298 Strehlke on the Acoustic Figures of Plates. 



These observations do not seem to lead to any certain result, 

 except that if 2a increases, <p increases also, in accordance 

 with what is observed in plates which are fixed between screws, 

 where the distance between A and B may be increased ad 

 libitum, by fixing the plate at a greater or less distance from its 

 middle. Thus, if the brass plate, No. 2, (in which 2a =0-177, 

 and (p = 46-56') was fixed between screws at a point of the 

 principal axis to the right from B, 2a was 0.341, and 

 <p=51 -53' ; if to the left from B, 2a was 0-148, and <p=44-16'. 

 If the plate was fixed at any other point the tone remained the 

 same, but the axis of the hyperbola was perpendicular to that 

 of the former figure. 



Another very simple acoustic figure is obtained by support- 

 ing the sides D CD' (fig. 3) at the middle, and producing 

 the vibration at one of the corners ; it consists of two hyper- 

 bolic branches, the principal axis of which coincides with the 

 diagonal of the square : sometimes fig. 4 is produced, the 

 major axis of which is always in the direction of the principal 

 axis of the hyperbola in fig. 2. 



The formation of this figure seems to be fully accounted for 

 by the theory of undulations, for in a vessel of the same form 

 as the plate, and filled with liquid, the interferences of the 

 undulations will produce the square C D C' D', provided 

 the resistance which the undulations experience in the direc- 

 tions C C', and D D', is equal ; if not, and if the resistance to 

 the direction D D', is greater than to that of C C', the angles 

 of the square will be changed into hyperbolic corners, and 

 the longer axis of the ellipse will be in the direction C C', and 

 the shorter in that of D D' ; and if further, the resistance 

 in the same direction is unequal, the figure will become irre- 

 gular with regard to its opposite parts. 



The difference of the two axes in fig. 4, is proportionate to 

 the distance between the summits of the hyperbola in fig. 2, for 



On the brass plate No. 1, C C' was = 30"'-58 D D' = 27"'-92, and AB = 6 // '-27 



Ditto ditto No. 2, =31 -36 =28-03 =6-12 



On a brass plate of the same di-1 Q n .QC on QC o QQ 



mension - I " " 



On the copper plate No. 3, =29 -53 ,, =29 -03 =3 -58 



On two copper plates, on which A B had been found to be 



