14 AT.T. K>. T. TERADA. 



ClfT* 



where S is the volume aud a the velocity of the sound wave in 

 air. Sondhauss^^ ohtained experimentally 



H = 52400 o* /SV- (length in mm.) 



These results have been discussed by I^ord Kayleigh"' in his 

 classical paper on resonance. On the other hand, the correction 

 for the open end of a cylindrical resonator has been treated both 

 experimentally and theoretically by many physicists/^ beside the 

 worthies above quoted. The jiresent experiments furnish in some 

 measure the intermediate stage of transition from the first case 

 to the second. As will be seen from the above result, when the 

 length of the air column is small, the pitch is nearly proportional 

 to n'f and also nearly so with /~- or /S"- ; and when the area of 

 the aperture gradually approaches a complete circle, the curves n 

 to ^' tend to the values given by the ])revious results for the 

 open pipe. 



It is an established fact that for a similar resonator, the 

 pitch is inversely i)roportional to its homologous dimensions. 

 Hence, the above results may be applied to other pipes with 

 diflerent diameters, if n and /"' be multiplied by the ratio (the 

 diameter of the glass pipe above experimented on / the diameter 

 of the other pipe) and o^ by (the same ratio).-^^ 



1) Sondliauss, Poüg. Ann. LXXXI. pp. 245, 357, ISöO. 



1) Rayleigli, Phil. Trans. CLXI. pp. 77-118. 



.".) Poisson, Mem. de I'Acad. des Sei. 1SI7, II, .",05. Savart, Ann. d. Chim. t. XXIV, 

 I82.'î. Hopkins, Cam. Pliii. Trans. V, ]8;]8^. Quet, Journ. d. Liouville, XX, 1, 1855. 

 WfrliK-ini, Ann. d. Ciiiiii. ot I'iiys. (n), XXIII, 4.34 ; and XXXI, ?.8ö, 1848-51. Zam- 

 miner, Po-g. Ann., XlVII, lS.3,,]85ri, Gripon, Ann. d. Chim. Ill, .384, 1874. Ray-leigh, 

 I'hil. Mag. (5J III, 4.-.(;. Posapqnet, ihid IV, 291, 1S77 ; and VI, 6.3, 1878. Koenig, 

 Wied. Ann. .^(iO, 1881. Blaikley, Phil. mag. (5) VII, r.9, 1879. 



Ilfiiiiholtz, Crelle, Bd. .57, ISC.O ; Gpsannnelte Ahiiandlnngen Ed. I. 



