It has been suggested that an effective discriminant of the small- for-dates (SFD) foetus could be constructed from foetal measurements obtained ultrasonically at an estimated gestational age of 34-36 weeks. To examine this conjecture, a study of singleton pregnancies was carried out at the University Department of Midwifery, Queen Mother's Hospital, Glasgow. Although seven foetal dimensions had been scheduled for measurement, Neilson, Whitfield and Aitchison (1980) found that a simple discrimination procedure based on the product of foetal trunk area and crown-rump length misclassified only 6% of the SFD and 12% of the non-SFD infants in the sample. The work described in this thesis follows on from, and extends, their analysis. By considering more complicated functions of the variables, and different kinds of discriminant, it was hoped to find-a classification rule with lower error rates. It was also hoped to construct an accurate predictor of Birthweight Score - a measure of the atypicality of a recorded birthweight for gestational age at birth. An aim of more theoretical interest was to assess the relative performance of some commonly-used discrimination procedures on the same real data set. (Abstract shortened by ProQuest.).