The paper of yesterday inclosed, will give you a clue to the designs of the faction which has used Sedgwick for its organ. His immediate prompter will be seen both in his speech and in his propositions. Whether more be seriously aimed at than to embarrass the others which have been long depending, is by some doubted. Perhaps this may be one of the objects; but you understand the game behind the Curtain too well not to perceive the old trick of turning every contingency into a resource for accumulating force in the Government. It would seem however that less subtlety has prevailed in this than in some other instances. The ostensible reason for the provisional army is not only absurd; but remote from the present sensations of the public; and at the same time disarms the projectors of the cavil and calumny used with most success against the commercial propositions, towit, that they tended to provoke war by an unnecessary alarm and irritation to G. Britain. The commercial propositions were the subject of yesterday and will probably be resumed today. We admit that the change of appearances may require something further, but we contend that they ought to make part of our Code until the end be obtained; and that they will be proper whether we are to be at peace or war. In the former case they will have their intended operation: In the latter they will put our Extive. on the right ground for negocia[tion.]