410 On the Measurement of Young's Modulus. 



and 47rV«2 = ^ + ^j- 



so that 



4^(*/-0 =|~(<?-^. . ■ . (7) 



The bifilar periods still satisfy equation (1), so that 



as before. 



"1 — ?l l 



III. Statical Method. 



The apparatus of the first method also lends itself readily 

 to the statical measurement of the stretch modulus. Let the 

 bar of the needle be divided in centimetres and let a small 

 weight, say 100 grams, be hung on the needle at a succession 

 of measured distances from the centre. Then in each position 

 the small weight produces a known difference in the tensions 

 of the suspending wires, and with a small mirror attached 

 to the needle, the differences of extension of the wires may 

 be read by a beam of light reflected on to a scale. 



If the small mass hung on the needle is iv, the distance 

 between the vertical wires is 2a, and the distance of the scale 

 from the mirror on the needle is h, it is easily seen that if 

 a displacement z of w along the needle produces a dis- 

 placement y of the spot on the scale, 



a 1 y x > 



For if the displacement z of w turns the needle through an 

 angle 0, one wire is stretched 2ad more than the other, and 



the tension on that wire is increased by an amount ——more 



J 2a 



than the tension on the other. So that 



wgz __ 2a6 _ 2a y 



2a I I 2Ji 



The chief precaution required in this experiment besides 

 those usual in measuring a stretch modulus is to place the 

 mirror so that the displacement of the spot on the scale due 

 to the bifilar motion of the needle is at right angles to that 

 due to the stretching of the wires. 



