316 Mr Sang's Analysis of the Vibratmi qf Wires. 



traces on the other are gradually dying away; and thus the 

 line appears to move gradually onwards. 



Although, in ordinary cases of vision, the light which conti- 

 nually enters the eye cause no increase of brilliancy, the im- 

 pression of the final brightness is not instantaneous. If an ob- 

 ject be viewed for a time less than sufficient for the attainment 

 of this final brightness, the intensity of the impression must de- 

 pend on the duration of the glance, as well as on the natural 

 brilliancy of the object. Wherever, then, the trajectile moves 

 more slowly, the impression of its path must be more vivid ; 

 since, from a given length of the curve, a greater quantity of 

 light is sent into the eye. The aggregate brightness of the 

 whole line making up, as it were, that of the ball when viewed 

 at rest, the optical illusion is irresistible — that the matter of the 

 line, unchanged in quantity, is merely subjected to a variation 

 in its arrangement. 



The five varieties of Fig. 1. show the successive appearances 

 of this curve at four equal intervals of time ; the variation in 

 the thickness of the lines is intended as a faint indication of the 

 varying brilliancy of the actual appearance. 



When the direction in which the ball is drawn aside makes 

 equal angles with X and Y, the whole curve is included in a 

 square ; and the ellipse, at its greatest width, becomes a perfect 

 circle. In this case, the axes of the ellipse do not vary in di- 

 rection, but, as is shown in Fig. ^, lie always along the two 

 diagonals. 



The beauty of the trajectory described by the extremity of 

 the round wire, arises chiefly from this circumstance, that its 

 successive traces lie very close together, and that the eye has 

 thus sufficient time for studying and comprehending its form. 

 Were the distance between these traces perceptible, the eye 

 would be perplexed by the rapidly changing and intricate form 

 of the curve ; and, instead of pleasure, we would have the fa- 

 tigue of an unavailing attempt to follow out its mazes. Ran- 

 dom compressions of the wire can hardly produce any fine ef- 

 fect ; but, when the times of vibration have been carefully ad- 

 justed to some simple ratio, other curves, more surprising cer- 

 tainly, and perhaps more beautiful than the ellipse, are exhibit- 

 ed. I shall examine minutely only one of these. 



