Moduli of Rigidity for Spruce. 849 



(1879), and assuming the partial ellipsoidal elasticity of 

 St. Venant to hold, is given in a paper on "The Torsion 

 resulting from Flexure in Prisms with Cross-sections of 

 Uni-axial Symmetry only," by A. W. Young, M.A., Ethel 

 M. Elderton, and Karl Pearson, F.R.S. (Cambridge Uni- 

 versity Press, 1918). The shortness and incompleteness of 

 the table — for neither the humidity nor the density of the 

 wood is given, both of which have an important bearing on 

 the values of the elastic coefficients — and the fact that the 

 authors had to refer back prior to 1880, indicates further 

 the lack of information about the elastic properties of 

 timber. 



The values of the moduli were determined from torsion 

 experiments on prisms of spruce of rectangular cross-section. 

 Most of the prisms were about 12 inches long, and the length 

 of the longest side of any cross-section did not exceed 

 1^ inches. A photograph of the apparatus used is shown 

 in PI. IX. fig. 1. 



The two shafts could revolve freely in ball-bearings, and 

 each shaft was fitted with a pulley, one of which was fixed 

 when an experiment was being performed. The torque was 

 transmitted to the other pulley and thence to the specimen 

 by weights placed in a scale-pan, which was suspended from 

 the periphery of the pulley by a fine wire. The effective 

 radius of the couple was 2 inches. The shafts were provided 

 with jaws, into which the test pieces were fixed b} wooden 

 wedges, and alignment of the axis of the test pieces with 

 the axes of the shafts was effected by a scribing-block. One 

 of the shafts had a slight end play, so that longitudinal 

 tension was avoided. It was found possible to obtain con- 

 tinuous stress-strain curves with increments of load of ,} () lb. 

 in the scale-pan, equivalent to increments of torque of ^ lb. 

 inch. 



An optical method was used to measure the angles of 

 twist. Two frames, each supporting a small mirror, were 

 fixed to the test piece by pointed set screws, so that the axis 

 of each of the pair of screws in a frame was in a line inter- 

 secting the axis of the test piece at right angles (see PI. IX. 

 fig. 1). When the frames were fixed in position, the distance 

 'between the axes of each pair of screws was that over which 

 the angles of twist were measured. This distance was 

 usually about 2 inches. The magnitudes of the angles were 

 obtained by noting the apparent motion of the cross-wires 

 of a pair of telescopes along scales placed opposite to the 

 mirrors and reflected down the telescopes. Each scale was 

 about 50 inches from the corresponding mirror, and was 



