367 



is equal to the sum of the products of eacli of the ordinates 

 into its abscissa divided by the sum of the ordinates, that is 



*o = -(•*!/)/-?/ =/*f(s)dx/ff{*)dx (76) 



This for the curve with the constants + m, - n, will be 



rpgq 



s e — f* m+ ie-™ V dx = P»"p- 2 _ r( m p +2 ) 



A general formula for the computation of ' standard 

 deviation,' ' skewness,' etc., will ordinarily be too complex 

 to be of utility. Actual calculations can readily be made 

 after (77) is numerically evaluated. 





A jldx=Af^e-™ v dx=l (78) 



In such a case therefore we must have, see (70), 

 A = pn m y!r ™±k (79) 



14. Approximate integration.— Ordinarily the value of 

 the integral between limits can be found with sufficient 

 accuracy from seven equidistant ordinates, since this would 

 give an exact result if the curve were representable by an 

 equation of the seventh degree, as has been shewn by the 

 writer.' The necessary formula is : 



A/ydx =-± { 41 (ft + ft) + 216(ft + ft) + 27<ft + ft) + 272ft } 

 which is very nearly given by J [...(80) 



A/ydx = ± j 8 (ft + ft) + 42(;/, + ft) + 5(ft + ft) + 53ft | (81) 

 The whole question of approximate integration by means 

 of such formula? (80, 81) will be dealt with in another 



1 This Journal. Vol. xxxiv, 1900, pp. 70-71. 

 ■ Formula (81) is much batfa rthan 



