Sample weight mean diameter, g(n)=ⁿΣ_i=1x_i⁴/ⁿΣ_i=1x_i³ is a biased estimate of population weight mean diameter, Γ=∫₀^∞x⁴f_x(x)dx/∫₀^∞x³f_x(x)dx Results of Monte Carlo simulation with a truncated log-normal distribution, which resembles actual particle size distribution, indicate that bias of g(n) is generally less than 10% of Γ, when sample size, n, is larger than about 50.
The correlation for relatively small bias, -B{g(n)}/Γ=Φ[D²(x³)/n{E(x³)}²] which was obtained from results of simulation with some other parent populations of x can be applied a also to the case of truncated log-normal distribution.
An approximate eqation, B{g(n)}/Γ=-1/n[E(x⁷)/E(x⁴)E(x³)-E(x⁶)/{E(x³)}²] has been derived through a theoretical consideration with no restriction of particle size distribution. This equation can be rewritten into the same form with the former experimental correlation.
With this theoretically derived approximate equation, one can calculate bias of sample weight mean diameter of an arbitrary size distribution.

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This paper deals with the requisite air pressure to blow off the plugged granular layer in pipes. A theoretical equation as to the requisite air pressure, associated with the length of the plugged layer in various kinds of pipes, is presented. In experiments polyethylene pellets were used as the plugged granular material, and acrylic straight pipes as well as six kinds of bend pipes, whose inner diameter consisting of 25, 50, 77 and 100mm, were used as test pipes.
Experimental results regarding the requisite pressure to blow off the plugged materials in pipes were summarized in the following:
(1) Less air pressure was required for the pipe of smaller ratio of curveture radius to the inner diameter.
(2) In case of vertically arranged pipes the requisite air pressure was independent of the pipe diameter, whereas highr air pressure is required for the pipes of smaller diameters when pipes are arranged horizontally.
(3) The negative pressure operation and the positive pressure operation in the present experiments exhibited similar characteristics concerning the relation between the requisite air pressure and the plugged layer's dimensions.

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Investigating ball mill grinding from the kinetic point of view, the authors studied the effect of properties of samples and feed weight on grinding rate constant of first order.
Used samples were silica glass, borosilica glass, soda glass, quartz, feldspar, limestone, marble, gypsum and talc. The pebble mill consisted of a 12.8cm-diameter by 13.2cm-long cylinder, and the tests were done at the speed of 88.1% of critical one. The grinding medium was 40 balls, each of which has a diameter of 3cm and their total weight was 1180g.
The experiments were performed on -14+20 mesh feed size to obtain grinding rate constant K. The following correlation of dimensionless Vickers hardness H_V and K was obtained K∝H_V^-0.23
Futhermore, dimensionless feed weight W had large effect on grinding rate constant K, and the correlation of H_V, W and K was obtained K∝H_V^-0.23·W^-1.5

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Regression equations for controlling sand mixing units in casting process by a small-scale on-line computer are presented. Exponential smoothing method is used jointly to predict slow variation of sand properties, resulting in reducing storage requirement for control computer.
Controller consists of two hierarchial computing systems; an off-line large scale fast computer and a small scale on-line computer (mini-computer). The former revises the regression coefficients in a daily mode, by which the latter decides steering variables for the day's operation.
Experiments are carried out in some commercial plant. The results do not show any observable differences between the usual operation by human controller and computer controlled experiments.

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