the fourth, and the victory fell to another who had never taken the first place except at the last. Still, this apparent injustice was counterbalanced by the fact that the last contest was really the most difficult, while a certain average excellence in the former contests was required of everyone who entered the pentathlon at all; also it was no small merit to keep a place among the victors in all five contests, though it might not be the first or second. Of course these are merely hypotheses; we have not sufficient materials for attaining certainty in this matter. A number of other gymnastic exercises were of greater importance for the gymnasium than for the public games. Among those which were merely preliminary training for more serious tasks we have already mentioned the dumb-bells and the quintain. Others bear some resemblance to our own gymnastics; thus, for instance, exercises in bending the knees, which were especially popular at Sparta, and also practised by girls there; thrusting the arms forward and backward whilst standing on tiptoe, hopping on one foot, or changing the foot, etc. Ball was also included among the games of a semi-gymnastic character, as with us, too, it plays some part in gymnastic exercises; rope-pulling was also a favourite practice, but throughout the whole of antiquity far the most popular recreative game in the gymnastic schools was ball-playing, and there were special places devoted to it, just as there were afterwards in the baths or thermae. The ancient writers mention several other occupations of this kind, half-way between serious exercises and mere games; undoubtedly there were many others concerning which we have no information, and the relief in Fig. 134 probably shows us one of these. It seems to represent a game with a large hard ball, which was thrown up into the air and caught on the thigh, and, perhaps, thrown up again into the air from there. [Illustration: FIG. 134.]