Al. a. Tchouproff 
203 
But we cannot start with (28) in the calculation of the mathematical expec- 
tation of (2^/ — I'^f, just as we cannot obtain the further terms in the development 
of E {I'r — I'r)' in powers of IjN. For these purposes Sheppard's method must 
be put into a slightly changed form : more than three terms must be retained in 
(27). In the calculation of the terms of order 1/iV^-, we must at the same time 
rely on the formulae of § III of the second Chapter and on the following relations 
easily deduced from them : 
.(30), 
1 
Ew' djji,' 
Ew'- 
.(31), 
E(o'-d/J,%^ dfJ^'r, = [^l,■,+r■^ P'-, + 2"ri+i Mr.+i ' f^n f^r-z 
1^ 
'-(32). 
3 1 
(2) To get the exact value of terras of order in the development of 
E{v\^ — fjb^^) {v j.,^ — fjb^^) in powers of 1/^, it is necessary to start from 
Vf — flj. = (dfMj.' — I'/J'r-l <^') — ( roi)'d/j,'r_i — /X^^o O) 
+ 
r(r-l) 
2~ 
7-(r-l) , , r (r-l)(r-2 ) 
~o ^ " '•-2 a 
r-3 ^ ^ ■ 
14—2 
