Di-jet event rates have been measured for deep-inelastic scattering in the
kinematic domain 5 less than or similar to Q(2) less than or similar to 100
GeV2 and 10(-4) less than or similar to xBj less than or similar to 10(-2)
, and for jet transverse moments squared p(t)(*2) greater than or similar t
o Q(2). The analysis is based on data collected with the H1 detector at HER
A in 1994 corresponding to an integrated luminosity of about 2 pb(-1). Jets
are defined using a cone algorithm in the photon-proton centre of mass sys
tem requiring jet transverse momenta of at least 5 GeV. The di-jet event ra
tes are shown as a function of Q(2) and x(Bj). Leading order models of poin
t-like interacting photons fail to describe the data. Models which add reso
lved interacting photons or which implement the colour dipole model give a
good description of the di-jet event rate. This is also the case for next-t
o-leading order calculations including contributions from direct and resolv
ed photons.