A Note on the Minimum Value of the Horizontal Component in the Kryvyi Rih Basin Based on the Magnetic Surveys of P. T. Pasalsky in 1898 and 1900
Abstract Generated abstract
This note reexamines P. T. Pasalsky’s reported minimum values of the horizontal component of terrestrial magnetic intensity in the Kryvyi Rih basin from surveys conducted in 1898 and 1900. Using Pasalsky’s original notebooks and recomputing observations at points A, B, and station No. 143, the author checks instrument constants, deflection distances, and numerical reductions, identifying misprints and computational errors affecting the reported values. The recalculation indicates that point A did not have a lower horizontal intensity than station No. 143, and that the true minimum for the surveyed data was approximately 0.0411 C.G.S. units at station No. 143 rather than the published 0.0548, increasing the inferred amplitude of horizontal intensity values to 0.6719.
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Wild’s instrument was compared before V. D. Dudetskii’s trip at the Irkutsk Observatory, whereby the reduction factor proved to be somewhat different than in 1910. Since the deflections had been observed near Voronov at a small distance, at Vorogovo and Osinovskii at both small and large distances, and at the more northern points at a large distance, in anticipation of such a possibility in Irkutsk, in addition to the period of oscillations \(T\), the deflections \(u_1\) and \(u_2\) were observed at small and large distances. The following table gives the results of determining from these observations the corresponding reduction factors \(B_1\) and \(B_2\):
| Time | \(T\) | \(u_1\) | \(u_2\) | \(B_1\) | \(B_2\) |
|---|---|---|---|---|---|
| 5 25–5 29 a | 23 30.8 | 4.2968 | 2.8847 | ||
| 5 43–5 51 a | 10 22.6 | 4.2968 | 2.8847 | ||
| 5 53–5 01 a | 10 22.6 | 4.2968 | 2.8847 | ||
| 6 38–6 55 a | 3.3489 | 4.2968 | 2.8847 | ||
| 10 23–10 39 a | 3.4498 | 4.2956 | 2.8817 | ||
| 10 52–11 05 a | 10 17.9 | 4.2956 | 2.8817 | ||
| 11 08–11 18 a | 23 23.6 | 4.2956 | 2.8817 | ||
| 11 36–11 59 a | 3.4572 | 4.2973 | |||
| 0 01–0 09 p | 10 17.6 | 4.2973 | |||
| 0 11–0 20 p | 23 18.6 | 4.2973 | |||
| 3 30–3 41 p | 23 16.8 | 4.3000 | |||
| 3 53–4 09 p | 3.4570 | 4.3000 | |||
| 4 17–4 28 p | 23 17.2 | 4.3000 | |||
| Mean | \(4.2974 \mp 0.0009\) | \(2.8837 \mp 0.0008\) |
The uncertainty in the values of \(H\), caused by the correction for the diurnal variation and by observational errors, is of the order of \(0.0001\) C.G.S. unit.
Owing to the fact that the Muro inclinometer had not been calibrated and studied beforehand, the values of the inclination \(J\) must be regarded as having errors of the order of \(5\)—\(10'\).
B. P. Weinberg.
A Note on the Minimum Value of the Horizontal Component in the Kryvyi Rih Basin According to the Magnetic Surveys of P. T. Pasalsky in 1898 and 1900.
In the posthumous work of P. T. Pasalsky, “On the Study of the Distribution of Magnetism on the Earth’s Surface” (Zap. Nov. Univ., 85, 1–547, 1901), on p. 250 it is said:
“The extreme limits of the horizontal intensity found by us are:
| Station no. | Latitude | Longitude | Horizontal intensity | |
|---|---|---|---|---|
| Maximum . . | 215 | \(48^\circ 19' 3''\) | \(3^\circ 13' 0''\) | 0.7130 |
| Minimum . . | 143 | \(21' 24''\) | \(12' 9''\) | 0.0548 |
| Amplitude . . | 0.6582“ |
On p. 110 P. T. Pasalsky wrote:
“In September 1900 I set out for the region of the magnetic anomalies I had investigated near the Zheltaya River, with the special purpose of making observations on variations of the earth’s magnetism, and selected for
for this purpose two points with a very large difference in horizontal intensity. In the first of them (point A), the mean of 39 observations of the horizontal intensity gave \(H = 0.04253\); in the second (point B), from the same number of observations, \(H = 0.46396\). The note to Chapter 3 reads: “At this point the horizontal intensity is less than the smallest of those observed in 1898 (see point 143, Chapter VI); it is located at a distance of 3 meters north of No. 143.”
In processing the results of P. T. Pasalsky’s observations in the Crimea in 19001 and having at my disposal only his notebooks, in which there were also observations at points A and B, I recomputed the latter and became objectively convinced that in 1900 Pasalsky worked with the same theodolite as in 1898, and that the constants of this theodolite had not undergone noticeable changes.
For the observations at point B (with \(\bar{E}\) equal to 16 cm), the inverse calculation, from the value \(H = 0.46396\), of the magnitude of the magnetic moment \(M_0\), using the same values of the constants \(Q\) and \(\alpha\) as Pasalsky used (loc. cit., p. 211, where the value of \(Q\) is given for a distance of 16 cm), gave a value of \(M_0\) very close to the values of \(M_0\) obtained from observations at those points where, in 1900, observations both of oscillations and of deflections were made. For point A, however—the only one where the distance was equal to 21 cm—there was obtained (for the moment \(7^{\mathrm h} 53^{\mathrm m}\) a)—with a correspondingly changed value of \(Q\)—the value \(H = 0.05371\), which differs greatly from the value \(H = 0.04253\) given by Pasalsky.
This discrepancy compelled me to check, from the late man’s original manuscripts, the computations for point No. 143—the only one where, in 1898, the observations were also made at a distance of 21 cm—and this check revealed a whole series of misprints and errors in these computations (such as: \(\lg E = 2.32214\), and \(2 \lg E = 4.62428\); \(\varphi = 30^\circ 46' 24''\) instead of \(\varphi = 35^\circ 46' 24''\), etc.), something I had never once encountered when checking his other computations.
Having accordingly corrected the value of \(Q\) (namely, taking \(\lg Q = \overline{7}.33439\) instead of the incorrect value \(\lg Q = \overline{7}.23393\) adopted by Pasalsky—in the same units (mgr., mm.) that Pasalsky used, converting only the final results—\(M_0\) and \(H\)—into C.G.S. units) and having corrected the misprint in the value of \(\varphi\), I obtained for point No. 143 \(H = 0.0411\). For point A, with the incorrect value of \(Q\), there was obtained for \(H\) precisely the value \(0.04253\), while with \(Q\) correctly computed it turned out that \(H = 0.05355\).
Thus point A, at which, according to Pasalsky’s supposition, the horizontal intensity is less than even at point No. 143, where the smallest value of \(H\) was observed in 1898, in fact yielded, in this respect, to the latter point, which actually gave the smallest value of \(H\), not \(0.0548\), but \(0.0411\), so that the “amplitude” of the values of \(H\) is not \(0.6582\), but \(0.6719\).
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B. P. Weinberg. “Magnetic Survey of the Crimea, Carried Out in 1900 by P. T. Pasalsky.” Proceedings of the Academy of Sciences, 33, No. 10, 1915, p. 18. ↩