OF ARTS AND SCIENCES. 219 



ing numbers represent one of several measurements which I made on 

 wire of the same diameter : — 



Wire 100 cm. in length 2 waves to 5 mm. 



" 50 cm. " 4 " " 



Thus the wave lengths were found to be proportional to the lengths 

 of the wire. The interference of waves in an elliptical vessel, caused 

 by producing the vibrations at the two foci, and described by the 

 brothers Weher in their Wellenlehre, can be beautifully shown by this 

 method. 



No. XVII.— VIBRATIONS OF CIRCULAR AND ELLIPTI- 

 CAL PLATES. 



By Francis E. Cabot. 



Presented May 14, 1879. 



The experiments from which the results given in the following 

 paper were obtained were made with the idea of finding out whether 

 a change in the ellipticity of a plate would have any effect on the 

 nodal lines of such a plate. , 



I had seven plates of the same material, of equal thickness: one was 

 a circle with a diameter of eight inches, and the others were ellipses, 

 all having their major axes eight inches in length, and their minor 

 axes decreasing, each by an inch, from seven to two inches in length. 

 The ellipses I clamped close to the edge at both extremities of the 

 minor axis. They were bowed at one extremity of the major axis. 

 The circle was clamped close to the edge, at both extremities of a 

 diameter, and bowed at 90° from the clamp. 



Under these conditions, the nodal lines gave a series of similarly 

 situated curves, which changed their curvature and position corre- 

 spondingly to the change in the ellipticity of the plates. The circle 

 gave a star-shaped figure with six points connected by curves of nearly 

 equal curvature (Fig. 1). The ellipse whose minor axis was seven 

 inches in length gave a line nearly an inch in breadth from the clamp 

 to the point of clamping with two whose ends were equally distant 

 from the major axis at the edge of the plate (Fig. 2). The curves, as 

 we see by the figures, are of nearly the same curvature as the curves 



