Problems of countercurrent multiple contact extraction are solved using plate efficiencis, in the case where the equilibrium line is straight. For the extraction of solids we assumed uniform concentration of the underflow, the immiscibility of underflow with overflow, and the constant underflow.
The number of actual plates required for a given separation defined as Eq. (3), may be calculated by Eq. (9). Relations between the over-all plate efficiency Eop, individual plate efficiency E_M or E_B and extraction factor β are also obtained. The individual efficiencies are defined as Eq. (1)-(2). The over-all plate efficiency E_op, consists of E and ε/N as Eq. (11), where E means the over-all plate efficiency when it is assumed that β_N equals β, and ε/G is the correction factor. Fig. 2a and 2b are the charts for calculation of E. Fig. 3, 4 and 5 are the charts for calculation of ε, for several types of operation when distribution constant γ=1 and wf=0. The calculation may be simplified by using these chart.

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In order to make the relation clear among carbonizing temperature, carbonizing time and width of chamber of coke oven, the author analysed the relation among these factors mathematicaly.
As a conclusion, the author derived the following approximation formula:
ε: width of chamber,
T: C₁/1, 000,
C₁: temperatute of the inside wall of carbonizing chamber,
t: carbonizing time.
The author ascertained that this formula coincided considerably well with the practice when comparing it with the data of a small experimental oven, and that the carbonization process of coke oven was analogous approximately to the formation of ice.

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(1) Experimental equations were obtained to enable us to compare each impeller characterestics, concerning power consumptions of concentric agitation for both cases: namely, in the first place, that of water alone; in the other, that of mixture of water and air bubbles, which were blown through a nozzle in the center of the tank bottom. Turbine and paddle type impellers and 26cm diameter cylindrical tank were used.
(2) In the case of agitation, accompanied by aeration, -as for turbine and paddle type impellers- marked and little decrease of consumption of power were observed, respectively, comparing with that of agitation with no aeration. For both types of impellers effects of nozzle diameters (1-5mmφ) and of air rates (0.26-4.94m3air/min/m³ water) on power consumptions were negligible.
(3) Determinations were made as follows:
In the case of agitation with no aeration:
for turbine type impellers
for paddle type impellers
In the case of agitation, accompanied by aeratiom:
for turbine typ
for paddle types
where:
(4) Effects of tank diameter, impeller position in the tank, liquid depth and of physical properties of liquid were not studied.

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We have studied on the characteristics of several jet pumps, the nozzles of which are different each other in their shapes, sizes and number of holes.
According to our experiments,
(1) The optimum operating condition was
ξ, φ, ε being the ratio of back pressure to driving pressure (pd-ps)/(pn-ps), the discharge coefficient of nozzle, the cross area ratio of nozzle to diffuser throat, respectively.
(2) The characteristics of jet pumps could ba shown by α' and β/μd as in Fig. 8, α' being the compression ratio (pd-pw)/(ps-pw), pw being the water vapour tension (kg/cm²ab.). As the result, the preferable value of ξ seems to be 0.4-0.5.
(3) Using a nozzle not smoothed up its inner shape, the characteristic might not always be wronger, but should become unstable, for φ varied with the driving pressure.
It is the most desirable to keep φ nearly 100% constant and to use the nozzle with several holes, so that the operation may be stable, and the mixing of air and water may be effective in the diffuser
(4) The characteristics depend slightly on the distance from nozzle to diffuser, the length of diffuser throat and the inclination of th enlarging part of diffuser.

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