Crushing is accomplished by dropping a steel ball on a plunger resting on the samples (Stoneware) in a steel mortar. The experimental results are as follows:
The residue of crushed products R in percent is given by the equation
(I)
R=f(y) (II)
where, x: particle size in mm
σ: max. stress by eq. (17), e: base of natural logarithm
σ₀: stat. stress by eq. (17), k, n, c: Constants
A: gross work input to crushing in kgm by eq. (15)
Eq. (1) is applicable in the following cases:
1. Free crushing, in which fines 100 mesh minus are removed.
2. Choke crushing, in which, Residue (100 mesh plus)≥75%
Eq. (2) is applicable in the choke crushing, in which, Residue (100 mesh plus)<75%
We have found close similarity between these equations and the corresponding experimental data, regardless of the ball weight or the drop height.
Comparing these equations with those of Rittinger's, we have proved that the former ones are more useful than the latter ones.

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Size distribution of various kinds of powder was obtained by two liquid sedimentation methods (Andreasen and Kelly) and by air elutriation method. The specific surface area of powder was also measured by Blaine's method. The residue distribution can be given by the following Rosin-Rammler's formula.
where n is about 0.2-2.4.
The results by the sedimentation methods did not often coincide with those by the air elutriation method. The cyclone points on a size distribution figure, which were obtained from the measured collection efficiencies η, the approximate calculation (η=R) and assumed cut size of powder particle used, were shown along or slightly below (coarser than) the air elutriation curve. From these results, we can approximately estimate the collection efficiency of a cyclone.
The specific surface area did not give good correlation with the collection efficiency of the cyclone.

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Assuming the fracture occurs when the stress is widely over the allowable one, grinding would cease just as the stress arrives at its limit, since it would gradually decrease as the fracture is in progress. As the final value of specific surface of particles S_∞, in the above condition, would depend upon the energy-efficiency, the author proposed the following equation: where K was termed the “Comminution Coefficient.”
Rittinger's and Kick's law and others were approximately explained by the inter-relation of K and S_∞ in this concept.
This equation was verified by grinding tests with frictional forces which took place among particles packed in a steel mortar, and with impact of the drop-weight.
From both kinds of tests for several ceramic materials, it was found out that S_∞ was proportional to 0.4 power of force, and that k_f and k_i Were constants for materials of similar type of force, independent of the numerical value, although dependent upon the capacity.
It was suggested that the ratio of k_f to k_i of each material at the same hold-up would be an important variable in comminution, which was probably fixed according to its inner structure.
The comparison of particle-size distributions of typical samples in both Kinds of grinding was briefly discussed.

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From the high-speed photographic study of velocity change of a steel ball falling on pulverized material, which experiments were intended for measuring the depth of the penetration of the ball into the material, the relation between the penetration and impact force was investigated. The result, with the theoretical analysis of the stress concentration under the ball taken into consideration, has led to the following formula representing the maximum impact stress produced in the pulverized material:
where
F: Coefficient of stress concentration
f: Coefficient of impact force
γ: Specific gravity of the ball
D: Diameter of the ball
h: Depth of the penetration
d: Mean diameter of particles
e: Void ratio
e₀: Limit void ratio
Z: Falling height of the ball
a, b, c: Constant
By this formula, many empirical facts, hitherto obtained concerning a ball-mill grinder, are explained exactly.

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The basic considerations on the designing of industrial sonic agglomeration apparatus are described in this paper. The following results are obtained from the studies.
(1) To produce a comparatively pure tone by a sound generator, the ports of the generator should be formed by circular and rectangular holes as shown in Fig. 3 (I). In this case, the percentage of acoustic energy concentrated in the fundamental wave is 96 under the condition of l=2a, where l is periodic distance between centers of adjacent ports and a diameter of circular port or width of rectangular port.
(2) The acoustic output power of a sound generator is given by where W_A is acoustic output power, C conversion factor of unit, η_A acoustic conversion efficiency, α(1+k) over-all discharge coefficient, N_q number of ports, A₀ mean opening area of a port, P₁ chamber pressure, P₂ exhaust-side pressure, T₁ temperature of gas in pressure chamber, R_G gas costant, k specific heat ratio and g acceralation of gravity.
(3) The acoustic intensity in an agglomeration tower is approximately expressed as where I is mean acoustic intensity, D diameter of the agglomeration tower and β experimental constant.
(4) The agglomeration process of aerosol particles in a sound field is given by where I_A is agglomeration index, λ agglomeration coefficient and t time.

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