84 M. Savart on the Improvement of the Pipes of Organs. 



Suppose, for example, that we have a certain number of 

 closed prismatic square pipes which give the same sound. 

 Let us then take the ordinate length for the O Y, in Plate 

 I. Fig. 7, and the sides of the base for the abscissa O X, and 

 refer them to two rectangular axes. It is clear that we may, 

 by this procedure, construct a curve which will give the di- 

 mensions of all the pipes intermediate to those which experi- 

 ence has determined. The curve represented in the figure is 

 constructed in this way. The ordinate O Y is the length of 

 a pipe infinitely small, which would give the sound sol 3 ; and 

 the abscissa O X, of the same length as O Y, represents the 

 side of a square plate of air infinitely small, made to vibrate 

 in all the extent of this side, which would, consequently, give 



the same sound sol \\ All the other parts of the curve have 

 been obtained by experiment. 



It is unnecessary to remark, that this curve will be the 

 same in all sounds, for which we should undertake to con- 

 struct it ; and it follows from this, that the number of vibra- 

 tions are reciprocally proportional to the linear dimensions, in 

 pipes of similar form. 



I shall now conclude these observations with a few remarks 

 on the German top, an instrument which is at present unex- 

 plained. This top is a hollow sphere, perforated with a 

 hole, whose edges are sharp ; and, when a rapid rotatory 

 motion is given it, a very pure sound is produced. The 

 cause of this will be obvious, if we remark, that, in blowing 

 against the sharp edge of the orifice of the sphere, either with 

 a small port-vent, or with the mouth, it will yield the same 

 sound as when it is in rotation. In the first case, it is the 

 current of air which is driven against the edges of the orifice ; 

 and, in the other case, it is the sharp edges of the orifices 

 which strike the external air, which comes to the same thing ; 

 and the fluid contained in the sphere, though it be carried by 

 the motion of rotation, is not allowed to vibrate, as if this mo- 

 tion did not exist. 



We may, therefore, by means of the law of the number of 

 vibrations being reciprocal to the linear dimensions for pipes 

 of a similar form, determine, a priori, the sound of one of these 

 instruments, in the case where its cavity is exactly spherical. 



