A comprehensive scheme for the analysis and use of thermal neutron scattering data is described. Experimental work was carrie out with a 4-rotor high speed chopper system operated in conjunction wlth a multicounter multlchannel neutron time-of-flight system. The results are reduced to a scattering law, which is a function S of two variables ( alpha and beta ) representing the momentum and energy transferred in the scattering process. The scattering law can be divided into interference and self-terms; for the application to neutron spectrum calculations it is sufficient to consider the lnterference term as a small correction to - the self-term. The self-term is the double Fourier transformation of the self-correlation function of Van Hove, which represents the motlon of an lndividual atom in the system. This function can be represented as a gaussian distribution of the atomic position plus correction terms. The width of this gaussian distribution is a function of time and its double differential with respect to time is the velocity correlation function for an atom in the system. Thus the velocity correlation function is the function which makes the major contribution to the scatterlng cross sections. In estimating the accuracy to which measurements, analysis, and calculationsmore » of the scattering law need be made, it is necessary to evaluate a sensitivity function for each neutron spectrum problem, and thus for each scattering law a variety of sensitivity functions need to be evaluated. Two slmple examples are discussed which show, separately, the effect of absorption and temperature gradients. (auth)« less