508 JOURNAL OF THE SOCIETY OF COSMETIC CHEMISTS sitivities of the three visual colour receptors (the so-called colour matching functions). Colour can also be measured by various pieces of apparatus, types of calorimeter, which abbreviate the calculation method. It must be admitted that there is not yet complete certainty as to the true values of the response functions of the receptor mechanisms, but they can be con- ventionally evaluated in terms of standard conditions of observation as colour matching functions, which give all that is necessary for the speci- fication of colour in terms of chromaticity and luminance for the normal or "standard" observer. The system set up by the Commission Inter- ß nationale de l'Eclairage has many convenient features and is almost universally used: Fig. 8 shows the colour matching functions of the system, Fig. 9 the chromaticity diagram in which the calculated or measured values are usually exhibited. 2O 1'6 14 1'7--- •.o o.s 0.6 0----/ , 400 500 600 700 Wavelength, nm Figure 8 The CIE colour matching functions: these are analagues to the response functions, but adapted to the purposes of chromaticity measurement. The first deduction from this specification of colour is the nature and finite extent of "colour space": no colours can be more saturated than the spectral colours and the "purple boundary" which joins the red and violet

EYESWEET AND COLOUR SCIENCE IN COSMETICS 509 ends of the spectrum locus on the chromaticity diagram. Among surface colours none can be lighter than the perfect white diffuser, which reflects all that falls upon it, or darker than the perfect black, which reflects nothing. A little thought shows that within this colour space there can only be a finite number of colours which the eye can distinguish. This follows because there is a limit to the smallness of colour difference which the eye can detect, often called the threshold or limen of perception. Thus colour space can be thought of as occupied by a number of cells, like those of a honey- comb but extending in all directions, each cell having a diameter equal to the threshold of colour difference perception. One has only to divide the volume of colour space by the volume of a cell to obtain the total number of distinguishable colours. In practice this is not so simple as it sounds, since the size of cell is not constant and no linear distortion of colour space will make it so. Experimental determinations of cell size are also far from com- plete, but a fairly reliable estimate was made by Nickerson and Newhall (8). The figure was 7• million colours, just distinguishable by highly skilled observers under the best possible conditions. This number is to be divided by four to give the number of easily distinguishable colours, then by eight to give the number in the pigment range, then by two to give the probable number of colours which are of cosmetic interest (although it is becoming increasingly doubtful whether there is such a thing as a colour which is not of cosmetic interest). The result is of the order of 100,000. Even this reduced number is very large and it may be that cosmetically different colours are more widely spaced than has been assumed above. It is clear, even so, that the cosmetic chemist is concerned in the pro- duction and control of a rather large number of colours and the question arises whether the techniques of colour measurement could be of any assistance. The best photoelectric colorimeters can distinguish colour differences which are imperceptible to the eye, but their absolute accuracy is poor: they excel at measuring differences, so that the method of appli- cation to colour control would be the measurement of differences between test samples and an appropriate permanent standard, such as a glazed ceramic tile, selected from a limited number which cover the field of interest. These standards would be calibrated once for all by careful spectrophoto- metry, followed by calculation of chromaticity. These methods of exact colour measurement are not only appropriate to quality control during manufacture they also form the basis of colour formulation for the production of new colours, i.e. the empirical relation between a chromaticity desired for fashion reasons and composition in