Most methods of diagramming are based on the work of Alonzo Reed and Brainerd Kellogg in their book Higher Lessons in English, first published in 1877, though the method has been updated with recent understanding of grammar.
Reed and Kellogg were preceded by, and their work probably informed by, W. S. Clark, who published his "balloon" method of depicting grammar in his 1847 book A Practical Grammar: In Which Words, Phrases & Sentences are Classified According to Their Offices and Their Various Relationships to Each Another. (For a discussion and description of Clark's balloon architecture, see Chapter 2 of Kitty Burns Florey’s book listed in Further Reading below.)
In recent years, the Reed-Kellogg system has somewhat fallen out of use among linguists. While some teachers continue to use the Reed-Kellogg system, others have discouraged it in favor of the tree diagram, which orders words differently. X-bar theory is considered to be a more accurate representation of the structures upon which the rules of natural-language syntax operate.
Reed and Kellogg defend their system in the preface to their grammar:
The Objections to the Diagram.--The fact that the pictorial diagram groups the parts of a sentence according to their offices and relations, and not in the order of speech, has been spoken of as a fault. It is, on the contrary, a merit, for it teaches the pupil to look through the literary order and discover the logical order. He thus learns what the literary order really is, and sees that this may be varied indefinitely, so long as the logical relations are kept clear.
The assertion that correct diagrams can be made mechanically is not borne out by the facts. It is easier to avoid precision in oral analysis than in written. The diagram drives the pupil to a most searching examination of the sentence, brings him face to face with every difficulty, and compels a decision on every point.
Modifiers of the subject, predicate, or object are placed below the base line. Adjectives and adverbs (including articles) are placed on slanted lines below the word they modify. Prepositional phrases are also placed beneath the word they modify; the preposition goes on a slanted line and the slanted line leads to a horizontal line on which the object of the preposition is placed. Compound subjects, predicates, objects, etc. are drawn as multiple horizontal lines stacked vertically, joined at each end by a fan of diagonal lines; the coordinating conjunction goes on a vertical line through the left ends of the horizontal lines.
Compound sentences are composed of two independent clauses connected by a coordinating conjunction. Each clause is diagrammed separately; the verbs of the two clauses are joined by a dotted line which goes vertically, then horizontally with the conjunction written on the line, and then vertically again.
Any adjectives or prepositional phrases modifying the participial branch off of the small horizontal line, as if the participle were a noun.
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