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PROCEEDINGS OF THE AMERICAN ACADEMY. 



with a very light coating of smoke was drawn under it by hand while 

 the wire was vibrating. The resulting curve shows the displacement of 

 the given part of the wire as a function of the time, and it can be proved 

 that a single curve of this kind, together with Young's law, is enough 

 for the complete determination of a vibration form. A number of these 

 curves, corresponding to the three simplest alicpiot cases, are reproduced 



Figure 4. The case J. The upper figures show the configurations of the 

 string at intervals of T/12, the first from to T/S, and the second from Tj 3 to 

 2T/Z; the return to equilibrium is through forms symmetric to those of the upper 

 figure. The lower figures show the motion of the points \, \, and \. 



photographically, much enlarged, in Figure G, and their resemblance to 

 the calculated curves of Figures 3, 4, and 5 is another and a final verifica- 

 tion of the conclusions of the last two sections. 



This section will describe a number of observations which have been 

 made by this method to test Krigar-Menzel's law for the simpler rational 

 cases. It will be remembered that, according to this law, the motion of 

 the point bowed in the rational case p/q, is an ascent with a constant 



