Moduli of Rigidity for Spruce. 853 



lest pieces, the values of 8 U 8 2 , -v/- 2 and J2 \/^ 2 



c x V ^ c 2 V ^! 



could be obtained by trial from the curve, and hence the 

 values of yuy and y, 2 . The writer is not aware of any previous 

 record of the second method, but by making the ratios of the 

 lengths of the sides of the cross-sections such that the ratios 



of -~ were equal to 1*4 or 1*5, and avoiding the steep part 



Pi 

 of the curve corresponding with values of {3 2 greater than 

 about 4*6, it was found capable of the accuracy aimed at 

 throughout the experiments, i. e. an error of less than 1 per 

 ■cent. 



Six types of experiments were performed : — 



(1) Torsion about axis XOX, breadth of cross- section in 



direction YOY, thickness in direction ZO/1. 



(2) Torsion about axis XOX, breadth of cross-section in 



direction ZOZ, thickness in direction YOY. 



(3) Torsion about axis YOY, breadth of cross-section in 



direction ZOZ, thickness in direction XOX. 



(4) Torsion about axis YOY, breadth of cross-section in 



direction XOX, thickness in direction ZOZ. 



(5) Torsion about axis ZOZ, breadth of cross-section in 



direction XOX, thickness in direction YOY. 



(6) Torsion about axis ZOZ, breadth of cross-section in 



direction YOY, thickness in direction XOX. 



From experiments type (1), values of yuxy were obtained. 



From experiments type (2), values of ybzx and y,xy were 

 obtained. 



From experiments type (3), values of fiyz and fjuocy were 

 obtained. 



From experiments type'(4) ? values of y^xy were obtained. 



From experiments type (5), values of yuyz and jjlzx were 

 obtained. 



From experiments type (6), values of fxyz and y,zx were 

 obtained. 



For most of the experiments of types (1) and (4 1 



equation (1) was used. Since the values of \ / ^— -^ and 

 \ ' — — were somewhere about 0*2, it was not necessary to 



V fAZX 



make the pieces excessively thin in order to calculate yuvy 

 with the required accuracy, and in many cases the cross- 

 sections were made square. For all the experiments of the 

 other types, with a few exceptions, equations (2) and (3), in 

 conjunction with the graph in fig. 2, were employed. 



