The differences of the languages under comparison can be appreciated most correctly by means of these three headings; but it must not be forgotten that any language may use the first and one of the last two methods, and that in languages which have a substantive verb conjugated with and without auxiliary verbs, all three may be employed. I. WHEN THE NOTION OF BEING IS EXPRESSED INDEPENDENTLY. I must except from this class all instances where the substantive verb is formed from a radical, inasmuch as this root, like any other, must assume the verbal form, and thus come under one of the two other divisions. In such case it expresses the notion of Being, either by an auxiliary, as in the German _Ich bin gewesen_, or simply in the form, as, _I am_. When it is remembered that the substantive verbs of all languages are derived from concrete conceptions and impart to these merely the general notion of Being, the above becomes still more obvious. Now if there is no root-form for the substantive verb, and yet it is expressed independently, and not by another verbal form, this can only be done either by the position of the governing and governed words, or by linguistic elements which are not properly verbs, but only become so by this use. In the former case the substantive verb is merely understood, in the latter it appears in a definite word, but without a fixed radical. 1. _When the notion of Being is understood._ One of the most common forms of sentences in American languages is to bring together an adjective and a substantive, the substantive verb being omitted. Mexican: _in Pedro qualli_, the Peter (is) good. Totonaca: _aquit chixco_, I (am) a man. Huasteca: _naxe uxum ibaua tzichniel_, this woman (is) not thy servant. In the Mixteca language such expressions have a peculiar arrangement. The adjective must precede the substantive, or rather the predicate must precede the subject, as in the reverse case the words are understood separately, and are not connected into a sentence: _quadza ñaha_, the woman is bad; _ñaha quadza_, the bad woman.