After an apposite discourse to introduce the subject, the first course taken, was to demonstrate the advantages of understanding the right use of geometrical terms in our descriptions of the varieties of shape, both in nature and art. Every thing deserving the title of beautiful, and every grand object, assume an outline of definite character: these are to be found in the different classes of geometrical figures; the former in undulating lines of elliptic curves, and grandeur in angular dispositions of figure. All motion assumes a curved direction[1]. The primary and leading object of the discourse was to prove the fact of original beauty: and that a curved line was beautiful in an abstract point of view, free from all associations. For this purpose there were designed many diagrams on large black painted boards. [p002] The explanation commenced with six or more parallel lines at equal distances, and equal length, in an horizontal position to the eye of the audience, _Fig._ 1; and another set of the same number of lines drawn perpendicular, _Fig._ 2: these were demonstrated to possess not the slightest character or principle of beauty in them, either as separate lines, or collectively, however many. [Illustration: _Fig._ 1.] [Illustration: _Fig._ 2.] [Illustration: _Fig._ 3.] [Illustration: _Fig._ 4.] The next diagram consisted of six or more radiating lines from a centre, _Fig._ 3, and a corresponding number in an horizontal direction, but of unequal quantities; they diminished like a flight of steps, _Fig._ 4. It was then shown that the first means of combining the six or more lines, which had been first drawn, so as to please the eye, without creating any geometrical figure, was the radiating principle. Our eye not only can tolerate that union of lines, but receive the impression as pleasing in character; while all lines parallel to each other, being right [p003] lines, and viewed as a flight of steps, or pile of planks, opposite the observer, are disagreeable. Upon the former principle it is, that the rays of the sun, and rays of light generally, are so attractive and beautiful. It is from this circumstance that right lines drawn in an inclined position to the plane of the picture, derive an interest from the angles engendered through the imagination. [Illustration: _Fig._ 5.] [Illustration: _Fig._ 6.] [Illustration: _Fig._ 7.] [Illustration: _Fig._ 8.]