CONSTITUTION OF MATTER AND ANALYTICAL THEORIES DP HEAT. 47 



(vii) Let T{x,0) - f{x) = ff^{x)dx, 0<^<7r. Then fXx) is finite and 



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continuous. At every point of G^,f'(x) is non-existent and has a discontinuity 

 of the second kind. At all other points f^(x) = f (x) and is finite and continuous; 

 further, fl (x) exists and is finite at every point of 6^2- 



Now it is easily seen that |-^ F(eJn , o| exists and is finite. Therefore 

 at any point of G^, f"(x) is non-existent but V(x, ^)| exists and is finite. 



