  Let t_a be the Dehn twist about a circle a on an orientable surface. It is
well known that for each circle b and an integer n, I(t_a^n(b),b)=|n|I(a,b)^2,
where I(,) is the geometric intersection number. We prove a similar formula for
circles on nonorientable surfaces. As a corollary we prove some algebraic
properties of twists on nonorientable surfaces. We also prove that if M(N) is
the mapping class group of a nonorientable surface N, then up to a finite
number of exceptions, the centraliser of the subgroup of M(N) generated by the
twists is equal to the centre of M(N) and is generated by twists about circles
isotopic to boundary components of N.
