32 
PROFESSOR K. PEARSON ON MATHEMATICAL CONTRIBUTIONS 
"1 ( ~)r }■> 2 /)■> 1 O ') 1 O'* ^ rn 1 rp r.-> fjn 2 
r 24 r 34 / iv I 1 plT.?!, '.,34 '/ i v I ,, iv 
+ /W 3 & 13 + A6A& 13 + 1 3 
+ 
1 r r ^ 7’ 7' 
±Z;/ 23 ' 24' 34 // /// 
/Wh 
24?% !)?% Q?% A?’o 
// /// iv I 
% % *v v + 
1% r 2 «, 
XZ,/ 23 / 24 '34 ///„, i 
/3 2 /3 3 ^ 4 
< W + <W 
P2P3P4 
4 . - -' la'lSf . H' 3 8 / " , /// I 24r l3 r 13 r l4 r 24 / //,, iv I 24? 'l3 r 18 r S3 r 84 / '/ 
+ /W 3 & 311 + A/Wh 211 h AAAA 121 
+ 
24r i2 r l4 r 23^24 / n„ . j v - i 24r l3 r 14 r 23 r 24 ///„. i 
A AAA 
v x v 3 n 1 lv + 
v ' v " v ’" v iv I 24r 12 r l3 r 14 r 34 / , iv 
A AAA 111 1 + A AAA 31 1 
+ ~ 
24? , i 3 ?' , i3?’ 2 3?’34 , „ ,,, 24 ?%o?' , 14 ?^3?'3 4 , ,, ,,, 
yA-0' t ')’• rr 
' // rr/ . “12' 14' 23' 34 / // '/' iv I “ J 13 14 23 34 / /'/ i v 
aaaa 4,11,1 ^•* 
i 24? ’l2’ ? ’l3 ? ’l4 ? ’84 / m ; v i 24?%2?%p’24^34 I ” iv i 2 4 0 3 04^24^34 ' /// ; v 
+ A a J t o A + ~q~q~q~q A A A 1V + A A A 1 
AAAA 
24/1 o? oq?v» ,?’< 
AAAA 
AAAA 
24?%, r t 
i —'12'23'24'34 ” "> iv i 24 M 3 A3A4A4 // /// ; v i MAs^A''34 n m iv 
-h A A A + nVflfl A A A + ,3 0/0 0 A A A 
P1P2P3P4 P1P0P3P4 P1P2P3P4 
. (lxsxiii.). 
. In the case of three variables, we must cancel in the above expression all terms 
involving A- Thus we shall have 3 instead of 6 first order terms, 6 instead of 21 
second order terms, 10 instead of 56 third order terms, and 15 instead of 126 fourth 
order terms—a much more manageable series. 
I give below the extra term necessary for calculating the value of (Q — Qo)/Qo as 
far as the fifth order terms in the case of three variables. 
Fifth Order Terms for Three Variables. 
1 C rji 0 rit 5 m 5 Pa/)’ 4/ji 
F I dM_ v " v >11 I . ; 3_1_ v m / , Tl2_ v ' v " I rfv ; 12 v m / 
IIW , l * v * + Aft % + Aft + ftftft ’* ’« 
+ 
5?’ al 4 ? 
31 ' 23 i. III 
57bo 4 Tc 
v ' v rn I 
FFA 3 4 A/S,/33 
12__23 U 
+ 
5?% 0 4 r 
12 ‘ 31 / '/ 
fldsd:) 
Viqo 4 /j> r> 7 ’ 4 o> 1 0^ 7 * ^ 
^23_7_31 // rr, , 23 * 12 // /// I xu/ 31 y 12 ,, / 
/Si/d^g 3 * A^3 4 3 /3i/3o^ ; 
T 4 Ui Uo 
10/’ 3 r 2 10)’ 3 v 2 10}’ 3 }’ 2 
i - lu/ 31 '23 ’! III i -*- u/ 12 '23 / ’I III i xv "l2 '31 / // /// 
+ ftftft + ftftft V * V * 1,1 + ^Aft ** 
1 0}’ 3 r 2 
xu/ 23 '31 u n . Ill 
10?’ 3 - 2 
tyC\ r r 3 m rr 
23 7 12 / // n, . ^ u/ 23 7 31 7 12 / " nr 
+ 25 51 / rr /// | 25 12 / ,r /,' \ ... . , 
o o o ^1^2 ^4 + —o o V 1 V -i V 2 + - / 3 i/ g o/ g ~ V 1 V S t'g 
+ 
20?’3i ?% 2 ?’q 3 / n ,// . 
■ftftft- + 
20?% o 3 ?%,?% 
12 '23'31 /■„, //,„ /// 
aOr r 2 r 2 
t/u/ 0‘J' Q1 / lO 
_ v ' v " r _i_ ~" :_ 23 '_ 3i . 'l g. ,, " v >» 
W 3 3 ' 3 1 + fijfiA VsV ' 3t - 2 
30?%i?%o 2 ?’oq 2 , „ ,,, . 30/%,?%., 2 ? 2 
i vvr/ 31 , 12 '28 / f' m i vv/ 12 23 31 / // n/ 
+-ftftft-^'' +Tftft^" s%% 
. (lxxxiv.). 
