32 THE ROYAL SOCIETY OF CANADA 



Since a occurs to the fourth power it must be measured carefully. 

 Select four places of the wire at equidistant intervals and measure the 

 radius at those places in two directions at right angles. Correct for 

 any zero error on the gauge. 



In the experiment quoted 



ti = 50-2 seconds 



a = 000115 feet 



16x7rx30-5 x 0-262 ^ 11.04 



" 5x50.22x.000lT^ P°""^^^^ P^^ ^^- ^'' 



= 5-3 X 10^° poundals per sq. foot 

 = 1 -65 X 10^ pounds per sq. ft. 



The value of n can also be deduced from an experiment in which 

 by means of two delicate spring balances (reading to 10 gms., say) 

 and a piece of fine string, couples can be applied to twist the ball 

 through successive angles of 2;r, 47:, 67:, Sit, etc., deducing the average 

 value of the ratio of the couple G to the angular displacement 6, 



and using the formula n = — — 

 d ;ra* 



Experiment IV. — Young's Modulus of the Suspension Wire. — 

 If the ball is lifted up in the hands so that the wire is relieved of its 

 weight and the hands suddenly removed, the ball drops and then 

 vibrates up and down. The motion is simple harmonic and the period 

 is given by 



t2 = 2;r 



Mass of ball 



Ratio of force to elongation of wire for forces parallel 

 to the length of the wire. 



If Y = Young's Modulus of the metal composing the wire, and if 

 a force F produces an elongation e 



Y = ^/^^' = ?.lL 

 e/l e Tra^ 



F TrYa^ 



1 

 27r 



M 



Ya2 orY = 



4;rMl 

 ta^a* 



U is so short that a stop watch must be used and the time occupied by 

 a large number of vibrations recorded as nearly as possible. 



