Mr Sang's Analysis of the Vih'ation of Wires* 315 



the rectangle towards C, but reaches the side CD previous to 



its reaching BC, by the time — The curve must therefore 



n 



touch BC at a distance from C, denoted by h ver -. Leaving 



n 



this point of contact, the trajectile will reach the side AD at a 



distance from A, denoted by b ver — . In this way the 



'' n 



straight line is slowly converted into an ellipse, which goes on 

 dilating itself until, when the number of vibrations has amount* 

 ed to i n, the points of contact have reached the middles of 

 the sides of the rectangle. After this, the ellipse slowly col- 

 lapses, and at last merges into the straight line DB ; thus ex- 

 hibiting all the phases that were obtained, by supposing v to 

 pass through all values from O to U. From this position the 

 ellipse again gradually expands, the points of contact returning 

 along the sides of the rectangle ; but there is this remarkable 

 distinction between the motions, that the movement, which was 

 at first sinistral, has now become dextral. 



When there is any considerable disparity between the stiff- 

 ness of the wire in the two principal directions, there is no dif- 

 ficulty in recognising them. A careful attention to the pheno^ 

 mena above described, enables us to detect them, however small 

 the difference may be. The directions of greatest and least 

 flexibility evidently bisect the angles made by the crossing of 

 the two diagonals : these, then, are at once found ; but we have 

 yet to determine which is the direction of greatest, which that 

 of least, flexibility ; and for this we have only to notice, that 

 the contacts of the trajectory, with the two sides parallel to the 

 direction of least flexibility, always move along those sides in 

 the same direction with the motion of the trajectile. 



Since the impression which light makes upon the retina of 

 the eye endures for about the fifth part of a second, the im* 

 pressions of several complete circuits must be co-existent. Did 

 the trajectile retrace accurately the same path, that would ap- 

 pear an immoveable ellipse of light ; but since at each new re- 

 volution it departs a little from its former course, the aggregate 

 line must receive continual accessions on the one side, while the 



