_sung_ and _song_; change of consonant as in _dead_ and _death_; change
of accent; actual abbreviation). Each and every one of these types of
grammatical element or modification has this peculiarity, that it may
not, in the vast majority of cases, be used independently but needs to
be somehow attached to or welded with a radical element in order to
convey an intelligible notion. We had better, therefore, modify our
formula, A + b, to A + (b), the round brackets symbolizing the
incapacity of an element to stand alone. The grammatical element,
moreover, is not only non-existent except as associated with a radical
one, it does not even, as a rule, obtain its measure of significance
unless it is associated with a particular class of radical elements.
Thus, the _-s_ of English _he hits_ symbolizes an utterly different
notion from the _-s_ of _books_, merely because _hit_ and _book_ are
differently classified as to function. We must hasten to observe,
however, that while the radical element may, on occasion, be identical
with the word, it does not follow that it may always, or even
customarily, be used as a word. Thus, the _hort-_ "garden" of such Latin
forms as _hortus_, _horti_, and _horto_ is as much of an abstraction,
though one yielding a more easily apprehended significance, than the
_-ing_ of _singing_. Neither exists as an independently intelligible and
satisfying element of speech. Both the radical element, as such, and the
grammatical element, therefore, are reached only by a process of
abstraction. It seemed proper to symbolize _sing-er_ as A + (b);
_hort-us_ must be symbolized as (A) + (b).

[Footnote 1: We shall reserve capitals for radical elements.]

[Footnote 2: These words are not here used in a narrowly technical
sense.]