There is a personal and political mystery underlying this transaction which history will probably never solve. Only a few points of information have come to light, and they serve to embarrass rather than aid the solution. The first is that Calhoun, although the friend and protégé of Douglas, and also himself personally pledged to submission, came to the Governor and urged him to join in the new programme as to slavery,--alleging that the Administration had changed its policy, and now favored this plan,--and tempted Walker with a prospect of the Presidency if he would concur. Walker declared such a change impossible, and indignantly spurned the proposal. The second is that one Martin, a department clerk, was, after confidential instructions from Secretary Thompson and Secretary Cobb, of Buchanan's Cabinet, sent to Kansas in October, ostensibly on department business; that he spent his time in the lobby and the secret caucuses of the convention. Martin testifies that these Cabinet members favored submission, but that Thompson wished it understood that he was unwilling to oppose the admission of Kansas "if a pro-slavery constitution should be made and sent directly to Congress by the convention." A wink was as good as a nod with that body, or rather with the cabal which controlled it; and after a virtuous dumb-show of opposition, it made a pretense of yielding to the inevitable, and acted on the official suggestion. This theory is the more plausible because Martin testifies further that he himself drafted the slavery provision which was finally adopted. The third point is that the President inexcusably abandoned his pledges to the Governor and adopted this Cobb-Thompson-Calhoun contrivance, instead of keeping his word and dismissing Calhoun, as honor dictated. This course becomes especially remarkable in view of the fact that the change did not occur until after Walker's rejection of the fraudulent Oxford returns, which action placed the legislative power of the Territory in the hands of the newly elected free-State Legislature, as already related. On the same day (October 22, 1857) on which Walker and Stanton issued their proclamation rejecting the fraudulent returns, President Buchanan wrote another highly commendatory letter to Governor Walker. As it has never before been published, its full text will have special historical interest. WASHINGTON CITY, 22d October, 1857.