COMPLETE TITLE: The Art of Acting. Part I. Deriving Rules from a New Principle, for Touching the Passions in a Natural Manner. An Essay of General Use, to those, who hear, or speak in Public, and to the Practisers of many of the Elegant Arts; As Painters, Sculptors, and Designers: But Adapted, in Particular, to the Stage: With View to quicken the Delight of Audiences, and form a Judgment of the Actors, in their Good, or Bad, Performances. 

The Art of Acting, a 416 line poem, was Aaron Hill's last version of his theories on acting before the Essay on the Art of Acting (see).
The text, published in 1746 as the first section of a work that in the intention of the author was to be more extensive, was republished in the third volume (pp. 387-408) of The Works of the Late Aaron Hill, Esq.; In Four Volumes. Consisting of Letters on Various Subjects, And of Original Poems, Moral and Facetious, With an Essay on the Art of Acting (London, Printed for the Benefit of the Family, 1753; second edition: London, Printed for the Benefit of the Family, 1754).
Online text (1753 edition): Vol. I - Vol. II - Vol. III - Vol. IV