QUADRATURE COEFFICIENTS. 
In a large amount of recent quadrature work we have found that Sheppard's 
formula (c) given in Biometrika, I, p. 276, gives very satisfactory results, and 
Mr P. F. Everitt has tabled the values of the three coefhcients. His manuscript 
table has proved so useful that we reproduce it here, as others may also find it a 
help. It will eventually appear in the Tables for Statisticians and Biometricians. 
The formula supposes the quadrated area to be divided into p trapezettes on 
bases of equal size h. Then Ac the chordal area is given by 
Ac = h{\z^ + ZT^ + z.,+ ... +Zp-i + izp), 
where Zo, z^, Z2 ... Zp^^, Zp are the equally spaced ordinates. 
The required area of the curve is then 
Area = Ac+G, ((2, - z^) - (z.p - Zp^,)} h 
- {{z., - z^) - {zp^-, - Zp^.,)] h . ■ 
+ C3 {(^3 - z.^ - {zp_. - Zp_.,)} h. 
Here Cj, Cg, C3 are certain functions of p and are provided for each value of p in 
the accompanying Table. They are selected to give the best result, provided we 
stop at third terminal differences. 
