JOURNAL OF THE SOCIETY OF COSMETIC CHEMISTS determinations can be registered on one point of the graph. The graph should be inspected daily: a mere glance is often quite sufficient to see whether or not there is any widening of the spaces, which means variations in the particu- lar quality which is being assessed and the density of the marking can be mentally registered so a statistical average and trends can then easily be seen even although the analytical or laboratory method may have quite a gross error. The aim should be to narrow the variations between the dots, which means that the quality is then becoming much more regular and the height of the grouping of the dots should also be examined to see whether or not it is staying steady, going up or going down, depending, of course, on the particular property. It may be a sign of improvement if the trend is upward or, on the other hand, it may even be a fault. Certainly if it is level it means that quality in that respect is being maintained. A very good example of this method of treatment was observed in regard to a particular emulsion where complaints were received that it was not stable. Examination of the facts indicated that the emulsion had been stored in a very hot place, which was some sort of an explanation, but as complaints of this type were unusual, an investigation was carried out in order to try to find any reasons for this untoward happening. The control laboratory figures were inspected for that particular day and they showed no positive sign that anything out of the ordinary was occurring. A series of day-to- day reference specimens was then examined by incubating them at a high temperature. It was found that in certain of them the emulsion broke, while others remained stable. An inspection of the particular control values for those days on which the emulsion broke again disclosed nothing seriously amiss with the product, but on inspection of the dating of the samples it appeared that the earlier ones were more likely to break than those made at the end of the period under examination. The works control values were then examined by grouping them and determining the average values for each week, and it was then noticed that there was a slight trend in so far as the later emulsions were more finely dispersed. This gave an apparent clue to the situation and it was then discovered that the samples which lacked stability were produced on days when the output was very high, with the result that they had not been homogenised according to the standard procedure. If, however, the control values had been plotted accord- ing to the visual plan which has been outlined, this variation would have been seen and steps taken in time to have prevented any sehsibly large number of jars reaching the consumer. To sum up, therefore, I would say to those who are engaged in factory operations that they must never forget that the daily production of any given article is a form of experimentation on the majestic scale. They must remember that the observant eye can detect variations, but cannot assess them in scientific form. Numerical values are scientific, but if these values !58

STATISTICAL METHODS IN THE COSMETIC INDUSTRY are presented to the eye in proper form, correlation of many factors can readily be perceived by the eye at a speed which more orthodox methods can detect, but only long after the events have happened. In viewing the chart it is well to bear in mind that production in a factory is not an experiment carried out with that meticulous care which is exercised, or should be, in the actual laboratory and that variations are inevitable. Many of these are not within the ambit of precise control, so that the results of the majestic experiment can only be interpreted when the number of batches is large. In making observations of any series of figures, one must always have in mind what they individually mean. For example, pH values. Too often they are looked on as ordinary figures and variations are interpreted quite wrongly. To take an arithmetical mean except in certain cases in quite wrong since the pH scale is logarithmic. The mid-point between pH 7.5 and 6.5 may be 7, but half-way between pH 4 and pH 5 is certainly not 4.5. It is more like 4.26. The pH unit describes an order of magnitude and the absolute magnitude of a difference in pH value varies according to the position on the pH scale. All values and all things must be looked at in relation to their probable accuracy, their environment and their relative value. With this in mind perhaps my listeners may be asking themselves why they are looking at me ? STATISTICAL METHODS IN THE COSMETIC INDUSTRY: PART III By A. W. MIDDLETON, B.Sc., PH.D., F.R.I.C.* THE USE OF PROBIT ANALYSIS IN THE DEFINITION OF THE PARTICLE SIZE OF AN EMULSION PROBIT ANALYSIS was described in Part II of this series • and subse- quently Stanko, Fiedler and Sperandio•' have published data (Table 2 of their article, p. 43) showing the particle size distribution of seven different emulsions. Their data can be used to provide a more detailed example of the application of probit analysis than that given in Part II, and to show how the particle size of emulsions can be defined by the mean size and the standard deviation of the distribution of log diameters. An emulsion consists of a number of globules of liquid suspended in another liquid in which it is insoluble. When it is manufactured, the sizes of the globules are arbitrarily determined, dependent upon the concentration * Chesebrough Manufacturing Co., Ltd., London, N.W. 10. 159