584 Professor Ernest G. Coker [Feb. 18, 



mechanical measurements only, and is therefore particularly adapted 

 for engineering work. In some cases it requires considerable care to 

 obtain accurate values of each quantity separately, especially if one 

 stress is very much smaller than the other, as then minute errors of 

 observation become a large percentage of the value of the lesser stress ; 

 but possibly this difficulty would be met with in any other method. 



Lines of Principal Stress. 



Reference has already been made to the fact that any state of 

 stress at a point in a plane may be represented by a pair of stresses 

 at right angles through the point. If a simple case is taken of a 

 plate subjected to tension by forces uniformly applied at the ends, 

 the state of stress in the body may be imagined as being represented 

 by equally spaced stress lines continued throughout the plate, and the 

 intensity 'may be indicated by the spacing, and the kind of stress by 

 the character of the line drawn. If another stress system is applied 

 perpendicularly to the first, it may be indicated in the same manner, 

 and the condition of the body is then shown by a network of lines, 

 which may be looked upon as pulled or pushed according to the 

 circumstances existing in the body due to the external loading. 

 Such simple cases do not often occur, but whatever may be the 

 character of the stress distribution in a plane, it can be represented 

 conventionally by two systems of orthogonal curves spaced in some 

 manner which the external loads and boundaries of the plate 

 dictate. If, for example, two symmetrically disposed notches are cut 

 in a tension memljer, it is clear that equally spaced tension lines 

 above and below must be crowded together as they pass the narrow 

 neck, and those at the sides will probably come closer together than 

 do those in the centre, thereby indicating a high stress intensity at 

 the middle points of the notches. Lines of principal stress may be 

 drawn from the data provided by experiment, if advantage be taken 

 of the property possessed by stressed material of causing the two 

 systems of retarded rays to vibrate, one in the direction of the major 

 principal stress, and the other in the direction of the minor principal 

 stress. 



Between crossed Nicol's prisms a loaded plate shows, in general, 

 dark bands, which mark the positions of all points where the direc- 

 tions of principal stress correspond to the axes of the polarizer and 

 analyser, and by varying the angular positions of these latter a series 

 of bands is obtained, each corresponding to definite directions of 

 the axes of stress. 



If, for example, the case of a simple tension member is taken, 

 with notches in it on each side as shown, dark bands are observed 

 like those shown in the accompanying figure, and these change their 

 positions as the axes of the optical apparatus are rotated. A 



