260 THE BRACED AECH. [CHAP. XIV. 



For the exact values of A and B, we have the following table : 



For the values of y we have the following table : 



It will be seen that for the semi-circle the locus is a straight 

 line, for which y = \irr = 1.5708 r. Thus, for any given case 

 that is, I, A and r given we can easily calculate K. Then 

 from our tables, for given value of a, we can find A, B and y for 

 values of /3 of 0, -&ths, ^ths, etc., of a. These values inserted 

 in the equation for y above, will enable us to plot the curve or 

 locus cdeik, which being once known, the rest is easy. We 

 have thus by a union of analytical results with our graphical 

 method a very easy and practical solution of this important 

 case. We may, if we choose, only use our method to determine 

 the horizontal thrust and vertical reaction as shown by the Fig. 

 91, and then calculate the strains by the method of moments. 

 The availability and ease of the method here given, as com- 

 pared with calculation, will be seen from a consideration of the 



