PLANE STRAIN IN BIPOLAR CO-ORDINATES. 
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large compared to the other coefficients. Hence, when the hole is at a considerable 
distance from the straight edge, the stress in the straight edge approximates to 
T {1 — C cos 2/3(1—cos (3)} 
where C is a small positive constant. 
This shows that the stress in the straight edge is a minimum at the mid-point, 
increases to a maximum as we move outwards, then diminishes to a second minimum, 
and finally increases steadily to the value T at infinity, where /3 = 0. 
In fig. 4 we have plotted the graphs of the stresses in the boundaries for a case in 
Fig. 4. 
which the hole is fairly near to the straight edge, a, = Q'8, for which the shortest dis¬ 
tance between the two boundaries is approximately one-third of the radius of the circle. 
It will be noted that the general character of the stresses is not affected by the proximity 
of the straight edge. It will be remembered that when the hole is at a great distance 
from the straight edge there are maximum stresses of 3T at the extremities of the 
diameter perpendicular to the straight edge, with points of maximum compression 
numerically equal to T lying between. For a. ] = 0'8 we find that the maxima occur 
at the same places but are increased, the increase being more marked at the point 
nearest to the straight.edge, where the tension is 4'366T, while its value at the point 
most remote from the straight edge is 3'266T. The stress in the straight edge also 
maintains the same general character as it exhibits when the hole is at a great distance 
2 s 2 
