We are now encountered with a troublesome problem of unifying frequencies, as 50 cycles and 60 cycles are used equally, and are being developed with almost equal rate in our country. The Japanese Electrical Association organised a commitee to investigate the matter with a view of unifying the frequencies.
Eor this purpose it is important to study how the characteristics of machines will change by changes of cycles and wether they can be remodeled as to suit the changed frequency.
In this paper the anthers treat these two problems on the alternator, the induction motor and the transformer. The probable figures are given when 60 cycle machines are operated at 55 cycles and 50 cycles and also 50 cycle machines when operated at 55 cycles and 60 cycles. (S. M.)

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Various curves were plotted for practical conveniences:-
[1] Curves (A) (B) (C), which are recessary in designing the single layer coils giving certain self inductances.
[2] Curve (D), which shows the total ength of wire of the coil.
[3] Curves (E) (F), which determine the approximate value of natural resonant wave length of the coil.
[4] Curves (G) (H), which shows the approximate value of equivalent self capacity of the coil.

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The reflection loss in telephone circuits has been calculated by many authors from the variation of currents in the circuit. The writer proposes that the reflection loss should be expressed by the ratio of the electric power in the circuit. The formula is derived for the reflection loss from this stand point. The convenient diagram is then given which shows how the reflection loss varies for various impedances of the circuit. The degree of reduction of the reflection loss by the inequality ratio transformer is considered in this connection. The coefficient of reflection is investigated by a diagram which is similar to the foregoing diagram of the reflection loss.

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A description is made on the theory, construction and the operation of the permeameter devised by the writer as well as some experimental studies on it. The permeameter is a double bar and double yoke type. The reluctance of the yoke and gaps are compensated by the magnetising coils on the yoke which are excited and regulated independently. The criterion of the proper compensation is the condition that the magnetomotive force applied between two fixed points in the specimen is exactly consumed by the magnetic reluctance at that portion. This condition is confirmed by proving that the magnetic potential difference between those two points is zero.
Experiments show that the permeameter gives satisfactory results in the measurement of magnetic properties of solid and sheet materials of iron and steel. The accuracy and the consistency of the readings taken at different times exceed all that is required by most of the commercially precise magnetic measurements.

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Inductances of coils in polygonal form are not yet treated except in the case of rectangle.⁽¹⁾ In this paper the triangular, the hexagonal and the octagonal cases are treated with some calculations of the mutual inductances between two linear conductors in general, assuming the permeability of the medium to be always unity throughout the space. The chief merit of the formulae consist in their accuracy even in the case of small number of turns and considerable length of pitch.
Contents of each section are as follows:
1. The mutual inductance between any two straight linear conductors not parallel to each other is calculated in general form by means of the Neumann's formula _??_, the result of which is identical with that of the F. F. Martens's _??_Equation (1)_??_.
2. The mutual inductance between two parallel straight conductors are treated _?_Equation(2)_??_.
3-5. The self inductances of cylindrical coils of rectangular polygonal sections (triangular, hexagonal and octagonal) are treated after the manner of Dr. A. Esau. _??_Equation (4), (5) and (6)_??_. A coil is considered to be made up of separate folygons, so that the self inductance of the coil may be equal to the sum of the self inductances of the separate turns plus the sum of the mutual inductances between each turns.
6-8. The self-inductances of plane coils having the same forms are given. _??_Equation (7), (8) and (9)_??_.
9. Some remarks are made concerning the inductance of the coil as a function of the number of sides, the relation between the cylindrical coils and the plane coils, and the available limits of the formulae.
Readers are warmly recommended to refer to the papers published by Prof. F. F. Martens⁽²⁾ and Dr. A. Esau.⁽¹⁾

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