38 
Proceedings of the Royal Society of Edinburgh. [Sess. 
III. — A New Experimental Method of investigating Certain 
Systems of Stress. By G. H. Gulliver, B.Sc., A.M.I.Mech.E., 
Lecturer in Engineering in the University of Edinburgh. (Plates 
I.- VI.) 
(MS. received June 24, 1909. Read July 12, 1909.) 
On several occasions the writer has called attention to the peculiar 
deformation phenomenon known as Liiders’ lines. When a bar of iron 
or of steel experiences a permanent strain, the deformation takes place, 
at least mainly, by slidings along certain surfaces within the body of 
the piece, and the traces of these surfaces upon the external faces of 
the bar are the lines of Liiders. The surfaces of sliding, as has been 
stated before, are inclined at an angle of about 50° to the maximum 
principal tension (or minimum compression), and at 40° to the maximum 
principal compression (or minimum tension), and they are parallel to 
the intermediate principal stress. These surfaces are really irregular, 
but the disturbances due to the crystalline nature of the metal and 
the random direction of the cleavage planes are neglected in what 
follows ; such disturbances are usually small in a metal of normal struc- 
ture, and cannot be detected by the naked eye. The general form of 
a surface of sliding may be a simple plane or a cone, or it may be very 
complex. 
In a number of practical cases in which pieces of rectangular section 
are employed, it is nearly correct to say that the directions of two of the 
principal stresses remain, at all points of the body, parallel to one face of 
the piece, and the third principal stress is zero. Under these conditions a 
careful examination of the lines of Liiders, found on a plane face after the 
bar has been deformed, will give the information necessary to determine 
some of the surfaces of sliding. If the two principal stresses, of which 
the directions are parallel to the face under consideration, be a tension 
and a compression respectively, the lines of Liiders will be inclined at 50° 
to the first and at 40° to the second ; but if these stresses are both 
tensions or both compressions, the lines will be normal to the direction 
of the (numerically) greater. If one of the two stresses is zero, the 
lines of Liiders may be either normal to, or inclined to the direction 
of the other. These results follow directly from the condition that 
