Vibrations of Rifle Barrels. 



339 



. positions of the nodes were found by noting the position of the points 

 of support which did not damp the vibrations in each mode examined. 

 The results were as follows : — 



Table III. 









Distance of 





Frequency. 



Period. 



nearest node 







from muzzle. 





Per sec. 



sec. 



in. 





66 



0-015 



12 -5 



Mode 11 



172 



-00575 



8-6 



Mode III 



395 



-00253 



6-5 



In case 3, again, the value found for % was 0*00173 second, hence 

 for the assumed ammunition t\ = 0*00346 second. 

 We can now construct a table of the value of q mn . 



Table IV. 



Values of q nm for m = 1 to m = 3, n = 1 to n = 3. 







T, 



T, 



tl 



4-3 



1 -64 



0-72 





8-6 



3-28 



1 -44 



h 



17-2 



4-92 



2-94 



The abscissa on Diagram 11, which corresponds to the time % 

 will be 



For Mode I 2ir®L = 42°-5. 



Ti 



„ Mode II 2ttA = 111° 



T2 



„ Mode III 2tt A = 250°. 



If then Diagram 1 1 had curves for all values on it, we should, in order 

 to determine the deflection (due to vibration evoked in the with mode by 

 the nth term of the harmonic series) of the muzzle as the shot leaves it, 

 merely have to take the ordinate of the curve for which q = q nm at the 



abscissa 2tt ~- , and multiply this ordinate by 6 m pdK n as given in 

 l«i 



Table I, but the diagram, to avoid confusion, has shown on it only 

 curves relating to a few values of q. 



Using, however, the values of q nm given in Table IV, and computing 

 nm for these values, by 24 it is found that 



