Ductile Materials under Combined Stress. 99 



Now in the use of this instrument fa is of a larger order than 

 any of the other quantities, but if the other quantities <f> 1} 6 l , 

 2 , and a are all zero, it is evident that <f> and fa are exactly 

 equal. 



Hence (f>— (fa— <f) 1 )(l + 20 1 + cx,) 



to quantities of the orders 



&«, tf, e;\ e 2 \ ai \ 



Now put fa=fa=0. 



Then the ray lies in the plane COA, and 



COZ = COP-LOP=COP-KOP 

 = COP-(AOP-AOK) 



= ^+<?i-(J : -0i)+«i 



= 20 1 +« 1 . 



Hence if we make the reflexion of the optical axis in the 

 first mirror parallel to the axis of the telescope, the value 

 of (f> becomes fa— fa, or the scale-reading divided by the 

 distance to the scale is the twist between the mirrors to 

 the orders of small quantities stated above. This adjustment 

 is made by the use of the adjusting-screws of the lower 

 mirror, the telescope being sighted so as to have the lower 

 mirror at the centre of its field, and then the mirror adjusted 

 so that a point similarly situated with respect to the specimen 

 as the centre of the lower mirror appears at the centre of 

 the field. 



The adjustment was tested by turning the specimen as a 

 whole through an angle of 0*1, when it was found that the 

 scale-reading changed through an angle corresponding usually 

 to about 0-001. 



The greatest value of fa was about 0*05, the cube of which 

 is 0-000125 ; the corresponding value of fa would be about 

 one-eighth of fa or 0*006, and fa 2 would be 0-00004. The 

 error of <f> would hence be about 0*25 per cent., which is 

 quite negligible. 



It will be noticed that azimuthal errors in the settings of 

 the mirrors are of no effect, being parts of fa 2 and fa, changes 

 of which alone affect the value of (/>. 



37. The Effect of Bending. — Unfortunately, the effect of 

 bending * was not investigated until the series of tests had 



t For the suggestion that I should investigate the effect of bending, 

 I am indebted to Mr. E. G. Coker, Assist. Prof, of Civil Engineering, 

 McGill University. 



H2 



