S04 Strehlke on the Acoustic Figures of Plates. 



side, whilst the vibration is produced at the middle of a side. 

 It consists of the two branches of a hyperbola, the principal 



Fig. 14. 



Fig. 15. 



Fig. 16. 



axis of which is in the direction of A B in Fig. 2, and of the 

 ellipse F F and D D', of which D and D' are smaller than 

 F and F. 



On the brass plate No. 2, F and e were taken as the com- 

 mencement of the co-ordinates, and the equations for the two 

 ellipses were 



y* = 5-3477 + 1-6366 . x - 0-6725 a? 

 and y 2 = 2-8798 . x (11"'-01 - *) 



Fig. 14 is formed by supporting the plate at A C B D, so 

 that D B = A B ; and by producing the vibration in E, the 

 long axis of A C B F, and of the central ellipse, is in the same 

 direction as the principal axis of the hyperbola in Fig. 2. On 

 the brass plate No. 2, the figure was not quite closed at 

 A and B. 



Figs. 11 and 12 may further be transformed into Figs. 15 and 

 16: if the plate is supported at A B, and at a point of the 

 diagonal perpendicular on A B, at the distance of A B from 

 S, and the vibration is produced at E, E S being = -| A S. 

 In either case the ellipses of Figs. 11 and 12 seem to be 

 changed into hyperbolas, the principal axis of which is either 

 perpendicular to the diagonal A B (Fig. 15), or parallel to it. 

 The equation for D C (Fig. 15) was found to be 



2/ 2 = 80-546 . 1-7848 x - 0-9485 x*. 

 Fig. 6, which will be easily recognised as the repetition of a 

 more simple figure, is produced when the plate is supported at 



