390 Benton — Properties of Catgut Musical Strings. 



limited to finite time. Two of the curves obtained in this 

 manner are exhibited in figures 5 and 6, together with their 

 asymptotes as estimated. Such curves were taken after each 

 change of load ; but it is not thought to be of any interest 

 here to submit more than two of them, or to present tables of 

 the numerical data from which the curves are plotted. 



The results obtained in this manner are summarized in the 

 accompanying table. After any load had acted for a few days 

 it was removed, and the string left unloaded a few days before 

 the next load was applied. The individual readings were made 

 to thousandths of centimeters ; but the estimation of the length 

 to which the string tended at infinite time was carried out 

 only to hundredths. The first column of the table gives the 

 loads, in kilograms, placed upon the hanger, which itself 

 weighed about 0*5 kg. ; the third column gives the total elon- 

 gation after disappearance of the after-effect, estimated as 

 explained above ; the sixth column gives the after-effect, of 

 change of strain from the first instant (practically abont 60 

 seconds) after applying the load until final equilibrium is 

 reached, expressed as percentage of the total final strain ; the 

 other columns require no explanation. 



Violin E-string, 0-062 cm in diameter. 















Time 







Stress 



Total 





Young's 





the 



Mean 





in kgs. 



elonga- 





modulus 



After- 



load 



t emper- 



Load, in kgs. 



per 



tion in 



Strain. 



in kgs. 



effect. 



acted, 



ature, 





mm 2 . 



cms. 





per mm 2 . 





m 



days. 



° C. 



, 5 j (applied) ) 



1-66 



j 0-59 ) 



0-0044 



378 



j 30$ 

 1 33$ 



5 



24 



( (removed) j 





( 0*62 j 







5 



24 



1-0 (applied) 



3-31 



1-39 



0-0101 



328 



44$ 



6 



24 



1 *5 (removed) 



4-97 



2*26 



0-0164 



303 



26$ 



5 



25 



((applied) | 



( (removed) ) 



6-63 



j 2-70 ) 

 t 2-75 f 



0-0198 



335 



j 22$ 

 ( 29$ 



4 



7 



28 

 29 



6 j (applied) > 

 { (removed) ) 



8-29 



j 3-78 | 

 j 3-73 f 



0-0272 



304 



j 22$ 

 ( 29$ 



5 

 4 



31 



28 



3-0 (applied) 



9-95 



4-66 



0-0338 



294 



20$ 



8 



27 



3-5 (applied) 



11-60 



5-17 



0-0375 



310 



15$ 



6 



28 



Young's Modulus* — The mean value of Young's modulus 

 from these experiments comes out 322 kgs. per mm 2 , or 458,000 



* The values of Young's modulus given in the above table are obtained by 

 direct division of each stress by the corresponding strain. In strictness, 

 Young's modulus should be determined from the slope of the stress-strain 

 curve at the origin. But in the special case that the stress-strain curve is a 

 straight line, the quotient of stress by strain for any point of the curve gives 

 the same result as the slope at the origin. The data under discussion not 

 being sufficiently regular to determine the true form of the stress-strain 

 curve, it is taken as a straight line within the limits of the experiments ; and 

 this justifies the above method of determining Young's modulus. 



