Aug. i6, ipis Tensile Strength and Elasticity of Wool 381 



average breaking stress would lie between 55.994 — 0.404 = 55.590 dgm, 

 and 55.994 + 0.404 = 56.398 dgm. In this case the probable variation 

 of a single fiber would be 12.764 — i. e., we should expect that one-half 

 of the fibers would have a breaking stress lying somewhere between 

 43.230 and 68.758 dgm. 



At the same time that these observations were taken, a record was 

 kept of the ultimate strain of each fiber. But no account was taken of 

 the length of each fiber at the time stress was imposed. However, it 

 was evident that the ultimate strain was very slightly, if at all, a func- 

 tion of the breaking stress. 



BREAKING vSTRESS AND TENSILE STRENGTH' 



The first work on this project was the determining of the breaking 

 stress of the fibers and the probable variation in the same, for the pur- 

 pose of getting an average with a probable variation so small that it 

 could be disregarded. It was found, however, that the variation was 

 too great to give conclusive results even when using as high as 5,000 

 fibers per fleece. This was to be expected in part, as to compare wool 

 fibers without regard to their sizes does not seem to be practicable. 



It was decided, therefore, that the ultimate breaking stress of the 

 fibers was not what was wanted, but rather the quality of the fabric 

 woven from the wool. The strength of the fabric depends upon the 

 tensile strength of the fibers — i. e., the breaking stress divided by the 

 cross section of the fiber. 



Each fiber of coarse wool has a greater breaking stress than single 

 fibers of fi.ne wool, yet a piece of goods made from the fine wool will con- 

 tain many more fibers to the yard than one made from the coarse wool; 

 thus, the former may make the stronger cloth. It is therefore evident 

 that we must know the cross section of each fiber as well as the .breaking 

 stress. The results from testing the fibers on this basis is illustrated by 

 the following samples of wool: Rambouillet No. 6401 — breaking stress, 

 49-35 dgm.; tensile strength, 100.988. Shropshire No. 67 — breaking 

 stress, 140.00 dgm.; tensile strength, 119.886. It will be seen that 

 while the ratio of the breaking stress is i to 2.83, that of the tensile strength 



'Explanation of Terms Used: 



Length (Z,)= length of fiber tested, in millimeters. 



Diameter (i))=measured on the microscope with a micrometer eyepiece, i unit equal ls/'. 



Area (/l)=area of cross section of fiber. Formula 



4 

 Breaking stress (S)= force required to break fiber, in decigrams. 



Strain (£)= stretch or elongation of fiber, in millimeters. 



S 



A 



S 

 Tensile strength (jrS) = strength per unit area -r . However, to save time in our calculation we com- 



puted a value .^.^ which is the constant -XTS. 

 Elastic limit (£;L)= point at which if more force is applied, Hook's law p=K breaks down. 



Yotmg's modulus (V')=a formula used for measuring material which is based on Hook's law. 



Stress , . T. , LXS. 



7^ — r- = a constant. Formula, „.. . 

 Strain EXA 



Frobable variation (P V)=a value which in the 'ong run is greater than the variation of exactly one-h^ 



the fibers from the mean. 



