Knowledge of the (differential) emission measure function (with temperature), Y(Te), is likely to be of fundamental significance in attempts to understand the behaviour of any optically thin plasma - and this is certainly true of present studies of the solar atmosphere. In this latter case the gross temperature structure of material below 106K has been deduced from uv line measurements since the early 1960's and, since 1968, similar analyses of the material above 106K have been made using emission lines at x-ray wavelengths. In this latter case the validity, and even desirability, of published results has recently been quite strongly challenged. Comment is made upon those criticisms of early results and upon their relevance to present day analyses. In this paper the crucial value of fine temperature resolution in the determination of the emission measure function of this coronal material is argued.