K. Pearson 
277 
the values of P and Q have been tabulated for 8 to 20 ordinates inclusive by 
Mr Leslie Bramley-Moore. They are as follows : 
p 
0 
8 
128 filll 
•109 5833 
9 
■121 2054 
■094 6875 
10 
•115 8854 
•085 0694 
11 
•111 8779 
•078 3668 
12 
•108,7500 
•073,4375 
13 
•106,2405 
•069,6644 
14 
•104,1825 
■066,6856 
15 
•102,4639 
■064,2756 
16 
•101,0073 
•062,2863 
17 
•099,7569 
•060,6170 
18 
•098,6719 
•059,1964 
19 
•097,7214 
•057,9731 
20 
•096,8818 
■056,9087 
give 
results more close as r 
I rule than 
possesses the great advantage of only weighting particular ordinates in the 
correctional terms. 
Area 
Three Differences : 
1 p (9842p- • 
At- 
+ 
53970;j + 70407) 
80640 {p-2}{p -3){p - 4:) 
1 p (4802/j- - 23016^ + 22905) 
40320 {p-2){p-4!){p- 5) 
1_ p (3122j)^ - 12222p + 10935) 
80640 {p-4>)(p-5){p-()) 
{(Zi - zi) - - Zp_^)} h 
[{z^ - z^) - {zp^.^ - Zp_,)]h 
(/^)- 
Special and occasionally useful Cases. 
Case (iii). Mid-oi'dinates and two extreme ordinates known. 
(a) One Difference : 
1 2r) 
Area - -4 y - — [{h - z,) - (Zp - Zp_0} h 
If 2pj{2p — 1) be taken as approximately unity, this becomes a formula well-known 
on the continent as Parmentier's. 
(b) Two Differences : 
. . 1 2p (40w - 57) . , , 
Area = At- t^^ ^c,^ -■ w^., — {(^i - ^o) - {Zp - h 
+ 
180(2p-l)(2j9-3) 
2j) (5p - 6) 
180(2^-2)(2;>-3) 
