B. P. Weinberg.

Magnetic Expedition to Mongolia in 1913 (Author’s Abstract).

The article (Sept. 1915) consists of 15 chapters (about 2¼ printed sheets, with 2 maps, 18 photographs, and 5 diagrams) and one appendix (about 5 printed sheets with 4 maps). The chapters of the main article are: organization of the expedition; outline of the route; route survey; processing of the route survey; barometric leveling of the route; running of the chronometers; corrections of working chronometer No. 919; astronomical determinations; magnetic determinations en route; variational magnetic observations at Kosh-Agach, Kyakhta, and Tui; determination of the constants of the magnetometer; results of determinations of declination; results of determinations of the horizontal component; comparison of the results obtained with the results of other expeditions; general conclusion. The appendix, which constitutes an independent work by my companion and assistant, student I. A. Molchanov, “Explanatory Note to the Route Survey Urga—Kobdo,” is in turn divided into three chapters: the aim of the survey, the conditions of its conduct, description of the instruments, methods of observation and processing of the topographic material; outline of the route between Urga and Uliassutai; outline of the route between Uliassutai and Kobdo.

The results of the magnetic determinations were printed in the Bulletin of the Tomsk Technological Institute for 1918 (vol. 38, p. 2), and also (with reduction to 1910) in the summary of magnetic determinations indicated in the preceding abstract. In view of the lack of space, I shall dwell here only on details that clarify the degree of accuracy of the results obtained.

The provision of instruments left much to be desired; the reason was that up to the very moment of departure (July 13), from day to day, I hoped to receive the magnetometer which the Carnegie Institution was supposed to send at the end of May. Not risking further postponement of the departure, I set out with a portable magnetic theodolite by Bamberg, received from the Magnetic Commission of the Academy of Sciences, which made it possible to determine only the direction of the magnetic meridian and the horizontal component. For the astronomical determinations there served a small portable theodolite by Heyde, belonging to I. A. Molchanov, and two chronometers. The instruments used for the route survey, as well as all details concerning this survey, on the basis of which the geographical coordinates of the observation points along the route (1,500 versts) between Urga and Kobdo were fixed (a considerable part of it ran across the blank portion of the General Staff map), will be indicated in the detailed article.

Despite the severe trials, in the sense of jolts, to which the chronometers were subjected while being transported in a tarantass over the stony roads (and more often without any roads at all) in Mongolia and along the Chuya highway, their running was satisfactory. The errors caused by possible irregularity of rate were smaller than the errors from insufficient accuracy in the readings of the vertical and horizontal circles of the theodolite (1′.0–1′.5).

Bamberg’s instrument was checked by me at the Irkutsk Observatory before the journey, studied and partly compared with Bauer’s magnetometer in the winter in the physical laboratory of the Tomsk Technological Institute, and on April 3, 1914, checked at the Pavlovsk Observatory.

With respect to declination, the results of the comparison with Bauer’s instrument in the laboratory, given the proximity of measures and the difficulty of setting up in the same place (which at different times gave “Bamberg—Bauer” = −14′.6 and −18′.7), may be considered only preliminary in relation to the Pavlovsk

comparisons, which gave for the correction of the declination according to Bamberg \(-12'.0 \pm 0'.3\). The magnitude of this correction indicates the desirability of clarifying the causes of this, which the Pavlovsk Observatory intended to do.

In view of possible errors in the geographical coordinates and other sources of error, the errors in individual values of the declination must be considered to be of the order of \(\pm 5'\).

As for the determinations, with Bamberg’s instrument, of the horizontal component, the measurements of the angle of deflection \(\alpha\) (for reasons set out in detail in the article) are less accurate than the measurements of the period of oscillation \(T\), although, owing to the considerable damping of the oscillations, it was necessary to take so large an initial amplitude \(\alpha_1\) that even in the comparatively rarely used formula

\[ T_0 = T_a\left(1 - \frac{1}{16}\alpha_1\alpha_2\right), \]

where \(\alpha_2\) is the final amplitude, I sometimes had to replace the second term of the binomial by

\[ \frac{1}{4}\sin\frac{\alpha_1}{2}\sin\frac{\alpha_2}{2}. \]

The temperature coefficient—\(\beta_T\) for oscillations and \(\beta_a\) for deflections—was computed from observations in Irkutsk and from determinations in Tomsk. The characteristics of the determinations and the results are given in Table 1, in which \(\theta\) is the temperature, \(n_T\) and \(n_a\) are the numbers of observed oscillations and deflections, and \(p\) is the weight assigned in accordance with the mean errors \(\beta\), the temperature limits, and the degree of reliability of the initial data.

Table 1.

According to the data of Table I one obtains

\[ \begin{array}{c|cc|c} & \text{for magnet I} & \text{for magnet II} & \text{on average} \\ \beta_T = & 0.00021 & 0.00024 & 0.00022 \\ \beta_z = & 0.00049 & 0.00042 & 0.00046 \end{array} \]

With the aid of these coefficients all observations in Irkutsk and Pavlovsk were reduced to \(15^\circ\), and from them the conversion factors \(C_1 = H T_{15}^{2}\) and \(C_2 = H \sin \alpha_{15}\) were determined. The initial data and the values of \(C_1\) and \(C_2\) are given in Table II, where \(H\) denotes the values of the horizontal component according to the records of the observatory instruments.

Table II.

Hence it follows that the magnetic moment \(M_I\) of the first magnet, during the interval of time between the Irkutsk and Pavlovsk observations, decreased by \(1.0011 \pm 0.0010\) times according to the rocking observations and by \(1.0006 \pm 0.0009\) times according to the deflection observations; for the second magnet the corresponding numbers are \(1.0201 \pm 0.0007\) and \(1.0209 \pm 0.0012\).

In order to judge how \(M_I\) and \(M_{II}\) changed during the expedition, there were also calculated: 1) the relative values of \(M_I\) and \(M_{II}\) for those points where, with one and the same magnet, both rockings and deflections were observed, and 2) the ratios \(M_I : M_{II}\) for those points where rockings or deflections were observed with both magnets. The results of the calculations are given in Table III.

Table III.

Processing these data by the method of least squares—on the assumption of a linear change of \(M_I\) and \(M_{II}\) with time—gave, for the variation of the ratio \(M_I:M_{II}\) from the values of \(M_I\) and from the values of \(M_{II}\) separately, and from the ratios \(M_I:M_{II}\), almost identical values:

\[ M_I:M_{II}=1.1036+0.0010+(0.00022+0.00004)t, \]

\[ M_I:M_{II}=1.1042+0.0008+(0.00020+0.00003)t, \]

where \(t\) is the number of days elapsed since the time of the Irkutsk observations. However, comparison of the observed and computed values of \(M_I\), \(M_{II}\), and \(M_I:M_{II}\) shows that the values of \(H\) obtained with the aid of the final values of the reduction factors resulting from this, namely

\[ \text{for magnet I}\quad C_1=17.328+0.00007t,\quad C_2=1.0698-0.00004t \]

\[ \text{for magnet II}\quad C_1=19.203+0.0038t,\quad C_2=0.96182-0.00019t, \]

are less accurate than the values of \(T\) and even \(\alpha\). Therefore it will not be an exaggeration to regard the error in the values of \(H\), based on observations of swings only or of deflections only—and moreover for a single magnet—as being of the order of \(0.002H\). In the case where observations of both swings and deflections are available—especially with both magnets—the order of the error is considerably lower.