The present note is a continuation of a short paper which appeared in the Proceedings of the Royal Society of Edinburgh for session 1876–77. The problem in question is that referred to in Professor Tait's “Memoir on Knots,” viz.:—To find the number of possible arrangements of a set of n things, subject to the conditions that the first be not in the last or first place, the second not in the first or second place, the third not in the second or third place, and so on.