This research extends the "Purdue studies" of research library growth, presenting results that include library statistical trends during a 35-year period, 1951-1985. It serves to update Purdue's 9-report series (1965-1973) and is a validation study of Purdue's growth forecasts, 28 of which were published in 1965, then revised in 1971. The research libraries considered here represent 58 "first tier" American research libraries that were members of the Association of Research Libraries (ARL) in 1964, when the Purdue studies began; all are members still. The results describe 35 years of growth and change in library holdings, volumes added, professional and non-professional staff size, and in three expenditure categories--salaries, materials and binding, and total, plus university/main campus total and graduate enrollments, and Ph.D. degrees awarded. Growth trends are reported for eight "composite" libraries that differ in size, i.e., the average or mean; the median, first quartile and third quartile; and four collection (or holdings) subgroups, the "large,""medium-large,""medium-small," and "small." Correlational findings also show the strength of relationship, year-by-year, among the study variables. Trends and forecasts of 28 variable-and-composite combinations are shown in 8 tables and 28 figures. Some estimates of future growth through 1990 are presented, together with suggestions for future research. Appended materials include a listing of the nine Purdue reports; a listing of National Center for Education Statistics (NCES) data source documents; correlations of 16 variables year-by-year from 1951 to 1985 presented in the form of a conversation between two fictitious library directors, one newly-appointed and the other (retiring; and a description of the composition of ARL subgroups based on 1985 data. (40 references) (Author/BBM)