63 SECTION PHYSICS. 



exactly as in the case of cylindrical rods, and the partial vibrations 

 bear the same relation to the fundamental vibrations with rectangular 

 rods, which are not square in section, the number of vibrations will 

 depend on and be proportional to the thickness of the rod in the 

 direction in which the vibrations take place. If we increase that thick- 

 ness, we shall increase the number of vibrations in a given time ; if 

 we double the thickness, the number of vibrations will be twice as 

 many, and so, causing the rod to oscillate in one plane or in the other, 

 we shall get in the direction of the greatest thickness, the greatest 

 number of vibrations ; and if the length of the rod is such as would 

 produce musical tones, then the tone corresponding to the greatest 

 thickness will be the octave of the tone corresponding to the least 

 thickness, when the thickness in one direction is twice as great as in 

 the other. 



We may pass on from an ordinary rod of this kind, gradually 

 thinning away in one direction, and if necessary, thickening a 

 little in the other, and we pass to a thin reed or vibrating strip of 

 metal fixed at one end, and placing that in an opening, we get the 

 " free reed." It is only necessary to mention the free reed to recall 

 again the name of Sir Charles Wheatstone, who developed it so 

 much, and applied it, or caused it to be applied, to so many instru- 

 ments. The figures traced out by these kaleidophones, when they 

 are of different diameter in different directions, are very well known, 

 and may be produced in various ways. There are many pieces of 

 apparatus in the Exhibition which will show this. If the point 

 of suspension of one pendulum be attached freely to the bob of another 

 pendulum, so that they can swing in planes at right angles to one 

 another, and the two are set in vibration, then the bob of the lower 

 pendulum will trace out a curve which results from the two motions : 

 the same curves may be traced out by Mr. Tisley's beautiful appara- 

 tus, having two pendulums vibrating in planes at right angles to one 

 another, which are placed at the corner of a table, one at the end and 

 one at the side, so that the oscillations take place in two planes, 

 at right angles to one another, a point connected with both pendulums 

 will trace out the curves. By altering the length of the pendulum 

 or the times of oscillation, we may get a variety of different curves, and 

 may make the times of oscillation so nearly coincident as to produce 



