FROM CURRENT LITERATURE

A new method for determining $\dfrac{e}{m}$. In connection with the discussion concerning the discrepancy between the values of $\dfrac{e}{m}$ obtained spectroscopically and by means of ordinary phenomena with cathode rays (see UFN, 12, 4, 516, 1932), it seemed expedient to repeat the latter measurements, taking exact account of all possible errors. Such measurements have already been carried out by Kirchner, according to a new method proposed by him, and gave results closely coinciding with those obtained spectroscopically. Dennison has recently developed (following an idea of Lawrence) an entirely new, highly simple and ingenious method for determining a specific charge, in which the possible sources of error are reduced to a minimum. An evacuated brass box $B$ (see Fig. 1) contains six slits $A$, $S$, $D$, arranged on a circle of radius $r$. The slits $S$ and the outer slits $A$ and $D$ form a single whole with the box; the inner slits $A$ and $D$ are insulated from the outer ones and connected to a radio-frequency generator. The box $B$ is connected to the grounded end of the generator. During that half of the period when the inner portions are charged negatively, the electrons emitted by the filament $F$ undergo acceleration and emerge through the external slits $A$. Obviously, these electrons will possess all possible velocities from 0 up to the potential equal to the amplitude of the generator.

Fig. 1.

Further, the emitted electrons are bent by a magnetic field directed perpendicular to the plane of the drawing. On the basis of the well-known relation

$$ \frac{mv^2}{r} = Hev, $$

for each velocity $v$ one can choose a magnetic field $H$ at which the electron will be bent along an arc of radius $r$, i.e., geometrically, will be able to enter the Faraday cylinder $C$, connected to an electrometer. However, whether it enters there or not depends also on the potential that the inner slit $D$ will have at the moment the electron reaches it. It is obvious that if, for the given magnetic field $H$, the velocity of the electron is such that it traverses the arc $ASKD$ in a time exactly equal to a period of the generator, then such an electron, having passed through the outer slit $D$, will experience the action of a retarding potential exactly equal to the accelerating one and, consequently, will not be able to enter the Faraday cylinder. Therefore, there exists a definite value of the magnetic field at which the potential of the Faraday cylinder will be zero (practically, $+$ minimum). It is clear that for this case—

the velocity of the electron will simply be \(v=\dfrac{r\theta}{T}\), where \(\theta\) is the angle subtended by the circular path of the electron, and \(T\) is the period of oscillation of the generator; or, since \(\dfrac{1}{T}=\nu\) is equal to the frequency of the generator, \(v=2\theta\nu\). Combining this equation with the previously given

\[ \frac{mv^2}{2}=Hev, \]

we obtain:

\[ \frac{e}{m}=\frac{\theta\nu}{H}\ CGS\ M, \]

where \(\theta\) is expressed in radians, and \(H\) in gauss. The accuracy of the determination by this method proved to be very considerable. Thus, with fifty readings of the magnetic field (at constant generator frequency), the results proved so stable that the probable error of observation in determining \(\dfrac{e}{m}\) amounted to one unit in the fifth figure. The final result of 90 measurements at two frequencies differing by 30% is:

\[ \frac{e}{m}=(1.7592\pm0.0006)\times10^7\ CGS\ M. \]

This result is somewhat smaller than the spectroscopic value \(1.761\cdot10^7\ CGS\ M\), but is close to it and, in any case, smaller than the value obtained by Wolf (F. Wolf, “Ann. d. Phys.”, 83, 849, 1927) by ordinary measurements with deflection of cathode rays—\((1.7689\pm0.0018)\times10^7\). It agrees well with Kirchner’s results \([(1.7585\pm0.0012)\times10^7]\) and Dennington’s measurements. Thus the question of a possible difference between the value of the specific charge in optical phenomena and for free electrons may be regarded as definitively resolved in the negative (F. Dunnington, “Phys. Rev.”, 42, 734, 1932).

E. Shpolsky.