BY FINITE DIFFERENCES OF PHYSICAL PROBLEMS, ETC. 309 



Let {01), (23), &c., for example, represent these numerical values at the co-ordinate 

 points x = 0, y = h; x = 2h, y = 3h, &c., reckoned from the centre of an 

 arbitrarily chosen square as origin. Then at any tabular point 0, 



B /~ will be represented by p. | = -L {(10)-(TO)} 



Thus /i 2 ^ 2 / is the sum of the four nearest neighbours minus four times the value 

 at the point considered. 



and ^ - 



.Halfway between two tabular points, say at |-, 



' | will be represented by |^ = i {(10)-(00)}. 

 In the centre of four tabular values, e.g., at |-, J 



will be represented by = {(11) + (00)-(01)-(10)}. 



A point at which the difference equation obtaining throughout the body has to be 

 satisfied will be called a body-point. There must be enough known values of the 

 integral (f> on the boundary side of any body-point to make the said difference 

 equation completely determinate. Thus for ^ 2 there must be at least one layer of 

 points with known values of < on all sides of any body-point, for ^ 4 at least two 

 layers. It will be seen in 4 that at re-entrant angles a point may have sufficient 

 known values outside it and yet not be a body-point, because the body -equation Is 

 not to be satisfied there. A point at which the body-equation is not satisfied, but at 



