  In this paper we generalize and put in a new light part of ``Fouier analysis
on Number fields and Hecke's zeta function''[14] by Tate. We express the
relative Euler characteristic using purely adelic language. By using certain
natural normalization of Haar measure on adeles we obtain the relative
Riemann-Roch theorem. In particular we show that using our relative
normalization of the Haar measure on adeles we can obtain the relative
Riemann-Roch theorem from the adelic Poisson summation formulae. In addition,
using our methods we define the relative 'size of cohomology' numbers, i.e.
extract the $h^0$ and $h^1$ part of the relative Euler characteristic. Our
theory not only covers both absolute and relative cases, but also the case of
an arithmetic curve and a nonsingular, projective curve over a finite field.
