the Combination of Rectangular Vibrations. 219 



combination of 1 to 1 is obtained, and the bead describes a circle 

 passing into an oblique line ; but on opening the free limb to 

 an angle of about 30°, the figure changes into the complex curve 

 given by the ratio of 4 to 5. Opening the angle still further, 

 the curve expressing the ratio of 3 to 4 is obtained ; then at 

 45° 2 to 3; and at an angle of 75° the figure of 8 comes out, ex- 

 pressing the ratio of 1 to 2. In fact, by varying the angle an 

 entire series of combinations, more or less perfect, can be pro- 

 duced at will. 



In order to avoid the probable breaking of the wire by re- 

 peated bendings, I had a light hinge joint made at the bend ; 

 but it was less satisfactory than the simple bent wire, which, if 

 well annealed, will bear innumerable bendings, and can be re- 

 newed in a moment if broken. To obtain a steady figure, it is 

 better to make the final adjustment by slightly raising or de- 

 pressing the fixed wire. 



Fig. 1. Fig. 2. 



Figure 1 shows the instrument. The wire is capable of being 

 firmly fixed at any height in a support which is attached to a 

 heavy stand, more convenient in use than a vice. 



Not only may this arrangement be used for exhibiting the 

 combination of vibrations, but it also shows very prettily the for- 

 mation of nodes and ventral segments. Placing a piece of white 

 paper behind the instrument, or casting its shadow on a screen, 

 the vibration of the wire may be distinctly seen by a great 

 number of people. The fixed arm will then be noticed always 

 to vibrate as a whole, and the bend always to be a ventral 



segment. 



But on the free arm an instructive change is seen to take place 

 in the position of a node which is there formed. When the 

 arms are equal and parallel, and a ratio of 1 to 1 obtained, the 



