Bronson — Transverse Vibrations of Helical Springs. 59 



Art. X. — On the Transverse Vibrations of Helical Springs ; 

 by Howard L. Bronson. 



It lias been known for a long time that the pitch of a 

 stretched india-rubber cord rises very little, if at all, when its 

 length is increased by stretching. This peculiarity has been 

 recently investigated by T. J. Baker* and by Yiktor v. Lang.f 

 Both found that the apparent constancy in pitch is in some way 

 related to the fact that the length and tension are linearly re- 

 lated through a considerable range. 



Now if a linear relation between length and tension is the 

 only requisite for constancy of pitch, then certainly a helical 

 spring ought also to have a constant pitch for a considerable 

 change in length. This consideration, together with the fact 

 that a metal spring ought to be more uniform in its behavior 

 than a rubber cord, were the two things which suggested this 

 study of helical springs. 



Apparatus. 



The first thing necessary for the investigation was to find 

 suitable springs, which should have considerable range in size 

 and stiffness. Seven springs were made of brass wire which 

 seemed to have sufficient regularity and the desired range of 

 size. The following table gives for each spring the diameter 

 of wire used, the diameter of the mandrel on which it was 

 wound, its mass, and L', the approximate percentage increase 

 in length for an increase in tension of ten grams. 



Spring 1 

 Spring 2 

 Spring 3 

 Spring 4 

 Spring 5 

 Spring 6 

 Spring 7 



The relation between the length and tension was obtained 

 with the spring hung in a vertical position, the lengths being 

 read directly from a mirror scale. 



The accurate determination of the frequency was the most 

 difficult part of the work, but very consistent results were finally 

 obtained by the use of a chronograph. The time was furnished 

 by a clock with a seconds pendulum, which was arranged to 

 make one contact every complete vibration. These two-second 

 intervals were very uniform, and a comparison with the Yale 

 * Phil. Mag., vol. xlix. fWied. Ann., vol. Ixviii. 







Table I. 













Diam. 



of 







Diam. < 



Df Wire. 



Mandrel. 



Mass. 



L'. 



0*29 



mm. 



1-80 mm. 



1-283 gr. 



13 



0-29 





3-18 





1-298 



50 



0-42 





3-18 





2-210 



9 



0-46 





3-18 





3-769 



5 



0-46 





5-18 





6-058 



20 



0-91 





5 94 





24-750 



1 



0-46 





5*94 





6-536 



30 



