In this study, the buckling tests of pipe due to its own weight with the diameter 8mm and the length 1, 000-4, 500mm were examined.
As the results of this tests, the following conclusions were obtained.
(1) Empirical formula of deflection curve of the pipe;δ=δ₀(l/l₀)ⁿ (1)
where n=1.17-2.05
(2) Critical length of pipe obtained by using the strain energy of bending ΔUand the total work during the buckling ΔT;l_cr{n(n+1)²/2(2n-1[(n+1)2/2n+1+n-2/n+2-n²+3n/2n+3])}1/3·3EI/q (2)
(3) Relation betweenl_crandl_cr0or the ratio ofl_crandl_cr0l_cr=C·l_cr0={n(n+1)²/2×7.837(2n-1)[(n+1)²/2n+1+n-2/n+2-n²+3n/2n+3]}1/3·l_cr0(3)
For the abovevalue of n=1.17-2.05, the value ofCis less than 1.04, consequeently the above equations about the deflection's curve and the critical length are practically well enough appllcable.
l₀=length of pipe
l=arbitrqry length of pipe
δ₀=deflection of upper end
δ=deflection at the point of length
ΔU=strain energy of bending
ΔT=total work during buckling
l_cr=critical length of pipe
l_cr0=exact solution about critical length of pipe given by Timoshenko
C=coefficient

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The size distribution of grinding products in the fine size range is represented by Gaudin-Schuhumann equation,
y=100(x/k)α(1)
whereyis the cumulative weight percent finer than sizex, kis the size modulus and denotes the theoretical maximum-size in the assembly, andαis the distribution modulus, depending on the grinding device.
Assuming that equation (1) is valid only beyond the lower limits of y andαis a constant independent of grinding time, specific surfacearea is expressed by the following equation, S=f/ζ·F(α)·1/k(2)
wheress is specific surface area, ζis density and f is shape factor.
Combining equation (2) with Lewis equation, expressing the relation between grinding energy and size reduction is also derived as follows.t=C[F(α)]^n-1/n-1(k^1-n-k₀^1-n)(3)
wheretis grinding time (αgrindin energy), nandCare constants in Lewis equation, andk₀is the size modulus of feed.
Equation (2) is applicable to even the condition that the coefficient is infinite, namely, α-n+1=0 in Charles equation.
The validity of equation (2) and (3) is discussed from the experimental results of ball mill grinding of magnetite, hematite and limonite in our laboratory.

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In the present experiment, an attempt to promote the acid dissolution of zinc-ferrite was made to obtain a high zinc extraction in the electrolytic zinc process, and the following results were obtained.
(1) By an addition of Fe powder in the leaching solution, the dissolution rate of zinc-ferrite increases markedly. The increase in dissolution rate of zinc-ferrite increases markedly. The increase in dissolution rate is, however, not due to the direct contact of Fe powder with zinc-ferrite particles, but due to the action of Fe²⁺which is produced by the dissolution of Fe powder.
(2) The dissolution rate is enhanced by the cathodic polarization, which is achieved by the contact of zinc-ferrite particles with cathodically polarized electrodes.
(3) The addition of Fe²⁺as FeSO₄·E7H₂O in the leaching solution gives an increase in dissolution rate of zinc-ferrite. The simultaneous addition of Fe³⁺with Fe²⁺lowers the dissolution rate considerably.
These results suggest that the increase in dissolution rate by the above methods would be caused by the increase in concentration of anion vacancy at the surface of zinc-ferrite. This agrees with the conclusion of the previous papers.
From the discussion on the dissolution mechanism of oxides, based on the results of our works and others', it is concluded that the dissolution of the oxides containing Fe₃₊would be promoted under reducing conditions.

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Selective reduction of copper sulfate contained in sulfation-roasted calcine of complex sulfide are and leaching of zinc compounds (ZnO·E2ZnSO4, ZnO, ZnS) in the reduction-roasted calcine with 0.4N H₂SO₄were investigated.
If copper exists in a metallic state after the reduction, the copper will be left behind in leached residue by the leaching treatment, and then the separation of zinc from copper is to be attained only by the acid leaching of the reduced calcine. Furthermore, this method facilitates recovery of gold and silver beared in raw sulfide ores, because the gold and the silver will be allowed to behave together with the metallic copper in the leached residue when the copper is cast into moulds to prepare copper anodes for electrolytic refining.
However, if zinc sulfate in the sulfation-roasted calcine is converted into zinc sulfide during the reduction roasting, the leaching of zinc with 0.4N H₂SO₄may be hindered. Factors which have an effect on the conversion of the zinc sulfate were concentration of CO in a reducing gas-mixture composed of CO, CO₂and N₂, and reduction-roasting temperature. The degree of the conversion became higher with the greater CO-concentration and the higher reduction temperature. These conditions accelerated also formation of iron sulfide FeS from Fe₃O₄and SO₂which were produced in the reduction roasting: Fe₃O₄+10CO+3SO₂=3FeS+10CO₂
The iron sulfide evolved H₂S by a reaction with H₂SO₄ in the leach solution and the hydrogen sulfide promoted dissolution of the magnetite. Liberated Fe³⁺ion from dissolved magnetite attacked not only the zinc sulfide but also the metallic copper. Therefore, copper dissolution in the leaching treatment could not be avoided so far as the magnetite dissolved to any extent.
It was confirmed experimentally that the optimum conditions for the selective reduction roasting in a fluidized bed were as follows; the reduction temperature-500°C, the CO-concentration-20%(CO₂/CO=1.3) and roasting time 4hrs. The zinc extraction from the reduction-roasted calcine under those conditions with 0.4N H2SO4 was 92%, the copper dissolution 17% and the iron extration was 52%

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