854 Mr. H. Carrington on the 



In addition to the moduli, the following properties were 

 also measured for each test piece. The density when tested,, 

 density when dry, humidity, shrinkages in the directions 

 XOX and YOY, and the number of annual rings per inch. 

 In order to obtain the density when dry, the humidity and 

 shrinkages, each test piece was dried in an electrically- 

 heated stove at 104 0. for from 24 to 48 hours immediately 

 after testing. From the measurements and weights of the 

 pieces before and after drying, the properties were calculated, 

 obvious precautions being necessary because of convection 

 currents and the rapidity with which the pieces absorbed 

 moisture. The number of annual rings per inch was deduced, 

 from measurements of the thicknesses of the rings by a finely 

 divided scale. 



The values of the elastic limits and moduli of rupture were 

 calculated by expressions of the type 



Z x = jjlz*v.c . r.y, (4) 



where -\f -^— >1 and Z T is the stress in the middle of the 



C V fjuzx 



side 2b corresponding with the angle of twist per unit 

 length t. Value's of y corresponding with different values 



of - \ / — — > 1 were calculated by St. Yenant, and are 



c v ,xzx 

 reproduced in Todhunter & Pearson's ' Elasticity.' In calcu- 

 lating values of the elastic limit, the twist per unit length to 

 be used in equation (4) was obtained direct from the torque- 

 twist curves. In calculating values of the moduli of rupture, 

 it was assumed that the material remained elastic right up 

 to the maximum torque, and the twist was taken as pro- 

 portional to the twist at the elastic limit. 



The results of the experiments are given in Tables L, II.,. 

 and III. The balks are distinguished by the letters A, B, 

 C, D, and about 10 values of each constant were obtained for 

 each balk. 



The means of the values are tabulated and also the means 

 of the other properties. In order to give some idea of the 

 variations in the properties across each balk, the probable 

 variations of the values from the means were also tabulated. 

 These were calculated on the assumption that the values 

 obeyed the laws of probability and Peter's formula * was 

 used. 



* 'Theory of Errors and Least Square?.' Weld, Xew York (1916). 



