THE HISTORY OF THE RATIO $\dfrac{e}{m}$ IN RECENT YEARS¹

In 1929 the best value of the ratio $\dfrac{e}{m}$ from spectroscopic data was apparently $(1.761 \pm 0.001)\cdot 10^7\ CGSM$². The best value obtained by other means (deflection methods) was $(1.769 \pm 0.002)\cdot 10^7\ CGSM$. The discrepancy was so considerable that, for example, Birge considered it necessary to give two separate values instead of a single most probable one.

During 1930–1932 three new values for $\dfrac{e}{m}$ were obtained by deflection methods and one by spectroscopic measurements. All four of these values agreed with one another and were evidently accurate to a high degree. From them Birge³ derived, as the best value for $\dfrac{e}{m}$, $1.759 \pm 0.001$. In other words, the discrepancy that had existed in 1929 disappeared, and the error proved to lie in the data of measurements by deflection methods.

In the following two years three new values appeared for $\dfrac{e}{m}$, all three accidentally equal to $1.757$, and in 1936 Birge⁴ proposed $1.75762 \pm 0.00025$ as the most probable value. At present, however, it turns out that these “low” values were only preliminary results and that the final values now at our disposal are appreciably higher. Indeed, for example, Dunnington⁵, on the basis of his excellent work on the determination of $\dfrac{e}{m}$, gave $1.7584 \pm 0.0003$ as the most probable value. He found, however, that between the mean values from spectroscopic data and those obtained by deflection methods there exists a discrepancy of $0.0016$ units. This discrepancy, although it is only one fifth of that which existed in 1929, nevertheless, owing to the greatly increased accuracy of the measurements, is still almost three times the sum of the possible errors.

At present there are ten accurate values for the ratio $\dfrac{e}{m}$, six of which were obtained spectroscopically (by four different methods) and four by deflection methods (three different methods). Birge established that the discrepancy between the data obtained by one route and by the other is $0.0006$, exactly equal to the mean deviation which should be expected on the basis of the probable errors, and that the final mean is $1.75909 \pm 0.00024$.

These data were obtained as a result of recalculating each published value of $\dfrac{e}{m}$ with the aid of the following system of auxiliary constants⁶.

\[ \begin{aligned} c &= 299776 \pm 4\ \text{km/sec} \\ q &= 0.99993 \\ p &= 1.00048 \\ F &= 9651.31 + 0.80\ CGSM \\ A_{\mathrm H} &= 1.00813 \\ A_{\mathrm D} &= 2.01473 \\ A_{\mathrm{He}} &= 4.00389 \\ A_{\mathrm C} &= 12.0148 \end{aligned} \]

Each value was assessed in accordance with its own probable error, and usually this was the error indicated by the corresponding author. The data used (from 1 to 6 are spectroscopic, from 7 to 10 are by deflection methods) are given below:

(a) Distance between the He and H lines
1) \(1.7601 \pm 0.0008^7\)

(b) Distance between the \(H_\alpha\) and \(D_\alpha\) lines
2) \(1.7581 \pm 0.0004^8\)
3) \(1.7579 \pm 0.0004^9\)
4) \(1.7592 \pm 0.0005^{10}\)

(c) Refraction of X-rays
5) \(1.7601 \pm 0.0003^{11}\)

(d) Zeeman effect
6) \(1.7569 \pm 0.0007^{12}\)

(e) Direct measurements of velocity
7) \(1.7610 \pm 0.0010^{13}\)
8) \(1.7588 \pm 0.0009^{14}\)

(f) Magnetic deflection
9) \(1.7597 \pm 0.0004^5\)

(g) Crossed magnetic and electric fields
10) \(1.7571 \pm 0.0013^{15}\)

The six spectroscopic values give a mean of \(1.75895 \pm 0.00033\) \((1.82)^{16}\), the four others give \(1.75955 \pm 0.00033\) (0.99), and all ten, \(1.75909 \pm 0.00024\) (1.51), or, considering the mean of the two groups, \(1.75909 \pm 0.00017\) (1.07). The closeness to unity of this last ratio,

\[ \frac{R_e}{R_i}=1.07, \]

shows that the discrepancy between the two groups of data represents an average statistical deviation.

The circumstance that the simple mean value comes out equal to \(1.75890\) shows that the method of evaluation used in these calculations plays a comparatively small role.

As the most probable value for \(\frac{e}{m}\) at present, Birge recommends

\[ \frac{e}{m}=(1.7591 \pm 0.0003)\cdot 10^7\ \mathrm{CGSM}. \]

N. Khlebnikov, Moscow

Literature

1. R. T. Birge, Phys. Rev., 54, 792, 1938.
2. R. T. Birge, Rev. Mod. Phys., 1, 1, 1929.
3. R. T. Birge, Phys. Rev., 42, 733, 1932.
4. R. T. Birge, Phys. Rev., 42, 736, 1932.
5. F. G. Dunnington, Phys. Rev., 52, 475, 1937.
6. For the meaning of the symbols, see note 1.
7. W. V. Houston, Phys. Rev., 30, 608, 1927.
8. C. D. Shane and F. H. Spedding, Phys. Rev., 47, 33, 1935.
9. R. C. Williams, Phys. Rev., 54, 568, 1938.
10. W. V. Houston, private communication.
11. J. A. Bearden, Phys. Rev., 54, 698, 1938.
12. L. E. Kinsler and W. V. Houston. Phys. Rev., 46, 533, 1934.
13. C. T. Perry and E. L. Chaffee, Phys. Rev., 36, 904, 1930.
14. F. Kirchner, Ann. Phys., 12, 503, 1932.
15. A. E. Shaw, Phys. Rev., 54, 193, 1938.
16. On the probable errors and the ratios given in parentheses, see reference 5 (p. 500).