XLVII-XLVIIII 



CC\ \\lll 



the integral over a rang.- divided int., (] ci|iiul int'-rvalH /i by onlinatcH 



approximation is 



6y, 



(xvii), 



from which we can lind I lie weights to be attached to the succensive ordr 

 when the range of integration is divided into any number of intervals that I'K a 

 multiple of 6. For the case of 24 intervals, the Weddle weights are shown in 

 the hist column of the following table. 



111 the case of a curve having high contact with the #-axis at one limit of 

 integration, we may take our ordinates at any convenient interval and make their 

 number up to a multiple of 6 by adding a small number of zero ordinates ; a more 

 convenient form of the Weddle approximation in this case is 



' Kyo + ya + 2/6 +...) + 5 (yi + y 3 + :'/5 + ...) + (yi + y* + yt +)] .(xviii). 



Illustration. We will calculate 



/. 12 (21, 81) = f 



Jo 



- x}*>dx I [ l 

 I Jo 



* Formulae of the nature of Weddle's, while very suitable for the quadrature of mathematical functions, 

 are to be avoided in cases where the ordinates are determined by observation. They give unequal weights 

 to the ordinates and thus may markedly emphasise large random errors. 



11. II. 99 



