When applied in a particular language, the procedure [for describing utteances] yields a compact statement of what sequences of morphemes occur in the language, i.e. a formula for each utterance (sentence) structure in the language […].
- Harris (1946), a pag.161

6.3.RESULTANT CONSTRUCTION FORMULAE. [...] The final result, for each language which can be analyzed in this manner [positional analysis], takes the form of one or more sequences of substitution classes (‘utterance constructions’, ‘sentence type’). The formulae tell us that these are the sequences which occur. The final formulae therefore give us the limitations upon the freedom of occurrence of morphemes in the language, for they imply that no sequence of morphemes occur except those which can be derived from the formula. The utterance formulae are thus rather like the formulae for the phonetic structure of a language, and even like phonemic writing:all of these are formulae showing what occurs in the language.
- Harris (1946), a pag.178

In general, therefore, the formulae are based not only on the sequences involved but also on the suprasegmental features of the sequences substituted and of the utterances in which they are substituted. The formulae may thus correlate with phonemic junctures which express the limits of suprasegmental features.
- Harris (1946), a pag.179

The formulae also correlate with non-phonemic (structural) junctures, such as may be set up to mark the boundaries of intervals which serve as elements of the utterance structures.
- Harris (1946), a pag.179

The formulae shows what morpheme classes (or sequences) are syntactically zero, like 'Xx-' prefixes and '–Aa' suffixes in English […]; we can even learn from them that in English most prefixes, but relatively few suffixes, are syntactically zero. The formulae shows which morpheme classes occur by themselves in utterances, and which classes are bound not to other morpheme classes (as are most affixes) but to constructions, i.e. to sequences of classes: e.g. English '&' is limited to any class or extant class sequence; English 'T' is bound to a following noun phrase as a sort of phrase prefix […]; Hidatsa suffixes operate on the whole preciding word, whereas prefixes operate usually only on the immediately following stem […]. The fact that English '–Vv' suffixes ('-ed') are best added not to 'V¹' (verb morphemes) but to 'V³' (verb phrases including object, etc.), shows that '–ed' may best be regarded as a suffix of the whole verb phrase.
- Harris (1946), a pag.179

We can also learn from the formulae which morpheme classes are the heads and which are the closures of the sequences in which they appear: the closure is the class which always appears last; and the head is the class which can always substitute for the sequence, e.g. an 'N' morpheme for an 'N' –phrase sequence. The formulae can thus show which sequences are endocentric (e.g. 'A N = N') and which are exocentric (e.g. 'T A = N').
- Harris (1946), a pag.179

The formulae are devised in part on the basis of the order of classes in each sequence, and can therefore be used to show it explicitly or by means of the raised numberings. […]. They also enable us to indicate if certain classes occur always or only sometimes in a given sequence. If we write 'D A = A' and 'A N = N', and are free to apply or not to apply the results of one equation in the order, then we can derive from these equations the fact that 'N', 'A N', and 'D A N' all occur.
- Harris (1946), a pag.180

[…] the formulae in themselves are statements of selection, saying for instance that 'N V' sequences occur, but not 'N T'.
- Harris (1946), a pag.180

The formulae can be used as a source of information on the grammatical meaning of the morpheme classes symbolized in them. To do this, it is necessary to say that morpheme classes or class sequences which replace each other in various equations, i.e. which occur in identical morpheme-class environments, have similar functions or grammatical meanings Thus the 'N³' of 'N³ N⁴ Vd⁴' […] is shown to replace the 'N⁴' which is otherwise found after 'Vd' ; both of these represent the object of the 'Vd'.
- Harris (1946), a pag.180

The formulae also cannot in themselves indicate what meanings may be associated with the various positions or classes.Thus, in Hidatsa, of two formally equivalent words (with noun suffixes) before the clause-final word (which ends in a verbalizing 'F'), the first will normally indicate the subject and the second the object: 'ruwacּiri istacu ruxּiak' ‘one of them his eye opening (when one of them opened his eye)’. Such information about the meaning of positions and constructions have to be given in separate statements accompanying the formulae.
- Harris (1946), a pag.182

The formulae will also fail to give information about the complete distribution of any one morpheme, which may occur in various classes […], or about the frequency of morphemes or classes, or about the phonemic structure of various classes (e.g. the fact that Hidatsa 'F' or various English affixes are unstressed).
- Harris (1946), a pag.182