Bronson — Transverse Vibrations of Helical Springs. 61 



tional to the increase in tension, and then being decreased to 

 zero again. Immediately after this the relation between the 

 length and frequency was determined, starting with as short a 

 length as possible and increasing it up to the maximum length 

 obtained above and then decreasing it again as far as possible. 

 The relation between the length and tension was then again 

 obtained as in the first place. A. complete set of observations 

 for spring 1 is given in Table II. 











Table II. 









T. 



Out L. 



InL. 



L. 



Out n. 



In n. 



T. 



Out L. 



InL. 







9-32 



9-33 



10 



14-80 



14-69 







, 9-34 



9 34 



10 



10-02 



10-08 



11 



18-16 



18-01 



10 



10-07 



10-10 



20 



11-40 



11-48 



12 



20-43 



20-31 



20 



11-46 



11-49 



30 



12-81 



12-90 



13 



22-13 



22-04 . 



30 



12-88 



12-94 



40 



14*23 



14-32 



14 



23 45 



23-41 



40 



14-28' 



14-35 



50 



15-68 



15-76 



15 



2462 



24-50 



50 



15-73 



15*80 



60 



17-13 



17-18 



16 



25-49 



25-47 



60 



17-16 



17-21 



70 



18*60 





17 



18 



26-26 

 26 93 



26*22 



70 



18-64 





Here T is the tension measured in grams, L is the length 

 measured in cm., and n is the number of vibration per second. 

 "Out" means increasing, and "In" decreasing tension or 

 length. 



The first set of values between length and tension was pre- 

 liminary, taken to find the point at which the relation between 

 the length and tension ceased to be linear. This stretching of 

 the spring also served to remove certain very slight irregulari- 

 ties, as was evident when several length-tension sets were taken 

 in succession, in which case the behavior of the spring was 

 practically the same in all sets except the first. Therefore in 

 making the plots and calculations the mean of the length-fre- 

 quency and final length-tension sets were used, and in general 

 only these values have been recorded in the tables. 



Table III gives the mean values of L and n from Table II, 

 also the calculated values of n and the difference between the 

 observed and calculated values. 







Table III. (Spring 1 



•) 





T. 



L. 



L. 



Observed n. 



Calculated n. 



Difference. 







9-34 



10 



14-74 



15-08 



— 0-34 



10 



10-09 



11 



18-08 



18-16 



— 0-08 



20 



11-47 



12 



20-37 



20-37 



o-oo 



30 



12-91 



13 



22-08 



22-06 



+ 0-02 



40 



14-32 



14 



23-43 



23-41 



+ 0.02 



50 



15-76 



15 



24-56 



24-52 



-t- 0-04 



60 



17-19 



16 



25-48 



25-45 



+ 0-03 



70 



16-64 



17 



26-24 



26-24 



o-oo 







18 



26-93 



26-92 



+ o-oi 



