In a previous paper (Fucks, 1952, cited as I), several possibilities were outlined to describe the style of samples of literary texts by means of mathematical characteristics. The computing of practical examples, however, was confined to the most simple ones of these style characteristics. Most of them were derived from the frequency distributions of the properties of elementary units of the text themselves. It was, however, pointed out briefly, that the properties of groups of elementary units of the text can also be used to define characteristic numbers and, as an example, the values of an lik-matrix were given. To explain the aim of this paper, we assume the text to be divided into elements. The elements will be denoted by the numbers 1, 2, ..., A. It is perfectly arbitrary what parts of the text are chosen as elements: syllables, words, parts of the phrases, whole phrases, chapters, etc., or substantives, adjectives, verbs, etc., or cases of substantives, tenses of verbs, etc., or metric elements, and so on. The elements are to be considered as characterized by different marks, one or several of them for each element. These marks (or properties) can be chosen, within certain limits, in an arbitrary manner. However, to clarify our conception with the help of a special example, we shall generally in this paper, as in paper I, choose the words of a text as elements and the numbers of the syllables of the words as the interesting properties of these elements. Consequently, we shall now assume that the text is broken down into the words; and that these have been mixed together and then picked up, one after the other, perfectly at random and given the numbers 1, 2, ..., A. Theoretically, if we should repeat this procedure often enough, we should obtain the natural order of the original text as one of the different arrangements arising from picking up the words at random. We conclude, therefore, that we do not restrict the generality of our conclusions, if we start by marking the words of the text in their original order by the numbers 1, 2, ..., A. Now, let us assume that we have computed the values of pi, the proportion of the A words of a given text having i syllables and also the various characteristic numbers calculated in I, namely, i, the mean number of syllables per word; S =- E pilogpi, the 'entropy'; and i the 'trace', s. Considering these results, we ask how much of the structure of the text is described in an exact manner by these characteristic numbers. The answer is that our characteristic numbers do not tell us much more of the text than the vapour of a mixture of several fluids tells us about the fluid-structures proper, i.e. the real structure of the text does not enter into the characteristic numbers so far studied in detail. What we have taken into account with the characteristic numbers actually computed in I is the choice of a certain number, z, of words out of the reservoir V of the words of the language in which the text is written. The words enter into our characteristics as formed grammatically. But the grammatical forming process is contained in our characteristic numbers only in a rudimentary