One of the chief reasons why the bending strength is greater than the tensile strength in rocks, is that fractures can be caused on the parts of the rock also where the tensile stresses are not maximum, by the effect of Griffith cracks distributed at random in a specimen.
For the distribution of the strength of Griffith cracks, the present writer has adopted Weibull's distribution. It is because it has an advantage in being easily treated as compared with the normal distribution introduced by the other investigators, and because the two distributions are closely approximate unless the variation is too great, and the coefficient of uniformity m in Weibull's distribution can be related, by the use of Γ functions, to the coefficient of variation c.
By applying the theory of the probability of minimum value to the strength of Griffith cracks in a specimen, the distribution of the bending and tensile strengths can be calculated. The both strengths accord with Weibull's distribution, and the ratio of the two strengths are given as the function of m.
The experiments the writer carried on with Akiyoshi marble show that the bending and tensile strengths accord with the distribution by Weibull, and the ratio of the two strengths coincides with its theoretical value on a coefficient of confidence of 90%.
Theoretically the coefficients of variation of the two strengths are equal, and it has been tested in the experiment also that those of the experimental values are equal.

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In rocks the tensile strength S₀ is often substituted by the tensile stress S_t at the diameter of a cylindrical specimen which is weighted with a breaking load in the direction of the diameter, but in that case S_t is not always equal to S₀.
The experiments by the present writer, as well as by other investigators, show the result of S_t>S₀ in some rocks, and in others S_t<S₀.
To the distribution of the two strengths, the present writer applied the theory of the probability of minimum value of the strength of Griffith cracks. The theoretical ratio of the mean values of the two strengths is given as the function of the coefficient of uniformity m. And it is found that one of the chief causes for S_t<S₀ is the distribution of Griffith cracks in a rock specimen.
But there are other causes also, namely, the existence of compressive stress, the crush at the loaded end of the diameter, etc., by whose combined effects is brought about the relativity of S_t and S₀. Accordingly, in order to estimate the mean tensile strength S₀ in rocks, it would be more suitable to use the value obtained by the statistical treatment of the bending strength rather than to use S_t.

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The thermal expansions of the specimens injection-molded from nylon 6, 66, their copolymer, polyacetal and polycarbonate were measured, and the relationship between thermal expansion and dimensional changes caused by the relief of internal residual stress and crystallisation was discussed.
The results obtained were as follows:
1) The thermal expansion of the specimens injection-molded from the crystalline high polymers depends on the thermal history which influences on the crystallinity and the relief of the internal residual stress.
2) The apparent second order transition points are about 80°C for the unannealed molded specimens from nylon 6 and 66, about 100°C for their annealed molded specimens and 160°C for unannealed specimens from polycarbonate.
3) Above the apparent second order transition points, the relief of internal residual stresses and its velocity become larger and the apparent thermal expansion varies remarkably. Therefore, the coefficient of thermal expansion plotted against temperature reach a maximum at about 80°C for unannealed nylon 6 and 66 and at about 100°C for their annealed specimens, and at about 160°C for polycarbonate, and then these curves also reach a minimum at about 170°C for nylon 6 and 66, and above 200°C for polycarbonate, nearing to their melting regions.
As for nylon copolymer and polyacetal, no similar change to the above was found.
4) The coefficients of thermal expansion of the specimens with high crystallinity are smaller at lower temperatures than those having low crystallinity, but larger at higher temperatures.
5) The ratio of the coefficient of cubic expansion to that of linear expansion for unannealed specimen of nylon 6 is about 3 only when the temperature is below 100°C, and for annealed one the same value is obtained below 150°C.
6) The relationship between the coefficient of thermal expansion and temperature is similar to that between the dielectric loss tangent and temperature.

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The authors have inquired experimentally into the effects of the times of impressing the specimen and after unloading upon the Rockwell hardness numbers for plastics and steel.
The experiments have been carried out under the constant impressive load, 150kg, using the constant indentor, 1/4 inch steel ball. The materials of specimens tested are a soft steel and the five kinds of plastics, such as phenolic, urea, polyester, polystyrene and nylon.
As the results, two empirical formulas have been derived as follows: H_R=H₁-ΔH₀·(logt)^m (1) and H_R=(H₁-k·logt)+(n₁+l·logt){log(logt')} (2) where H_R is the total depth of indented hole under impressive loading in the scale of Rockwell hardness numbers, H₁ hardness numbers at impressive loading instant, ΔH₀ hardness numers' changes from H₁ to 10sec impressive loading's, H_R Rockwell hardness numbers, t duration of impressive loading, t' time after unloading, and H₁, k, l, m and n₁ are the constants proper to the materials.
Accordingly, the Rockwell hardness numbers HR₁ for the standard duration of impressive loading t₁ and time after unloading t'₁ may be obtained by the following formula H_R1=H_R+k·logt/t₁+n₁·log(logt'₁/logt')+l·{logt₁·log(logt'₁)-logt·log(logt')} (3) where H_R is the Rockwell hardness numbers of the material for any duration of impressive loading t and time after unloading t'.

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