We look at the electrical conductance of a regular packing system of conducting and insulating particles as a prolem of combination or probability. The conductance of the system is governed by electrical passages which may be made of conducting particles.
The number of passages of electricity is not calculated by the basic binominal equation, but it can be calculated by the following modified binominal equation which derived from the work of this report.
(Number of electric passages)=(n)2^n-1-8{((n/2)-1)·_n-1C_n-1+((n/2)-2)·_n-1C_n-2+…}
Since the equation described above is inapplicable to the calculation of P(p), where p>p_c′, we proposed some other equations.

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Crystalline cephalexin (CEX) was ground by agate centrifugal ball mill, and the relationship between the physicochemical properties of ground CEX and its degree of crystllinity was studied by means of X-ray diffraction analysis, the infrared (IR) spectral method, thermal analysis (DTA and DSC) and scanning electron microscopy (SEM). The intensities of the X-ray diffraction peaks of crystalline CEX (phase IV) decresased with increasing grinding time in an agate centrifugal ball mill. By grinding for 4hrs showed the same halo pattern as the noncrystalline solid (NC) obtained by the freeze-drying method. The crystallinity of ground CEX was determined by the X-ray diffraction and IR spectral methods. The degree of crystallinity determined by the X-ray diffraction method decreased with increasing grinding time. After 2hrs, it was 0%. At 62% relative humidity, the water content of ground CEX increased with increasing grinding time due to the conversion to a noncrystalline state. The dehydration and decomposition points of ground CEX were depressed with decreasing crystallinity.
The activation energy and mechanism of dehydration were determined by the thermal kinetic method using DSC (Criado's method). The product ground for 4hrs was about 2.5 times more soluble than the intact phase IV. The dehydration behavior and solubility of the product for 4hrs were different from those of the freeze-dried product, even though both products are X-ray diffractometically in a noncrystalline state.

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Depending upon the discharge mechanisms, grinding mills can be classified into two types with respect to their dynamic characteristics. One discharge type is characterized by the discharge flow rate in proportion to the holdup, as exemplified by a continuous tube mill having a perforated division head. The other is characterized by the internal classification type, in which only a fraction smaller than a certain cut size x_c can instantaneously be discharged.
On the other hand, a rate constant K of the selection function is modelled, that is, the product of K times holdup is divided into three regions in relationship to the holdup. Combining the mass size balance at the use of the kinetics of comminution with the discharge mechanism, simple interrelationships between the transient quantities of discharge rate, the holdup, the rate constant and the average particle size of the finished product are derived. From this, some indicial responses of holdup and average size are discussed at a step change of the feed rate.

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The optimum operating frequency and intensity of oscillating air applied to sieve fine powders are discussed.
As fundamental considerations, the non-linear Langevin equation, which describes the behaviours of a particle in a vertical oscillating fluid, is solved numerically. It is shown that the trajectory of a settling particle in the fluid obtained from the solution agrees closely with the experimental results. The behaviours of a particle on the sieve surface, which is in the oscillting fluid, is also analysed on the basis of this equation. The sieving rate of fine powders depends on the impact velocity between a particle and the sieve surface, because the velocity relates to the dispersion of agglomerates and the velocity of fine particles passing through an opening of the sieve. The number of collisions between a particle and the sieve surface is determined by the amplitude and frequency of oscillating air. These results show that there is an optimum condition of oscillating air applied to sieve fine powders.

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