Moduli of Rigidity for Spruce. 851 



2b and 2c = lengths of the sides of the cross-section, and 

 let 



v 



^ > 1. Then M = /x 1 ri f >c 3 /5, where 

 Pi 



^ \ 3 W; 6 B=1 (2/i — 1 ° 2 c V ujj 



When 



V-> 3 > *= 



1-0-630 f 



« , /Vi t 



v/ 



6 V ^ 2 



^ ' ^ 0-1875 



with an error of less than O'l per cent, and therefore 



0-1875 /M 



^V 



('-™°2\/2) 



! . . . (.) 



Thus the calculation of /a, by this equation required a 

 knowledge of /x 2 . 



This method could have been used for all the experiments, 

 but in some cases it would have'necessitated excessively thin 

 test pieces. This will be evident from a consideration of 



formula (1) ; for if \J — is greater than, or about unity, 



fi 2 



and since it is only approximately known, then r must be 

 small in order that the error in the value of 



f-^iv/S) 



shall be negligible. Excessively thin pieces were undesirable 

 because, for instance, of the impossibility of measuring the 

 thickness with sufficient accuracy, owing to the yielding 

 nature of the material and the difficulty in getting the surfaces 

 planed parallel. Also in cases where the thickness of the 

 pieces was in the direction of the width of the annual rings, 

 thin pieces were in most cases specially to be avoided, because 

 the thickness would have been comparable with the width of 

 the rings, and hence the proportion of autumn to spring- 

 wood may have varied from piece to piece. 



In the case of the second method, two experiments had to 

 be performed on each test piece. After the first experiment 

 the piece was cut so that the ratio of the sides was altered. 



* Todhunter & Pearson's 'Elasticity,' vol. ii. arts. 27 & 47. 

 t Ibid. art. 47, and 'Experimental Elasticity.' Searle, art. 40. 



