Strehlke on the Acoustic Figures of Plates. 303 



If the plate, instead of being supported, is fixed between a 

 screw at a point distant about one fourth of the side from it, 

 and half of the side from the edges, a remarkable transversion 

 of the Figs. 9 and 10 take place. Suppose two lines drawn 

 through the above point, parallel to the sides of the square, 

 and the four right angles to be 1, 2, 3, and 4 : if the plate is 

 fixed in angle 1, at the distance of a few lines from the point 

 of intersection, Fig. 9 will be formed ; if in angle 2, it will be 

 Fig. 10 ; in angle 3, Fig. 9; and in angle 4, Fig. 10 again : this 

 is always the case, and it is not even necessary that the point 

 where the plate is fixed should be always exactly at the same 

 distance from the point of intersection ; the distance of the 

 curves from each other only will be changed. 



The measurement of Fig. 12, on the copper plate No. 3, led 

 to the following result : e was considered as the commence- 

 ment of z and y, and the equation of the curve on the copper 

 plate No. 3 was 



?/ = 0-8904 . (143-2 - z 2 ) ; 



the calculation of y from which was found pretty nearly to 

 correspond with the result of observation. 



On the brass plate No. 1, the expression of the curve was 



2/2 = 0-899 . (144-8 - **), 

 and on the brass plate No. 2, 



7/ = 0-8962 . (334-58 - a 1 ). 



If half of the greater axis of the ellipse is made = a, and 

 half of the lesser axis = b, the length of the side of the plate 

 being = 1*000, it was found that 



on the copper plate a, was = 0-348 and b = 0*328 

 on the brass plate No. 1 = 0-350 = -332 



and on the brass plate No. 2 = 0-341 = -323 



or that, in general, the lesser axis of the ellipse is nearly one 

 sixth of the length of the side. 



If the plate is divided into four squares, Figs. 11 and 12 

 being repeated four times, will produce Fig. 13 or 14. 



Fig. 13 is obtained when the plate is supported at A B, and 

 at a third point, distant from any corner by one third of the 



