348 Mr. T. J. Baker on the Frequency of Transverse 



which these curves effect was found of advantage in the 

 calculations hereafter referred to. 



Inspection of the curve connecting length with tension 

 reveals that the relation is strictly linear between those points 

 at which the length of the cord becomes respectively 2^ and 

 5 times its natural length. 



Untrustworthy readings were obtained with further stretch- 

 ing because an increase of tension did not produce its full 

 effect until a very considerable time had elapsed. With the 

 smaller stretchings this difficulty was not encountered. 



The curve connecting length with frequency shows that 

 while the cord was doubling its natural length the pitch of 

 its note was rising rapidly; but that further extension was 

 practically without effect. 



When the cord had doubled its natural length, its frequency 

 of vibration was 91; and when its original length had been 

 sextupled the frequency was not more than 94. 



The discussion which follows relates to the conditions pre- 

 vailing during the period in which length and tension are 

 connected linearly. 



Since the observations show that equal increments of tension 

 (between the limits above mentioned) produce equal extensions; 

 and at the same time the sectional area is diminishing, it 

 appears that the value of Young's modulus must increase 

 with increasing extension. 



Experiments have been made on this point by Villari 

 (Pogg. Ann. cxliii.), by Rontgen {ibid, clix.), and by Mallock 

 (Proc. Hoy, Soc. 1889) ; but beyond ascertaining that 

 Young's modulus increases rapidly with increase of extension 

 no definite relations appear to have been discovered. 



The values of the modulus for the cord used in these expe- 

 riments were therefore calculated by the use of curves (i.) 

 and (ii.). 



In each case an extension of 1 cm. was chosen, and the 

 increase of tension required to produce this was 16 grams 

 weight. 



The mean value of the sectional areas before and after each 

 increase of tension was used in the calculation ; and for this 

 purpose curve (hi.) was employed. 



When the results are tabulated, it becomes apparent that 

 Young's modulus is proportional to the square of the stretched 

 length of the cord. 



The last column in the table exhibits this relation- 



