A explicit expression for the kernel function involved in the formal electric potential equation for the general case of n layered media, each layer being homogeneous and isotropic, is given in the form_??_
where
where_??_called the elementary symmetric expression of k1, ..., k_n-1 with their induced exponential functions of h₁, ..., h_n-1, _??_
and the symbol k_j, j=1, 2, ..., n-1, is resistivity factors, h_j layer-depth, λ a parameter and n the number of layers.
By making use of the general formula, the kernel function for the special case of five layered media is given in the paragraph 2·4. In section 3, the basic method of expressing the kernel function is suggested with an example such as n=6. Finally, some properties of the kernel function are explained in the subsequent section of the present paper.

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In this paper, the authors studied on the cutting mechanism of brittle materials as gypsum, cement, rock coal blocks.
Results obtained from these experiments are as follows Type of cutting mechanism changes from shear type to crack type as depth of cut and brittle index (ratioof compressive and tensile strength of material defined by the authors) increases, with larger fluctuations in cutting resistance.
2 Fluctuation in cutting resistance decreases as bit width increases.
3 Distance of peaks of cutting resistance increases as rake angle of bit decreases.
4 Cutting resistance of brittle materials in practical cutting conditions may be concluded as the press-in resistance of cutting edge.
5 When cutting brittle materials, tensile stress in the case of larger rake angle bit and shear stress in the case of smaller rake angle bit, takes the.most important role in cutting breakage occurance.

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In Taiheiyô Coal Mine, the “Honsô” (main seam) and the “Kasô” (lower seam) of Harutori coal bearing formation are now under working. In this mine, methane content in the whole exhaust gas is 25 to 28m³ per ton of out put. We assume that methane content increases as the working area goes deeper.
In this paper, occluded gas in the coal seam, speed of gas discharging, possible amount of methane for drainage, etc. shoold be treated.
(1) The coal seam is an only source of methane gas in this mine. The auther has tried to classify the occluded gas in the coal seam into self-spouting gas and non self-spouting gas from the practical point of view.
(2) The total gas content occluded in the coal seam lies between 5.8 and 6.00m³/t, made up of 1.80m³/t of self-spouting and 4.00 to 4.20m³/t of non self-spouting.
(3) Generally speaking, gas discharged from the entries in self-spouting, while that from the working long-wall faces is non self-spouting.
(4) When the coal is cut, 2.0m³/t of the non self-spouting gas is released from it within a week or so, and the remaining gas discharges gently.
(5) The gas which discharged in the term of initial disturbance is possible to be drained effectively. And the volume of gas discharged out of the working long-walls is presumed as 6.0m³/min in pure at minimum.
(6) The composition of obtained “pure” coal seam gas is as follows CH₄ 93-96% O₂ 0.1-2.7%
CO₂ tr-0.9 N₂ 3.2-4.5
(7) The composition of the original coal seam gas is difficult to determine except for large amount of self-spouting gas, because we could not get the sample gas of original state ever obtained gas has been influenced for few days already by ventilatin air before the sampling.

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Basing upon the results of the commercialization tests on copper smelting by converter using oxygenenriched air, proviously published, (refer Note 1), the project for putting this process into commercial practice was commenced at the Hitachi Mine in September 1956 and completed in April 1958. Thereafter, the operation of this process has been continuing in smooth performance.
The construction program may be summarized as follows:-
(1) Four of the existing converters were put into use after modifications and improvements.
(2) Wet blending is employed as a preliminary treatment for the converter feed ore which after pelletizing in a balling drum is dried to a moisture content of about 3%.
(3) Of the existing ten blast furnaces, seven were scrapped and only three preserved, of which one Is being utilized as an auxiliary unit.
(4) The oxygen producing plant is an air-separation unit with a capacity to produce 2, 000 cubic metres per hour of oxygen of 95% purity. The oxygen is stored in a-storage tank capable of, holding 2, 000 cubic' metres of oxygen. This is compressed by oxygen compressor and then automatically blended with air to the required oxygen density.
(5) The converter slag is treated by the ordinary ore dressing process, for which purpose a slag dressing plant with a capacity for treating 5, 000 tons of slag per month was installed.
(6) The No. 1 Sulfuric Acid Plant was expanded from its original production capacity of 3, 000 tons per month to 4, 500 tons per month by the addition of a gas flue of about 750 metres long from converter aisle with a washing tower in between, a drying tower, absorption tower and cooling units.
(7) The No. 2 Sulfuric Acid Plant was also expanded from its original production capacity of 3, 000 tons per month to 7, 000 tons per month by the addition of a drying tower, absorption tower, converting units and cooling units. Furthermore, with a view to treating the converter gas, cottrell precipitators wore added. In place of the Herresh off roasters, afluidized bed roaster of 80 tons per day capacity was newly installed. The surplus heat is recovered as steam for utilization at the refinery to which it is piped over a considerably long distance of 3, 500 meters.
(8) Improvements and modifications were made to all auxiliary installations to cope with the above.

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