FINE PARTICLES IN THE COSMETIC INDUSTRY 193 about fifteen diameters. There is no doubt that from this point of view the more dilute the suspension the better. However, 1 per cent concentration, whilst not ideal, does not give rise to errors approaching the overall error inherent in the method. The 1 per cent concentration is about the minimum to allow of reasonable accuracy in the weighing of the sampled fractions. The overall error in determinations of particle size by the Andreasen method has been estimated as =k 0.5 per cent. This may be true for an expe•t operator. The error may vary somewhat with the nature of the material. I would put the figure for a good operator as :• 1.5 per cent. One important feature of the Andreasen method which must be stressed is the necessity for close temperature control during the determination. Slight changes of temperature at the outside wall of a column will set up convection currents which will completely invalidate the method for the finer particles. Andreasen points out that convection hazards are less troublesome with more concentrated suspensions and considers this another point in fayour of using a suspension of initial concentration as high as 1 per cent. It has been considered that the zone of suction around the immersed tip of the pipette is far too widespread. It should, of course, be kept to a minimum by very careful steady suction at the time of sampling the suspen- sion. Even so, the withdrawal of the sample should not take longer than 15 seconds for water, and a little longer for more viscous fluids. Two other small points, but important ones' the column should be vertical and the determination carried out in a place free from vibrations. PARTICLE SIZE Having said so much of the measurement of particle size we come to the problem of what is the size of a particle ? As far as the microscope is concerned a particle on a slide will tend to rest with its smallest dimension in the vertical plane. The particle is normally viewed in silhouette so that one sees the projected area. The usual method is to match this area to a sphere of the same area or to a circumscribing rectangle, and the particle size is described in terms of such references. Where many particles have to be measured the dimension termed a statistical diameter is sometimes used. This is the length of the line bisecting the projected area of t,•he particle as it lies on the slide, and read off in the same direction for all particles measured. The particle size may also be described as the diameter of a sphere of the same surface area as the particle or again as the diameter of a sphere of volume (or weight) equal to that of the particle. In the case of sedimenta- tion methods, Stokes Law, of course, refers to spheres. Here the usual description of particle size is the diameter of a sphere of the same density

194 JOURNAL OF THE SOCIETY OF COSMETIC CHEMISTS as the particle which falls at the same speed as the particle. (This is the "diameter" used in Stokes Law above.) Correlation of these different descriptions of particle ,size have been made in some cases. They involve the establishment of shape factors for the particles. For instance, the total iurfaces of stones have been measured by wax dipping and their volumes by displacement in a fluid. In this way correlation may be obtained between an equivalent surface diameter and an equivalent volume diameter. This ratio may be considered to be constant for a given material in that it tends to fracture in a set way. For large particles of the size of pebbles the ratio does hold over quite a range of size. But whether this can be extended down to particles of 20 microns or less is debatable. Uneven particles have been classified to simulate a small number of geometrical shapes and this offers some means of assessing shape factors. AGGLOMERATION AND DISPERSION Particulate matter, particularly of 5 microns and finer, when placed in a liquid medium, may coalesce into agglomerates of particles. Where this occurs in sedimentation methods a clump of particles will behave as if it were one large particle, giving completely erroneous results. Checks should be made that the material does not coalesce in the liquid selected., Parallel trials should be made using a series of liquids and the one settling most slowly taken as free from agglomeration. Many effective dispersing agents have been used to combat agglomeration and references are dotted about through the literature. They seem to be specific for some materials. There does not seem to have been any systematic investigation of this phenomenon. It would seem that at least two factors are involved--wetting of the particles and electrostatic charges. Perhaps in some cases a wetting agent is also a good dispersing agent. There is no universal dispersing agent although sodium hexametaphosphate and pyrophosphate (0.001 to 0.01 per cent weight/volume of suspension) are useful in many instances. Other dispersing agents in common use are such compounds as sodium silicate, potassium citrate, sodium oxalate. Failing these there are many suitable organic liquids which are listed in the literature for specific materials. Some variation in dispersibility may occur in the case of natural minerals which may contain small, variable amounts of soluble salt occlusions, and in materials •vhich are themselves slightly soluble in the liquid selected. In conclusion, I would say that the work on particle size analysis has been increasing over the past ten years, as indicated by the symposia and conferences organised on the subject, notably in this country by Society of Chemical Industry, Institute of Mines and Metallurgy, and most recently by the Institute of Physics. The latter conference produced some clarifying concepts of the relative motion of particles and fluids, on light scattering by particles .and on particle shapes. It was also shown that the tiring work