The “infinitely dilute” resonance integral is considered in the unresolved region. The gamma-ray and fission widths are assumed constant so that the height of any resonance depends only on the resonance energy and the reduced neutron width. On the basis of this assumption, the γ'th moment of the area under the profile of an isolated resonance may be written as a combination of the integrals Any such integral may be expressed in terms of the integrals corresponding to j = 0 and j = 1, which are easily determined. Next, an expression for the γ'th moment of the resonance integral is derived for the case where resonances are scattered over an energy interval. In view of the lack of absolute unanimity among workers in this field, the derivation is performed without making any specific assumption about the level spacing distribution, allowance being made for energy dependence. From the results for an isolated resonance, this expression is capable of evaluation for any particular value of γ, once the form of the level spacing distribution has been chosen and the resonance density calculated.