SAMPLING AND ASSESSMENT OF POWDER MIXTURES 261 random sampling offers the most useful approach. In the example quoted, if the million tablets are contained in a single large drum it would be necessary to select tablets as samples from random points in the drum. These points in the drum •vould previously be designated with numbers and the selection of sampling points achieved by consultation with tables of random numbers. Sampling may be most beneficially achieved by a common-sense approach and comparing the use of the powder mixture or its next stage in processing with the method of sampling. Thus in the production of tablets, sampling is best achieved by taking individual tablets as individual spot samples, since the tabletting may be regarded as a sampling operation. It may be argued that machine vibration, etc. will cause a sampling bias by influencing segregation to occur within the hopper. However, all sampling operations are liable to promote some segregation and it is far more expedient to examine the final product than to use other techniques in this case. For pigment powder mixtures intended for cosmetic use, samples may be taken and examined by reflectance techniques. Sampling here may be achieved with the use of the more conventional thief or the reflectance measured directly using a light-probe technique (1) to sample the pigment mixture in situ. Much has been written on the subject of the sample size or unit of scrutiny. Poole, Taylor and Wall (2) found a relation between the observed coefficient of variation between sample concentrations C, and the number of particles taken in each spot sample N. log C=m log N+constant where the value of m has the value of --0.5 for completely randomized mixtures and zero for completely unmixed systems. These limiting con- ditions had earlier been described by Lacey (3) for binary mixtures of uniform powders, thus the standard deviation of sample concentration for an unmixed system, %, is given by C•o,-(xy) t and that for a randomized mixture, (•R, by •R = (xy/N)'• where x and y are the proportions of the two ingredients in the mixture. Since a statistical measure of variation in sample concentration is dependent upon the number of particles and hence the size of the sample, the scale of scrutiny must be set at the unit of the mass that is to be used either by a consumer or at the next stage of processing. In the case of

262 JOURNAL OF THE SOCIETY OF COSMETIC CHEMISTS t)harmaceutical tablets this unit of scrunity, therefore, consists of a single tablet. Train (4) in making this point, showed the errors that may arise in taking 20 or even 80 tablets for the assay sample. Thus a 10% variation of a sample of 20 tablets may mean a 40}/0 variation between individual tablets and for a sample of 80 tablets, this individual variation could be as high as 90%. However, before deciding on this unit of scrutiny the purpose of the sampling must also have been considered. In the example quoted, in order to determine the variation between individual doses, single tablets must be taken for individual samples. If the purpose of the sampling was to measure the mean content of drug in the tablets then samples of 80 tablets or even more should be taken and the bulk assayed. Where this bulk is large com- pared with that necessary for analysis it may be necessary to divide the sample. This may be achieved by dissolving the whole sample and taking an aliquot portion for analysis, but where this is not possible, care must be taken to ensure a correct division of the sample by size reduction of the component particles. When sampling cosmetic powders, an area of scrutiny suggests itself as a more probable unit, since the powder mixture will probably be used as a thin film of just a few, at most, particles in depth. The problem here is to avoid agglomerates of either pigment or diluent particles that would be shown by the so called "draw-down" test. Agglomeration of single com- ponents effectively reduces the number of particles, N, in the spot sample giving a larger measured coefficient of variation in the Poole, Taylor and Wall diagram. It may be necessary to overcome such tendencies towards agglomeration by using mixing machinery which also incorporates features bringing about size reduction in the preparation of such powder mixtures as described by Brock {5). ASSESSMENT OF POWDER MIXTURES In order to assess the powder mixtures, a number of mixing indices have been proposed. The basis of the majority of these involves the comparison of the measured standard deviation of sample concentration {s) with the estimated standard deviation of a completely randomized mixture Allowance may also be made for the standard deviation of a completely unmixed system (•o)' The utility of the standard deviation of the ran- domized mixture has been extended to mixtures of non-uniform powders by the Poole, Taylor and Wall (2) modifications to the formula of Stange (6)