From the Memoirs of Pyotr Nikolaevich Lebedev

A. K. Timiryazev

Of all my memories of P. N. Lebedev, the one that has remained especially vivid is the memory of how, under his guidance, I began carrying out my dissertation work, “On internal friction in rarefied gases and on the connection between slip and the phenomenon of a temperature jump at the boundary between a solid body and a rarefied gas.”

In essence, this work was closely connected with P. N. Lebedev’s own work, “Thermoelements in a Vacuum as an Instrument for Measuring Radiant Energy.” In the spring of 1911, the apparatus on which I was to work was ordered by P. N. from the mechanic A. I. Akulov. A schematic drawing of the apparatus is shown in Fig. 1). When the apparatus was ready, I had to pump the air out of it. And this presented great difficulties, since the apparatus consisted of metal and glass parts; where the glass tubes were inserted into the metal ones, leaks often arose, and they were not easy to seal. After the air was pumped out, it rather quickly leaked back in. It was necessary to take the whole apparatus apart and, after reassembling it, carefully coat it with varnish—a solution of shellac in alcohol, carefully filtered*). The work dragged on for months. At this

) In the drawing, BB* denotes a glass bell jar. Such bell jars were usually used to cover microscopes. Another interesting memory of P. N. is connected with this bell jar. When, at the beginning of 1911, I came to P. N., he took three glass bell jars from his cabinet and gave them to me. I said: one would be quite enough for me. He replied: no, take all three—and immediately explained why. “If you take one, you will be afraid of breaking it, and you will take care of it, and for that reason you will probably break it. But if you take three bell jars, you will know that you have spares; you will not take care of them, and all three will remain intact!” Here Pyotr Nikolaevich’s subtle knowledge of the psychology of those working in the laboratory was evident.

**) I owe this instruction to P. N. He explained that during filtration a precipitate is separated out, and that precisely this precipitate, if it is not filtered out, makes the shellac film brittle, so that a thin layer of shellac cracks easily. This example shows how finely Lebedev knew the technique of the physical experiment.

At that time P. N. came to me in the laboratory every day and tried in every possible way to encourage me. Finally, it was in the spring of 1911; P. N., entering the laboratory when I was not there and looking at the manometer (not shown in Fig. 1), saw that the leak had stopped. Then he took a visiting card, pierced it with a pencil, and put it on the eyepiece of the tube through which I observed the rotation of the torsion apparatus. On the card the letters p. f. were written in pencil (pour féliciter, to congratulate). I have kept this card; we reproduce a photocopy of it (Fig. 2)*.

Even earlier P. N. had predicted that the curves of the dependence of the deflection of the torsion apparatus on the gas pressure should have the form shown in Fig. 3. As is evident from the figure, the curves have a point of inflection. P. N. said that the gas pressure corresponding to the point of inflection should be inversely proportional to the magnitude of the gap between the suspended cylinder and the outer rotating one. He said to me: if you succeed in proving this theoretically and confirming it by your experiments, then it will be a very fine result of your dissertation work. I showed the theoretical calculation to P. N. in the autumn of 1911. I did not succeed in showing him the experimental result; by the time the experimental part was ready, P. N. was no longer alive.

Fig. 1.

Another conversation with P. N. also comes to mind, in the autumn of 1911, when he asked me: how does the deflection of the torsion apparatus depend on the molecular weight of the gas at large rarefactions, when the deflection itself is proportional to the gas pressure? I showed the relation I had derived for the moment of the quantity—

* On the next day, when P. N. came to me in the laboratory, he explained why he had pierced the card with a pencil and hung it on the eyepiece of the tube. He said: “At first I wanted to put the card on the table, but I thought, you will be so glad that the air leak has stopped that you will come into a state of ‘rapture of the feelings’ and will not notice the card lying on the table. But if the card is visible on the eyepiece of the tube, then when you want to look into it, you will literally run into it with your nose!”

of the motion \(g\), transmitted from the outer cylinder rotating with velocity \(v\) to the inner cylinder, suspended on a thin wire (see Fig. 1):

\[ g=\frac{f}{2-f}\,v\sqrt{\frac{M}{2\pi R_0T}}\,p. \]

As is evident from the formula, the measured effect \(g\) is proportional to \(\sqrt{M}\)—the square root of the molecular weight.

[Figure: handwritten signature “Petr Nikolaevich Lebedev.”]

Fig. 2.

Petr Nikolaevich in no way wished to agree with my conclusion. He thought that instead of the square root there should have been the first power of \(M\). He asked me: “And what quantities connected with the gas still enter into your formula?” I answered: “the gas constant \(R_0\).” Petr Nikolaevich, with his characteristic sharpness, said: “To hell with you and your gas constant!” and began walking back and forth across the room, his hands in his pockets. Then, stopping and turning toward me, he said: “You are absolutely right; you must have the square root of the molecular weight, and I shall prove it to you at once. Write down the usual expression for the kinetic energy for any mass.” I wrote: \(\frac{1}{2}Mv^2\).

\(2)\)

P. N. continued: “We shall discard \(\frac{1}{2}\). What remains is \(Mv^2\). P. N. continued further: “But your effect is proportional to the first power of the velocity \(v\). Therefore, the square root must be extracted from \(M\). Then you will get \(\sqrt{M}v\)!” Of course, no one

Fig. 3.

Repulsive force
Pressure

\(R_2 - R_1 = 0.0533\ \text{cm}\)
\(R_2 - R_1 = 0.100\ \text{cm}\)
\(R_2 - R_1 = 0.209\ \text{cm}\)
\(R_2 - R_1 = 0.406\ \text{cm}\)

\((0.001\ \text{mm})\) \((0.01\ \text{mm})\) \((0.1\ \text{mm})\) \((1.0\ \text{mm})\) \((10\ \text{mm})\) \((100\ \text{mm})\) \((1000\ \text{mm})\)

would regard this derivation proposed by P. N. as a rigorous proof! But it was one of those many examples of rapid calculation that revealed the basic regularity, something so characteristic of Pyotr Nikolaevich Lebedev. That is why this conversation has remained well preserved in my memory, with all its details.