I N an earlier paper1 we described a model of highenergy diffraction scattering based on the assumption that the asymptotic form of the scattering amplitude is isj(t). We also obtained from the model an integral equation for j(t), the shape of the diffraction peak. We should like, here, to report on approximate solutions to this integral equation obtained numerically on a computer. The results obtained have a number of features in common with experimentally observed diffraction peaks, and they seem sufficiently encouraging to warrant pursuing the model further. There were some oversimplifications in the original version of the model, the most serious of which was that the model was phrased in terms of only a single kind of particle (a "parton"?). We calculated cross sections, multiplicities, and so forth, only for this "particle" and made no attempt to predict from the behavior of these what the corresponding quantities for the spectrum of physically observable particles should be. There are really only two things with which this particle could be identified. It could be just any one of the existing spectrum of strongly interacting particles, or it could be a quark. In the first case, it must be assumed that at very high energies, all strongly interacting particles behave in the same way. In particular, all elastic scattering amplitudes should become equal; and indeed this is not too far from what is observed even at present energies. There is a difficulty with this interpretation, however, and it is that the average multiplicity predicted by the model for the basic particle is, asymptotically, constant. If our particle is itself any hadron, this prediction see~s to be at variance with experiment. 2 Thus the model might be, at best, only approximately true in some limited energy range. If, however, the second interpretation of our parton obtains and it is in fact a quark, then there is no difficulty with the multiplicity. It is only the quark multiplicity that is predicted to be a constant, not the multiplicity of observed hadrons. If the quark multiplicity is constant, then qq states will be produced with a mass which increases as the total energy of the reaction increases. States of qq with high mass also have high spin, so they will decay into hadrons. How many hadrons they decay into depends on quark dynamics and cannot therefore be predicted cleanly; nevertheless, one may expect that the higher the qq spin, the larger the number of stable hadrons which will finally be produced. Thus the multiplicity of observed hadrons will grow, albeit in a way we cannot easily predict, if our particle is identified with a quark. One further remark is worth making at this point. Whatever the interpretation of our particle, the model we have is not a model of the multiperipheral or multiRegge3 type, although it has certain similarities to these. Our model is mathematically equivalent to what one would obtain from a multi-Regge model with multiple exchange of a flat Pomeranchon having a trajectory of ap= 1, and for which the internal coupling constant vanishes like (logs)-1' 2• However, in a true multi-Regge theory the internal vertices cannot depend on the total energy, but only on the two adjacent momentum transfers and a Toller angle w.4 If one feels compelled to identify our model with some sort of diagram structure, the simplest diagram which might have the behavior we propose is that shown in Fig. 1.