346 ME. L. F. KICHARDSON : APPROXIMATE ARITHMETICAL SOLUTION 



The following results have been found : 



TABLE XIII. 



* P is the excess at the centre of the tabulated number - x over an integral of ft ] 4 < 0, which has 

 the same value and radial apace rate on the circumference, 

 t Q is twice the previous column divided by square of radius. 



The corresponding errors in the stresses cannot be determined easily. As a very 

 rough guide to them, take the second differences coefficient at the centre of the circle 

 measured along a diameter with co-ordinate difference equal to the radius, that is 



(twice error at centre)/( radius) 2 . These 

 differences are also tabulated and are seen to 

 be small. 



4 - 2 '4. Peculiarities at the angles of 135 

 degrees on the Upper Boundary. There are 

 three alternative ways of treating the relation 

 between the body and boundary equations at 

 the re-entrant angles. (See Table XIII.) 

 (a) The number (10) is determined so as 



to satisfy ft i\ = ^> an( ^ does no ^ en ^ er m ^ 

 the boundary equations at all. (10) is derived 



from (01) by means of the known value of 

 3x/3<?) half-way between them. Also (11) is 

 derived from (11) in a similar way. This is 

 the procedure which has been adopted in calculating Table XII. 



(6) The number (To) is determined so as to satisfy ft , 4 ^ = 0, but it also enters 



ll 



10 



Body 

 region 



01 



Boundary - 



