Since the heat conduction in a furnace wall may be regarded as a stochastic process, any boundary or initial condition may be represented by the sum of instantaneous heat sources coming out at the surface or inside of the wall with corresponding temperatures and phase differences.
Therefore, if the probability function of an instantaneous heat source having unit temperature (θ=1), being in existence at the surface or inside of the wall in question, be calculated, the given condition at any point may easily be worked out by the process of simply multiplying the distribution function by the corresponding temperature and superposing the products taking into account of the phase difference and the variation of the temperature.
This paper concerns mainly with the method of getting the probability distribution function mentioned above for the problems of one dimensional right angle coordinates, and the graphical and numerical methods were compared with those of Schmidt, Tanazawa and Takahashi.
This process was also extended to the method of getting the distribution function of unit temperature at any point, making use of the solution of steady heat source problem, and to this end it was proved that the solution of steady boundary conditions may be used to get the corresponding distribution function of instantaneous heat source having unit temperature irrespective of the form of the expression, functional form, empirical form, or any other forms.

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Gypsum has long been used as an excellent retarding agent of portland cement. It, however, has a drawback of making some troubles due to the extraordinary setting, for example, the false setting that comes from the dehydration in milling process.
The authors have tried to use calcium sulphite, an abundant and low price byproduct of sulphuric acid industry, etc., as a substitution of gypsum hoping that it would check the extraordinary setting, increase the strength, and decrease the construction of the cement. The experimental results have proved that calcium sulphite is better than gypsum in many respects.
The present paper contains the results of the investigations of the reaction mechanism between cement clinker and calcium sulphite using X-ray diffraction, chemical analysis, differential thermal analysis, thermo-balance in vacuo, and phase microscope, which led to the isolation of a new compound, a kind of cement bacillus, formed by the reaction of a component of cement clinker, tricalcium aluminate, with calcium sulphite.
(1) Synthetic tricalcium aluminate hydrated rapidly to form hexahydrate as confirmed by X-ray diffraction pattern. After a few days crystals of hexagonal plate were pictured by phase microscope.
(2) It was revealed that aggregations of needle crystals were formed by the reaction of 1 mole calcium sulphite with 1 mole tricalcium aluminate. The crystal form was similar to that of calcium sulphoaluminate. This new cement bacillus showed a two stage dehydration at 190° and 260°, and the oxidation occurred slightly at 500° and strongly at 700°C being in accord with the thermal chracteristics of calcium sulphite. The total amount of water driven off by the two stage dehydration is 23.64%, from which it was confirmed that water of crystallization was 7H₂O. The molecular formula of the new cement bacillus was fixed upon as 3CaO⋅Al₂O₃⋅CaSO₃⋅7H₂O which turns into 3CaO⋅Al₂O₃⋅CaSO₃⋅3H₂O after the first stage dehydration.
(3) When calcium sulphite was added jointly with gypsum the increase of the strength and the retardation of the setting of cement occurred more effectively than the separate use of the agents. In this case the velocity of formation of cement bacillus became slower, and also the trend was observed that the velocity of the formation of calcium sulphite bacillus was quite likely slower than that of gypsum bacillus.

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Studies on aluminium enamelling carried out so far have revealed that the pretreatment of aluminium plate is the most important. As reported in the first paper, (Journal of the Metal Finishing Society of Japan, 8 [7] 11 1957), the samples coated with film obtained by anodic oxidation in dilute solution of sodium perborate gave the good results with respect to the adhesive properties and the luster of the finished products.
The present paper contains the results of the investigations carried out in expectation of obtaining highly adhesive enamels by the formation of an intermediate layer having semiglass structure. It may be formed by the chemical reaction between the surface film, the coating of γ-alumina produced on metal surface by the anodic oxidation in aqueous solution of alkali borate, silicate and phosphate or their mixture, borosilicate, lead, and phosphate frits.
The results may be summarized as follows:
1. Good results in bending test of borosilicate enamel were obtained when the metal plates were pretreated by the solution of sodium borate, potassium borate, and water glass.
In the binary solutions the mixtures of lithium borate and water glass gave the most satisfactory results.
Among the ternary mixtures the solutions containing sodium borate and water glass as the main constituents gave especially good results.
The samples treated with the mixed solutions gave the better results in thermal shock tests than those treated with single component solution.
In all cases aqueous solutions containing potassium ion were found to be the most satisfactory.
2. Lithium borate gave the best results in the bending test of lead enamel although there was no difference among sodium metasilicate, sodium perborate and lithium borate in the results of thermal shock and adhesion tests.
The ternary solution of above three components gave the best results in bending test.
3. In the bending test of phosphate enamel sodium phosphate solution was the best, while above three solutions gave the results of about the same level as those of lead enamel in thermal shock and adherence test. The ternary mixture gave the best result.

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A systematic study on the E. M. F. between simple oxides and common glasses was carried out using a vacuum tube voltmeter for the cell Pt/solid oxide/glass melt/Pt set in a Pt ribbon resistance furnace.
Sodium silicate, potassium silicate, commercial window glass, lead glass, and borosilicate glass were used. All these glasses, except the window glass, were melted from pure materials in Pt-crucible. Solid oxides used were kaolin, SiO₂, Al₂O₃, ZrO₂, CaO, MgO, BaO, ZnO etc. Two types of solid oxide electrode were used. One was a Pt wire covered with a thin layer of a solid oxide being essentially the same as that used by Plumat, and the other was a small sintered rod whose one end was wound with Pt wire. The latter showed as good results as the former, provided that good contact was assured between Pt wire and the oxide rod.
Factors influencing the E. M. F. of above cells would certainly include (1) temperature distribution in the cell, (2) atmosphere, (3) oxgen pressure inside the molten glass. The effect of the factor (3) was investigated and was confirmed as being most influential.
Cell: Pt/kaolin/window glass/Pt was studied. It was confirmed that the change of the structure of kaolin took place during the preheating of the electrode and the kind of the cation absorbed in kaolin affected the E. M. F. greatly, though this problem ought to be studied more closely.
For the cells “Pt/simple oxide/glass melt/Pt” all mesaurements were carried out at 1000°C, because it has been reported that the temperature itself has little effect upon the E. M. F. of above mentioned cells in the temperature range from 900°C to 1300°C.
The E. M. F. of these cells suggested that the radius (r:Å) and the number of electric charge of the cation of the solid oxide electrode (z) have some relations to the EM. F. of the cell. For each glass the E. M. F. values were plotted against the parameter (r/z). The figure showed that the E. M. F. of oxide electrodes come upon a linear line. The plot for ZnO failed to fit on the line in many cases, which may probably be interpreted by the non rare gas type electronic structure of Zn⁺⁺. According to the figures (8-12) the straight lines may be represented by the equation,
V=A-B (r/z), where
V is E. M. F. (volt), A and B are the constants for each glass.
As B in above equation has nearly equal value for all glasses, suggesting that the electric charge was carried by same kind of cation. It will be possible to replace B by c(z_c/r_c) and obtain the equation in the following form,
V=A-c(z_c/r_c)/(z/r),
where z_c is the number of charge of the cation carrying the electric charge in molten glass, r_c the radius of cation, and c a constant representing the type of glass.

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