BEFORE the end of the week, the friends at Wyllys-Roof, after carefully examining all the facts within their knowledge, were confirmed in their first opinion, that the individual claiming to be William Stanley was an impostor. Mrs. Stanley was the last of the three to make up her mind decidedly, on the point; but at length, she also was convinced, that Mr. Clapp and this sailor had united in a conspiracy to obtain possession of her husband's estate. The chief reasons for believing this to be the case, consisted in the difference of CHARACTER and EXPRESSION between the claimant and William Stanley: the more Mr. Wyllys examined this point, the clearer it appeared to him, who had known his friend's only son from an infant, and had always felt much interested in him. As a child, and a boy, William Stanley had been of a morose temper, and of a sluggish, inactive mind--not positively stupid, but certainly far from clever; this claimant, on the contrary, had all the expression and manner of a shrewd, quick-witted man, who might be passionate, but who looked like a good-natured person, although his countenance was partially disfigured by traces of intemperance. These facts, added to the length of time which had elapsed since the reported death of the individual, the neglect to claim his inheritance, the suspicious circumstances under which this sailor now appeared, under the auspices of an obscure country lawyer, who bore an indifferent character, and to whom the peculiar circumstances of the Stanley estate were probably well known, all united in producing the belief in a conspiracy. There was no doubt, however, but that a strong case could be made out on the other hand by the claimant; it was evident that Mr. Reed was convinced of his identity; his resemblance to William Stanley, and to Mr. Stanley, the father, could not be denied; the similarity of the handwriting was also remarkable; his profession, his apparent age, his possession of the letters, his accurate knowledge of persons and places connected with the family, altogether amounted to an important body of evidence in his favour. It would require a volume in itself, to give the details of this singular case; but the general reader will probably care for little more than an outline of the proceedings. It would indeed, demand a legal hand to do full justice to the subject; those who are disposed to inquire more particularly into the matter, having a natural partiality, or acquired taste for the intricate uncertainties of the law, will probably have it in their power ere long, to follow the case throughout, in print; it is understood at Longbridge, that Mr. James Bernard, son of Judge Bernard, is engaged in writing a regular report, which, it is supposed, will shortly be published. In the mean time, we shall be compelled to confine ourselves chiefly to a general statement of the most important proceedings, more particularly connected with our narrative.