Undamped extra-short and very intense electromagnetic waves have been obtained by "magnetron", the intensity of the magnetic field being kept at the nearhood of its critical value, and a high voltage being applied to the anode.
The wave-lengths of this electromagnetic waves are approximately equal to the values calculated by the following semi-theoretical formula,
λ0=2×c×t,
where
λ0=semi-theoretical wave-length,
c=the velocity of light,
t=the time required by electrons for travelling the space between the cathode and the anode.
The wave-length is practically independent of the amount of filament-heating, but depends on the intensity of the magnetic field. The shortest wave obtatined in the present experiment was 17 centimeters. The present experiment is now being continued.

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Problems of electric circuit can not be solved generally by the differential equation when the circuit contains a resistance or an inductance, which is a function of the current. But, as we have to treat many such electric circuits containing variable constants in practical case, it may be convenient if we can solve the problem by a graphical method.
In chapter I of this paper it is shown that the fundamental equation of a simple electric circuit having variable constants can be reduced into the general form
P[f(P)]+F(P)dP/dθ=φ(θ)
in which f(P) and F(P) are the given functions of P, and φ(θ) the given function of θ, in chapter II the graphical method of solving the general equationis described in detail, and in chapter III five practical examples are treated by this graphical method.
The five examples are as follows;-
(1) The decay of transient current, when the electro-motive-force is suddenly removed, of a circuit containing a fixed resistance and a fixed inductance.
(Fig. 6a, Fig 6b, Fig 6c)
(2) The wave form of the charging current in charging a condenser by an alternating potential difference through a kenotron having variable resistance.
(Fig. 7a, Fig. 7b, Fig. 7c, Fig. 7e, Fig. 7f, Fig. 7g)
(3) The wave form of the current in an inductance coil with iron core having variable permeability, when an alternating potential difference is applied to the coil.
(Fig. 8a, Fig. 8b, Fig. 8c, Fig. 8d, Fig. 8e)
(4) The wave form of the terminal potential difference across a resistance load in which the half-wave rectified current is supplied by means of a variable resistance kenotron.
(Fig. 9a, Fig. 9b, Fig. 9c, Fig. 9d)
(5) The form of voltage rise in a self excited direct current shunt generator when the field switch is closed suddenly at a constant speed.
(Fig. 10a, Fig. 10b, Fig. 10c, Fig. 10d)

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In any electrical networks, it is usual to calculate the distribution of current and valtage with the aid of the kirchhoff's first and second laws. The calculation, however, often becomes tedlous if the network is complicated.
In such cases, sometimes it happens that the labour of computation is exceedingly reduced when we take steps as to suppose that the network were opened at a proper point or separated into two parts properly chosen and that then it were closed or they were jointed together afterward.
Moreover, there are such cases when it is necessary to calculate the distribution of current and voltage along a resultant network of two or more independent networks actually jointed together.
In the present paper, the statement and proofs of the fundamental laws are given which are to be employed in such cases, or in other words those to replace the kirchhoff's laws to save the labour of calculation are described.
They are then followed with illustrative examples.

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The writer proposes the resonant sharpcess of vibration galvanometer to be defined by ω0/2δ, where ω0 is 2π times the natural frequency of the moving system and δ is the damping factor.
There are two kinds of sharpness, the one is the intrinsic sharpness and the other is the working sharpness. It is described theoretically how the working sharpness is affected by the condition of the electric circuit, and the method of adjusting the working sharpness with no effect on the sensibility is explained.
The writer proposes a method of testing the vibraton galvanometer and the experimental results for five galvanometers are tabulated.

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A new electric wave projector is proposed in this paper. The principle of this wave projector is quite different from other reflecting system, and its directive effect is chiefly due to the action of wave director rod.
When several wave directors are arranged along a line with intervals equal to or more than a quater wave-length, the wave energy is transmitted chiefly along this line, and the row of these directors forms what the writer will call a "Wave Canal."
Now the projection of the sharpest beam of electric waves can be effected by the combination of a trigonal reflector and a wave canal. This combination will thus be called a "Wave Projector."
The directivity can be improved by increasing the number of director rods contained in the wave canal. For example, when the wave projector with 27 directors is used, the radiated power is almost confined to an angle of 5°. As an extreme case, when the sending and the receiving stations are connected with a line of wave canal, power transmission will be accomplished by electric waves.
Experiments have been also made using two or three parallel lines of wave canals erected before the trigonal reflector, and the results show that the directive effect of multi-canal projectors is not very much superior to the single canal system, so that the simpler single canal system seems to be preferable.
When a straight wave canal is arranged in front of the sending antenna, not exactly alony the line of reflection but making a certain angle with it, there will still be concentrated wave radiation along the canal.
The theoretical determination of the best condition of the canal becomes much involved, and the adjustment should rather be made experimentally.
In our experiments, the wave length was 440cms. and the length of each director being 180cms. and their interval 150cms.
The receiver was set at a distance of 50 metres, and the field was measured by means of a receiving antenna comprising either a thermo-couple or a crystal detector combined with a micro-ammeter.
With regard to this new wave projecting system, a preliminary report was presented to the Imperial Academy of Japan. (YAGI and UDA, Projector of the sharpest beam of electric waves. Proceedings Imp. Academy 2. 1926.)
Two papers relating to the same subject were also presented to the 3 rd PanPacific Science Congress held in Tokyo, Nov. 1926. (YAGI and UDA, A new electric wave projector and radio beacon. YAGI and UDA, On the feasibility of power transmission by electric waves.) (Sendai, March, 1927)

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In the measurement of phase difference between two alternating e.m.f.s by means of cathode ray oscillograph, the sence of the phase difference, i.e. lagging or leading, can be determined by the direction of rotation of the polar diagram on the fluorescent screen.
In the present paper the author introduces two methods for the determination of the direction of rotation. The principle of them bases on the superposition of certain kinds of e.m.f. on the plate voltage.
In the first method, this voltage is a sinusoidal e.m.f. A stationary sinusoidal corrugation will be seen along the circumference of the polar diagram, provided the following relation be fulfilled
nf=mf₁
where f denotes the frequency of rotation of polar diagram and f₁ that of the sinusoidal voltage superposed on the cathode voltage, m and n being some positive integers. Now, when mf₁ is slightly smaller than nf, the corrugation will rotate in the direction of rotation of the polar diagram. This method can be applied for the frequency range between several ten cycles and several ten thousand cycles.
In the second method, the modulation of cathode voltage is done by some special shaped e.m.f. The direction of rotation will be easily found from the form of corrugation superposed on the diagram. Such a special e.m.f. of variable frequency can easily be obtained by well-known "glimm" lamp pulsation generator. This method was successfully applied f₁ frequencies of range from few ten cycles to few hundred cycles.

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Sensibility and time-constant of Moll's linear thermopile are analytically studied, and some experimental results are compared with. In order to increases ensibility, there is optimum length of thermo-couple-element: and opening width of slit does not proportionally increase the sensibility. (see Fig. 4.) Time-Constant is independent on the width of slit opening.

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In the previous report, the writer stated that the amplitude of the shortwave oscillation current due to the surface discharge under a c. 50 cycle voltages increases with the time, until the breakdown point of solid dielectrics is approached. In this report, the writer investigates the same phenomena under about some solid dielectrics subjected to over-stressed condition.
Using, as a source of direct current, a kenotron rectifier fed with 50 cycles alternating current, and adjusting its filament current properly to prevent an excessive current, the writer has succeeded to obtain a stable equilibrium in the dielectrics even when they are operated beyond the max. point of the volt.-amp.-characteristics proposed by K.W. Wagner.
As soon as the solid dielectrics are over-stressed under the influence of ionized air, the strong short-wave oscillation, which has a definit frequency depending on the circuit constants, has been produced in the current when the sphere is negative against the plane electrode, while only feeble traces of oscillation could be detected in the current when the sphere is positive.
Although the oscillation results from the suddenness of the breakdown of air around the sphere electrode, it has been ascertained that the amplitude of the oscillation current depends remarkably on the condition of solid dielectrics.
Finally it has been remarked that connecting a semi-conductor closely to a short-gap, more stable and stronger oscillations have been obtained than in the case without a series short-gap. (March. 1927)

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