66 THE HUMAN MOTOR 



The moment of torsion M is expressed by the product of the 

 stress F into the diameter d, because the couple acts on the 

 axis. The industrial units were the kilogramme and the millimetre, 

 but to-day the gramme and the centimetre are adopted a unit 

 of moment 100 times less, so that, for the same angle of torsion, 

 the value in grammes-centimetres is 100 times bigger than in 

 kilogrammes-millimetres. Thus G is equal to 8,000 kilogrammes 

 for steel, 400 for oak, etc. Corresponding values 785 and 39 have 

 been arrived at for y, or grammes-centimetres 78'5xl0 3 and 

 3-9X10 3 . 



To twist an oak stick of 6 centimetres in diameter and 25 centi- 

 metres long through one radian (57, 18 approximately) there 

 must be a couple : 



60 4 V 1 



M = 3-9 X 10 3 . -^~- = 20X10 7 grammes-centimetres. 

 .250 



Between Young's modulus E and the modulus of rigidity G 

 there is the relation : 



R E 



the co-efficient a indicating the relation of the transversal con- 

 traction to the elongation of the stick. This (Poisson's) co- 

 efficient a is ^ for indiarubber according to the most correct 

 estimates, but It generally varies for different substances between 

 J and | . In bodies called anisotropic ( l ) it is greater than unity ; 

 it is a = 1'47 to 1'65 for cocoon silk. The modulus of rigidity 

 thus lies between 



E E 

 and 



n f\TT 



that is between E and -- -. 

 *> 16 



kg 



The system of - -, used to estimate E, does equally for G ; 

 2 



mm 



but the kilogramme being expressed by 981x1,000 dynes, or 

 0'981 x 10 6 in the C.G.S. System, and the square millimetre being 

 100 times smaller than the square centimetre, this system is 

 0-981 x 10 8 times less than the C.G.S. system. 

 It follows therefore that : 



0.9631X10'. 



( l ) When the elements of the volume of a substance vary in property 

 according to their " orientation," that substance is homogeneous and 

 " anisotroDJc " : otherwise it is " isotropic." 



