a Paper by Dr* Sondhauss. 



215 



Dr. Sondhauss expresses himself strongly as to the difficulty 

 which exists in determining accurately the pitch of the very un- 

 certain sound produced by tubes whose diameter is not small 

 compared with their length, an opinion which I entirely share. It 

 is indeed difficult to understand how Wertheim obtained results 

 of such precision. But I cannot agree with Dr. Sondhauss 

 when he goes on to say that resonance is not a sure guide in de- 

 termining accurately the pitch of a pipe; for it was by this me- 

 thod exclusively that the determinations recorded in my paper 

 were made. I have there given at length my reasons for adopt- 

 ing it, and for doubting the results of the method of blowing, 

 although such experiments as those of Wertheim go to show apos- 

 teriori that in his hands at least it was not unworthy of dependence. 



Other experiments of Wertheim are calculated from formula 

 (IX.) and show a tolerable agreement. The difference between 

 (IX.) and Helmholtz's theoretical formula (C) relates only to a 

 constant multiplier, and corresponds to a difference of pitch of 

 about a quarter of a semitone. The discordances are attributed 

 (no doubt correctly) to the unsuitable form of some of the vessels, 

 and consequent imperfect fulfilment of the theoretical condition 

 to which (C) is subject. 



We come next to vessels in the form of flasks with a cylindrical 

 neck of sensible length. Dr. Sondhauss gives a Table contain- 

 ing the results of a comparison of (VII.) with some experiments 

 of his own. The average discordance amounts to about a semi- 

 tone. Although it was evident beforehand that in most cases 

 the limitations on formula (A) were grossly violated, I thought 

 it worth while to calculate in accordance with (A) the theoretical 

 pitch, and have given the results in the form of a Table : — 



No. of 

 exp. 



a. 



Shape of 

 vessel. 



S, in 



cubic 



centims. 



L, in 



millims. 



Diam., in 

 millims. 



n, ob- 

 served. 



n, cal- 

 culated 

 from 



(VII.). 



n, cal- 

 culated 



from 



(A). 



1. 



2. 



3. 



4. 



5. 



6. 



7. 



8. 



9. 

 10. 

 11. 

 12. 

 13. 

 14. 

 15. 



341260 



Sphere. 

 Cylinder. 



Octagon. 



Sphere. 



Cylinder. 



Sphere. 



Cylinder. 



Sphere. 



171 



60-9 

 10-7 

 977 

 66-2 

 117-8 

 654-5 

 76-3 

 1178 

 132-4 

 923 

 8920 

 178 

 109 

 •80 



60 



19 



15 



13 

 175 

 183 

 193 

 118 



15 



44 

 205 



30 

 160 



11 

 22 



5-5 

 12-5 

 10 



9 

 11-6 

 18 

 26-5 

 205 

 25 3 

 27 

 25 

 36 

 18-5 



2 



2-2 



241-6 

 430-5 

 966-5 

 287-3 

 143-7 

 170-9 

 114 

 2560 

 574-7 

 362 

 85-4 

 761 

 152-2 

 812-7 

 1933 



246-9 

 454-5 

 959 

 311-2 

 155-2 

 170-4 

 106-7 

 285-6 

 589-5 

 429-2 

 83-2* 

 76-6 

 155-8 

 842-6 

 1926-2 



251-3 

 453-6 

 970 

 309-2 

 158-8 

 178-5 

 107-6 

 3061 

 600-2 

 441-4 

 83-7 

 766 

 159-1 

 825-4 

 1902 



















342740 

 344210 

 341260 

 344210 





* The result of the formula (VII.) ought evidently here to be greater 

 than that of (A). On a recalculation I find 85*8 instead of 83-2. 



