to equation (7.31), the partial sum originally represented by 
equation (7.9) becomes equation (7.32). In equation (7.32), 
the second expression is simply a more informative way to write 
the first expression. 
In the second expression, for each value of n, the term 
under the summation sign is a vector in the complex plane with 
an amplitude determined by the value of the radical, and a di- 
rection determined by the direction of the unit vector, 
expli(u 5.4% + WC one} I. For any fixed t, say ty, the 
direction of each vector is determined, and since YM on4y) 
has the properties of equation (7.32), the individual vectors 
in the sum point in all possible directions. 
To add vectors, the tail of the second is placed at the 
head of the first and the sum is the vector joining the head 
of the second with the tail of the first. The sum of the r 
vectors is this process repeated r times. 
The sum of these vectors for A, m and Aj small but 
finite is considered in the classical statistical problem of 
the random walk. The random walk problem is described in de- 
tail by Margineau and Murphy [1943] and Kennard [1938], and 
Brownian motion is described by Levy [1948], but the statement 
of the problem will be given again here for the sake of complete- 
ness. 
The classical problem concerns itself with a drunkard who 
starts out for home from a pub after a night of revelry. He 
strikes out in some direction and walks a distance Vy in that 
direction, but becomes confused and turns in a completely 
Balers 
