850 Mr. H. Carrino-ton on the 



placed so that the line of sight between the mirror and the 

 corresponding scale moved in a plane perpendicular to the- 

 axis of: the test piece. 



When conducting an experiment the load in the scale-pan 

 was increased by equal amounts, and the scales were read 

 after each increase. The scale readings were then plotted 

 against the torque, and resulted in a curve whose initial 

 portion was straight. The slope of this straight portion Avas- 

 involved in the calculation of the moduli. Although the 

 main object of the experiments was to obtain values of the 

 moduli, it was considered worth while to determine values 

 of the elastic limits and moduli of rupture when possible. 

 These were calculated from the values of twist and torque 

 where the curves ceased to be straight and from the maximum 

 torque. For most of the experiments plane scales were 

 used, and the error introduced was negligible. In other 

 cases, where the angle of twist at the elastic limit was 

 considerable, curved scales were employed. 



The prisms were obtained from balks representing four 

 different trees. In ever}' case the specimens were cut from 

 portions over 12 inches from the pith, and since the lengths- 

 of annual layers in the circumferential direction did not 

 exceed 1£ ins. corresponding with any cross-section, or about 

 2 ins. corresponding with the tested length of any prism, the 

 layers were sensibly plane surfaces. The specimens were 

 cut so that the annual layers were parallel, either to opposite 

 sides or ends, and the values of the moduli were calculated 

 on the assumption that the specimens had three planes of 

 elastic symmetry. 



The direction of the grain will be noted by ZOZ, the- 

 direction perpendicular to this and normal to the annual 

 layers by XOX, and the direction perpendicular to the other 

 two, which is thus tangential to the annual layers, by YOY.. 

 When a specimen with its length in the direction ZOZ is 

 twisted about its longitudinal axis, two values of the moduli 

 are involved, i.e. fiyz and [jlzx (pyz denotes the modulus of 

 rigidity corresponding with shear strain along planes OZX 

 and OXY, i. e. along the direction YOZ). 



The moduli were calculated from the slopes of the stress- 

 strain curves and the dimensions of the test pieces. Two 

 methods were used, and in order to explain them, consider a 

 prism of rectangular cross-section twisted about the longi- 

 tudinal axis, and let the two values of the moduli involved 

 be denoted by /xj and (x 2 . Also let M = twisting-moment 

 corresponding with the angle of twist per unit length t,. 



