DR. EVEEETT ON THE EIGIDITY OF GLASS. 189 



From the data above given the following elements will now be computed : — 



f, the fiexural rigidity of the rod, or the reciprocal of the amount of curvature per unit 



length of rod, per unit moment of bending couple. 

 t, the torsional rigidity of the rod, or the reciprocal of the amount of twist per unit 



length of rod, per unit moment of twisting couple. 



These two elements are functions of the thickness of the rod as well as of the material 

 of which it is composed. The following are functions of the material only : — 



n, the absolute rigidity, or reciprocal of the amount of shear per unit shearing 



force. 

 M, Young's modulus of elasticity, or reciprocal of the fraction of its length, by which 



a prismatic or cylindric rod of unit section is lengthened per unit stretching 



force, 

 k, the resistance to compression, in such sense that - is the compressibility, or the frac- 



tion of itself by which the volume is diminished under unit pressure per unit area 

 over the whole surface. 

 (T, Poisson's ratio, or the ratio of transverse contraction (in one dimension) to longitu- 

 dinal extension when a prismatic or cylindric rod is stretched longitudinally. This 

 ratio was supposed by PoissoN to have the same value (|-) for all materials, and was 

 first shown by Stokes* to be a function of two independent elements whose mutual 

 relation is different for different substances, and must be determined for each by 

 experiment. 



Of these quantities, a is the only one whose numerical value is independent of the 

 units employed. Our units are the centimetre and the weight of a gramme at Glasgow, 

 where the acceleration due to gravity is 981'4 centimetres per second generated per 

 second. 



To findy and t. Since the deviation of a reflected ray is double the angle through 

 which the mirror is turned, the relative angular movements of the mirrors per gramme, 

 in flexure and torsion respectively, are 



•04144 , -053185 



and 



2X271'8 2 X 277-3 • 



hence, since length of rod is 28-0 and arm of couple 31-4, 



/=31-4x28-0x.^f2t =11.533,000, 

 «=31-4x28-0x:^g5= 9,168,200. 

 The logarithms of/ and t are 7-06195 and 6-96228. 



* Cambridge Philosophical Transactions, April 1845. 



