The fibrograph is an optical instrument employing photovoltaic cells for scanning samples of parallel fibres and tracing a type of length- frequency curve. The theory is developed for a sample of parallel fibres in which the fibres are positioned at random. The geometrical interpreta tion of the resulting curve, or fibrogram, indicates simple length and area measurements that give various average lengths and statistical quantities, such as standard deviation and coefficient of variation. Experimental fibrograms are compared with the equivalent data derived from absolute length measurements, using a projection method. The waviness and taper of the fibres, along with other minor factors, cause the fibrogram to be too short. When the length coördinates are increased 19%, the fibrogram is equivalent to the curve obtained from absolute measurements. The instrument makes possible the rapid measurement of fibre length and fibre-length uniformity of raw fibre samples.

The values of the constant in the equation which relates permeability of a porous medium to the porosity and specific surface of the medium are determined for three cases. These experimental values are found to be consistent with the theoretical indications of Fowler and Hertel.

Kozeny's approximate solution to the problem of fluid flow through porous media is developed and the result is checked by experimental data on air flow through plugs of cotton, wool, rayon, and glass wool fibers. The solution gives WA=kγ02μ(τσ)(1−c)32c2(−δp2δx)for the isothermal linear flow of a gas. W/A is the macroscopic flux density; μ, the viscosity; γ0, the density of the gas at unit pressure; τ/σ, the volume of fibers divided by their surface area; c, the fraction of space occupied by fibers; δp2/δx, the macroscopic gradient of the square of the pressure; and k is a numerical constant which depends on the shape and orientations of the fluid passages. k was found experimentally to be 0.18, which is in approximate agreement with the value found for flow through media made up of spherical particles. The dependence of the flow on the factor c was checked over the approximate range from c=0.1 to c=more than 0.5. τ/σ and c have values for fineness and density of samples of fibers in fair agreement with independent determinations.