IN CYLINDRICAL TUBES. 



263 



column, that 10.88-6.78 = 4.10 must =2.-, which gives us - = 2.05, 



differing but .006 from the more accurate value. The error in the 

 two numbers above mentioned, 10.88 and 6.78, does not probably exceed 

 .01 or .02, and cannot, I conceive, exceed .04, and consequently, I think, 

 the utmost limit to the error in the corresponding numbers in the 

 fourth column cannot exceed .05, and is probably considerably less. The 

 same may be concluded respecting the numbers .47, .59, in the same 

 column. 



The above results may, then, be considered sufficiently accurate to 

 determine the fact of the magnitude of the displacement increasing 

 with increased values of X, though not sufficiently so to determine with 

 certainty the law of this corresponding increase. 



The displacement does not depend only on the value of \ ; it depends 

 also on the area of the mouth of the tube, as appears from the following 

 table. 



These values of the displacement of the nodes have been obtained 

 by the method mentioned in Art. 35, as that best applicable to small 

 tubes. The results in the second column of this table ought to be 

 the same as the two first in the last column of the former table; but 

 this method is liable, I conceive, to greater error and uncertainty than 

 the former, and to this, I doubt not, the discrepancy is due.' All 

 these latter results, however, are probably subject to an error of the same 



L L2 



