VOL. XC.] PHILOSOPHICAL TRANSACTIONS. ()25 



son, their repetition in a connected chain of inference may still be excusable. I 

 am persuaded also, that at least some of the positions maintained are incontrover- 

 tibly consistent with truth and nature; but should further experiments tend to con- 

 fute any opinions here suggested, I shall relinquish them with as much readiness as 

 I have long since abandoned the hypothesis which I once took the liberty of sub- 

 mitting to the R. s., on the functions of the crystalline lens. 



Explanation of the Figures in Plates 9 and 10. — Figs. 1 — 6 ; The section of a stream of air from a 

 tube .07 inch in diameter, as ascertained by measuring the breadth of the impression on the surface of a 

 liquid. The pressure impelling the current, was in fig. 1, 1 inch. Fig. 2, 2. Fig. 3, 3. Fig. 4, 4. 

 Fig. 5, 7. Fig. 6, 10. 



Figs. 7 — 12; A similar section, where the tube was .1 in diameter, compared with the section as in- 

 ferred from the experiments with 2 gages, which is represented by a dotted line. From this comparison 

 it appears, that where the velocity of the current was small, its central parts only displaced the liquid; 

 and that where it was great, it displaced, on meeting with resistance, a surface somewhat greater than 

 its own section. The pressure was in fig. 7, 1. Fig. 8, 2. Fig. 9, 3. Fig. 10, 4. Fig. 11, 7. 

 Fig. 12, 10. 



Figs. 13 — 20; a, the half section of a stream of air from a tube .1 in diameter, as inferred from ex- 

 periments with 2 water gages. The pressure was in fig. 13, .1. Fig. 14, .2. Fig. 15, .5. Fig 16, 1. 

 Fig. 17, 3. Fig. 18, 5. Fig. 19, 7. Fig. 20, 10. The fine lines, marked b, show the result of the 

 observations with an aperture .15 in diameter opposed to the stream; c with .3; and d with .5. 



Figs. 21 — 23; a, the half section of a current from a tube .3 in diameter, with a pressure of .5, of 

 1, and of 3. b shows the course of a portion next the axis of the current, equal in diameter to those 

 represented by the last figures. 



Fig. 24 ; The appearance of a stream of smoke forced very gently from a fine tube. Fig. 25 and 26, 

 the same appearance when the pressure is gradually increased. Fig. 27; see section 3. Fig. 28, the 

 perpendicular lines over each division of the horizontal line show, by their length and distance from that 

 line, the extent of pressure capable of producing, from the respective pipes, the harmonic notes indi- 

 cated by the figures placed opposite the beginning of each, according to the scale of 22 inches parallel to 

 them. The larger numbers, opposite the middle of each of these lines, show the number of vibrations 

 ©f the corresponding sound in a second. 



Figs. 29 — 33; see section 10. Fig. 34, the combination of 2 equal sounds constituting the interval 

 of an octave, supposing the progress and regress of the particles of air equable. Figs. 35, 36, 37, a 

 similar representation of a major 3d, major tone, and minor 6th. Fig. 38, a 4th, tempered about 2 

 commas. Fig. 39, a vibration of a similar nature, combined with subordinate vibrations of the same 

 kind in the ratios of 3, 5, and 7 . Fig. 40, a vibration represented by a curve of which the ordinatesare 

 the sines of circular arcs increasing uniformly, corresponding with the motion of a cycloidal pendulum, 

 combined with similar subordinate vibrations in the ratios of 3, 5, and 7. 



Figs. 41 and 42 ; Two different positions of a major 3d, composed of similar vibrations, as represented 

 by figures of sines. Fig. 43; a contracted representation of a series of vibrations, a, a simple uniform 

 sound, b, the beating of 2 equal sounds nearly in unison, as derived from rectilinear figures, c, the 

 beats of 2 equal sounds, derived from figures of sines, d, a musical consonance, making by its fre- 

 quent beats a fundamental harmonic, e, the imperfect beats of 2 unequal sounds. Fig. 44, various 

 forms of the orbit of a musical chord, when inflected, and when struck. Fig. 45, forms of the orbit, 

 when the sound is produced by means of a bow. Fig. 46, epitrochoidal curves, formed by combining a 

 simple rotation or vibration with other subordinate rotations or vibrations. Figs. 47 and 48, the succes- 

 sive forms of a tended chord, when inflected and let go, according to the construction of La Grange and 

 Euler. Fig. 49, the appearance of a vibrating chord which had been inflected in the middle, the 

 strongest lines representing the most luminous parts Fig. 50, the appearance of a vibrating chord, 

 when inflected at any other point than the middle. Fig. 51, the appearance of a chord, when put in 

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