 1,074 readings obtained by the authors with solutions of HCl, MgCl\(_2\), NaCl, ZnCl\(_2\), and KCl, 11 minima out of a possible 12 were observed, with 8 of them coinciding with the positions of the minima in Ellison’s works and 3 not coinciding. One peak, corresponding to contact position 21.4 on Ellison’s scale, is higher than could be expected on the basis of probability theory. But since the principal region in which the readings were made was known to the authors, the reading results cannot be entirely objective. With the same setup, 996 readings were made by 150 observers who had likewise never observed before. Their results gave only 6 peaks, with 3 of them not coinciding with Ellison’s results and none lying higher than could be expected on the basis of probability theory. The curve for 247 readings, obtained by three observers with the same solutions, had only 5 peaks, of which only one coincided with the position found by Ellison.

Next the authors themselves made 140 readings with shortened coils and obtained results similar to those in the first case, with the same minimum (21.4), exceeding the limits of probable coincidence, being noted. Then the tubes with solutions were completely removed from the coils. From 110 readings made by 23 observers who did not know of the change in the experimental conditions, results were obtained that were in good correspond-

in comparison with Ellison’s results for chlorides. Finally, a series of observations was made with an incorrect solution in the tubes. The readings of the minima on Ellison’s scale were as follows: 21.10; 21.08; 21.05; 21.38; 21.40; 21.45; 21.40; 21.75; 21.80; 21.70; 21.70; 21.95; 22.20; 22.20; 22.20; 22.45; 22.50; 22.50; 22.85; 22.85. The readings were made by observers from another institute, who did not know that the solutions were incorrect. Ellison gives the following readings for chlorides: 21.08; 21.40; 21.73; 21.85; 22.20; 22.50; 22.87. It is easy to see that the last series agrees with the preceding one within the limits of the accuracy of the measurements.

All the results obtained may be briefly summarized in the form of the following conclusions: 1) minima exist; 2) some minima coincide with Ellison’s data; 3) the majority of the minima obtained can be explained on the basis of accidental coincidences; 4) the minima may be explained by physiological and psychological causes or by conditions of the electrical circuit; 5) since minima were observed without a solution, with incorrect solutions, and with shortened coils, and since all of them are in good agreement with the published data, it follows that the minimum is not a function of the solution in the tube.

4. Observations with Positive Results

a) In addition to the work mentioned above^14, positive results in testing Ellison’s method were obtained by H. Joos and R. Gosling^19, who used a Wollaston prism as analyzer instead of a Nicol. The latter was placed so that the two beams polarized by it in mutually perpendicular planes were located in a horizontal plane. The polarizing Nicol was rotated until both beams reached approximately equal intensity. A narrow vertical slit was placed after the prism, the image of which was focused on a photographic plate. The photographs consisted of two sharp lines, formed by each beam separately. Any rotation of the plane of polarization caused an increase in the brightness of one beam and a decrease in that of the other. A synchronous motor, actuating an electrical switch, accurately regulated the exposure time, so that the exposure for all photographs was the same. The photographs were taken in succession; one in the position of the minimum, and the other outside it by 1–2 cm. The approximate position of the minimum was first established visually. In order to avoid erroneous results from accidental mechanical influences or from changes in the electrical circuit that might remain unnoticed, double exposures with direct and reverse currents in the coils were made for each position. Altogether 563 photographs were obtained, of which 225 were for water and 338 for various chemical compounds. The intensity of the lines was measured with a microphotometer. First, the difference in intensity of the two lines was determined when the contact was in the position of the minimum,

after it had been displaced and, finally, the difference between these two measurements was expressed as a percentage. The results of observations for two acids and three salts are as follows:

From consideration of the table it is evident that changes in the direction of the current also gave corresponding changes in the sign of the percentage, irrespective of whether the fields in the coils were of the same or of opposite directions. The algebraic and arithmetic means for water showed random distributions of the sign. Consequently, the results obtained confirm the reality and reproducibility of the minimum. The minimum is sharp because the difference in intensity is established, while the displacement of the movable contact was made by \(1\)—\(2\) cm. The positions of the minima are characteristic for each chemical compound.

b) Similar results were obtained by T. R. Boll \(^{20}\) on the basis of the method of “identifying unknowns,” which consisted of the following.

He renumbered solutions of three different salts with a concentration of \(10^{-7}\) and left them in the laboratory. Individual observers, who knew nothing either about the composition of the solutions or about the position of the contact, examined these solutions by means of the magneto-optical method, their concentration first being brought to \(10^{-10}\). All three solutions were identified and named completely correctly. Then the task was made more difficult. Solutions of seven salts and acids were taken, and only the list was known; but which solution belonged to the chemical compound listed remained unknown to the observers. Three solutions with a concentration of \(10^{-7}\) were taken, poured into one, diluted to a concentration of \(10^{-10}\), and handed over for determination of the mixture. Two observers worked in turn, without exchanging results, and each of them established three minima, the positions of which coincided completely. The probability of a random coincidence in this case is very small. From a large series of experiments, 83.3% of the determinations of unknowns were made correctly. This method was also successfully used by other investigators \(^{21}\). In the opinion of the authors, negative

the results obtained by some observers when checking Allison’s apparatus are explained by the complexity of this apparatus and by the experimenters’ insufficient mastery of the technique of operation; the position of the minimum, however, is undoubtedly a function of the solution.

From the survey of the literature it follows that Allison’s assertion of the existence of a delay time in the Faraday phenomenon is still poorly substantiated. The minima of light that were observed in the apparatus he constructed may have been caused by many different reasons, such as instability of the spark, oscillations in the oscillatory circuit, temperature phenomena, imperfections of the contact system, etc. The circumstance that stable minima in most cases were observed by Allison and his collaborators, and also by other persons, only in Allison’s laboratory, and that attempts to reproduce them under other conditions led to negative or uncertain results, compels one to suppose that their cause lies in some as yet unrevealed peculiarities of his apparatus, and only in this. The great interest aroused by Allison’s experiments is explained by the latter’s assertion that substances of extremely low concentration, of the order of \(10^{-10}\)–\(10^{-11}\), can be detected. Until now, the investigation of concentrations of such an order has been accessible only by radioactive methods. But for an enormous number of elements the method of radioactive analysis is inapplicable. If Allison’s discovery were confirmed, it would mark the beginning of a new epoch in the history of science. Unfortunately, there is every reason to believe that this is not so, although, as we have seen, some authors continue to insist on the reality and applicability of this method.

LITERATURE

1. F. Allison a. W. Beams, Phys. Rev. 29, 161, 1927.
2. Blondlot, C. R. 1882; Lodge, Phil. Mag. 1889; R. W. Wood, Phys. Optics 449, 1924.
3. F. Allison, Phys. Rev. 30, 66, 1927; 31, 313, 1928.
4. V. P. Rusakov, Usp. fizich. nauk, 13, 5, 762, 1933.
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6. J. Webb a. D. Morey, Phys. Rev. 44, 589, 1933.
7. F. Allison, J. Chem. Ed. 10, 73, 1933.
8. Rüdenberg, Elektrische Schaltvorgänge 396, 1929; Karapetoff, Trans. A. I. E. E. 48, 508, 1929; Rogowski, Flegler a. Tamm, Arch. Electrotech. 18, 4779, 1927.
9. Beams, Phys. Rev. 35, 24, 1930.
10. Schilprock, Z. Physik 46, 314, 1928.
11. Abraham a. Lemoine, Com. Ren. 130, 499, 1900.

1. H. W. Farwell and J. B. Hawkes, Phys. Rev., 47, 78, 1935.
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10. Mc. Ghee and Lawrenz, J. Am. Chem. Soc. 54, 405, 1932.