M. Savart on the Improvement of the Pipes of Organs. 83 



pend upon this, that the number of harmonics co-existing 

 with the principal sound are very inconsiderable. It is al- 

 most impossible, indeed, to obtain any of them in cubes. In 

 spheres, I have found that, the first sound being called ut lf the 

 second was ut 4 , the third sol± and the fourth ut 5 ; but, 

 from this great interval between the first and the second har- 

 monic, it is to be presumed, that I have not employed the 

 proper means for obtaining all the series. I may besides re- 

 mark, that the pipes which I employed had their embouchure 

 only a small number of degrees of the circumference of one 

 of their great circles, because I had it in view only to determine 

 the law of the numbers of vibrations in spherical masses of 

 air. It might have happened that the series of harmonics 

 would have been different, and more easily obtained, had the 

 embouchure been more extended ; and perhaps, also, the 

 sounds would have been stronger and more agreeable. The 

 sound ut^ is given by a sphere of air about 4| inches in diameter. 



In the case of curved tubes, it is important to remark, that 

 the material of which the sides are formed has a notable in- 

 fluence on the qualities of the sound, and on the number of 

 vibrations. The same is true of the thickness of the sides, 

 and, consequently, we must pay attention to this circum- 

 stance ; and in organ pipes of similar form, we must make the 

 thickness proportional to the linear dimensions of the masses 

 of air. 



The laws of the number of vibrations for pipes of similar 

 form, and for plates of air, conjointly with the law of Ber- 

 nouilli * for pipes made to vibrate with a full orifice, a law which 

 is sufficiently exact for columns of air of a small diameter, em- 

 brace very nearly all the cases which can occur in the con- 

 struction of organ pipes, whether closed or open. Notwith 

 standing this, I shall point out a very simple method for de- 

 termining immediately the dimensions of all pipes of similar 

 form, which are susceptible of giving the same sound, and of 

 which there are an infinity. 



• Namely, that the numbers of oscillations of columns of air, which 

 sound in pipes open at both ends, or shut at one end and open at the 

 other, are reciprocally proportional to the lengths of tho.se columns, pro- 

 vided that they vibrate with a full orifice. 



