Bronson — Transverse Vibrations of Helical Springs. 65 



ting strings, in fact the equation requires that the percentage 

 difference between the observed and calculated values of the 

 frequency for a given length shall be twice the percentage dif- 

 ference between the observed and calculated values of the 

 tension for the same length. If careful measurements are made 

 on the plot, this will be found to be approximately true. 



It is also seen in fig. 5 that n is apparently approaching a 

 maximum value. This fact made it seem desirable to carry the 

 curves considerably further beyond the point where the length 

 and tension are linearly related. Since for this case only a 



5 



T. n- 



/o' 



9 10 II 12 1^ /4 IS IS n /8 13 20 21 2Z J3 24 



single set of observations could be made with one spring, on 

 account of the permanent distortion produced, the most prac- 

 ticable method seemed to be to make two springs as nearly 

 alike as possible. This was accomplished quite satisfactorily by 

 cutting into two parts a very uniform spring and then adjust- 

 ing the two parts until they had as nearly as possible the same 

 mass, length and rate of extension. 



Springs 4 and 5 were treated in this way, but the results were 

 so similar that only those for 4 will be given. Table Y shows 

 how similar were the two parts into which spring 4 was made. 



An. Jour. Scl— Fourth Series, Yol. XVJII, No. 103.— July, 1904. 

 5 



