We investigate the distribution of the dark matter in the distant cluster of galaxies A 370 (z=0.375) on the basis of our new, ultra-deep, subarcsecond seeing CCD images showing evidence for three merging parts of the giant arc and of some new multiple image candidates. The number of constraints is thus considerably increased, allowing a reliable determination of the parameters of the assumed double elliptical potential. The net result is a remarkable quality of fit of the complex structure revealed by our new data along the giant arc. The dark matter lies in two clumps centered on the two brightest cluster galaxies, with similar orientation and ellipticity as their two envelopes. The individual line-of-sight velocity dispersion of each clump is around 850 km s-1, the global velocity dispersion being consistent with that measured for the cluster. The two dark clumps are characterized by small core radii: r(c) congruent-to 100 h-1 kpc. The redshift of the giant arc being available, the model is so constrained that it enables accurate determination of the redshift of three faint pairs of images, simply by assuming that they are double images of a distant source across the critical line at this redshift. In this model of the cluster A 370, as in the one recently obtained for MS2137-23, the distribution of the dark matter appears to follow the distribution of light and to be highly concentrated on the brightest galaxies. If confirmed, these results should give interesting constraints on the formation and evolution of cD clusters of galaxies.