The first volume contains mathematical problems, which appear to be college exercises (1814); the second volume is an essay on the projection of the sphere and spherical trigonometry, including an appendix on astronomy (1812); and the third volume is a lecture on natural philosophy, apparently prepared for delivery [n.d.].

This volume contains calculations of the distances of stars, eclipses, and longitude, made by William Maule, James Cresson, Joseph Jeanes, James James, and Robert Hutchinson, pupils in the Friends Academy, where Roberts was a teacher.