Onsager and Kaufman's calculation of the spontaneous magnetization of the Ising model: II

In 2011 I reviewed the calculation by Onsager and Kaufman of the spontaneous magnetization of the square-lattice Ising model, which Onsager announced in 1949 but never published. I have recently been alerted to further original papers that bear on the subject. It is quite clear that the draft paper on which I relied was indeed written by Onsager, who was working on the problem with Kaufman, and that they had two derivations of the result.