44 



Frqf. Maxwell t On Approximate Multiple [Mar. 12, 



group of four points on the axes, giving two disposable quan- 

 tities, and a group of eight points giving three disposable quan- 

 tities, we shall be able to satisfy the six equations, and to form an 

 expression for the integral which will be correct for any function 

 not exceeding the seventh degree. 



We assume 



r r udpd(i=^Pu,+ qt{u^,:) + Rt{uJ (4). 



J -I J -I 



The equations are 



P + 4^+8^ = 4, 



2 



Qp' + 2B{q' + r' 



3' 



Qp' + 2R(q' + r') = ^, 





BqV(q' + r') = 



15 



p = 



162' 



Q 



162 



B = 



31 

 162' 



The positions of the thirteen points are given in the annexed 

 figure. 



