Just at this time, Mr. Thomas L. Kane, of Pennsylvania,--son of the late Judge of the United States District Court for that State, and brother of the late Dr. Kane, the Arctic explorer,--solicited the Administration for employment as a mediator between the Mormons and the Federal Government. Mr. Kane was one of the few persons of education and social standing who were well acquainted with Mormon history. He had visited them at Winter Quarters, in Iowa, during their exodus from Nauvoo, in the capacity of a commissioner to enlist the Mormon battalion which served in the Mexican War. During an illness which attacked him there, he was treated with an unremitting kindness, for which his gratitude has been proportionate. Belonging to a family whose members have been distinguished by strong traits of individuality, not to say eccentricity, from that moment forward he displayed a practical interest in the welfare of the sect. It is said that he became a convert to the religious doctrines of Mormonism. Whether this be true at all, and, if so, to what extent, it would he profitless at the present time to inquire. For the purposes of this narrative, it is sufficient to assert only, what is unchallenged, that he was a sincere admirer of the Mormons as a people, and for a long series of years had defended them from every reproach with a zeal which many of his friends thought inordinate. Its experience in Kansas had familiarized the Cabinet with the use of secret agents; but, nevertheless, the proposition of Mr. Kane was coldly received. After a brief correspondence, he started for California, in no capacity a representative of the government, if he himself is to be believed, but bearing letters from Mr. Buchanan indorsing his character as a gentleman, and exhorting Federal officials to render him such courtesies as were within their power. Having arrived at San Francisco, he journeyed southward to the lately abandoned Mormon settlement of San Bernardino, near Los Angeles, travelling under the assumed name of Osborne, and proclaiming his business to be the collection of specimens for an entomological society in Philadelphia. There his real name and purpose were detected, but he succeeded in obtaining transportation to Salt Lake City, where he arrived on the 25th of February, 1858, and was greeted by Young and Kimball, and the rest of the Mormon magnates, as an old and cherished friend.