In spite of the difficulties presented by their cumbersome numerical signs, the Romans were yet able to perform complicated mathematical problems by means of the abacus and by a system of finger-counting. The truth of this statement is generally recognized; but when one turns to the various works on Roman private life for information as to the actual use of the second method he is doomed to disappointment. A quotation from one of the most recent writers is perhaps typical.' "In arithmetic mental calculation was emphasized, but the pupil was taught to use his fingers in a very elaborate way that is not now thoroughly understood." It is true that in Friedlinder and in Marquardt,2 somewhat fuller statements are found, but they are mainly based upon a later Greek writer, Nicholaus of Smyrna, and fail to present illustrations of any concrete problem, The passage which has long been regarded as a locus classicus is Quintilian 1. 10. 35 : numerorum quidem notitia non oratori modo sed cuicumque saltem primis litteris erudito necessaria est. In causis vero frequentissime versari solet: in quibus actor, non dico si circa summas trepidat, sed si digitorum saltem incerto aut indecoro gestu a computatione dissentit, iudicatur indoctus. No suggestion of an actual problem for computation is found until we come to Apuleius, who in defending himself from the charge of magic, is forced to touch upon the delicate question of Prudentilla's age and thus in rather vague language attempts to