The proposition in your letter of May the 16th, of adding an umpire to our discordant negotiators at Paris, struck me favorably on reading it, and reflection afterwards strengthened my first impressions. I made it therefore a subject of consultation with my coadjutors, as is our usage. For our government, although in theory subject to be directed by the unadvised will of the President, is, and from its origin has been, a very different thing in practice. The minor business in each department is done by the Head of the department, on consultation with the President alone. But all matters of importance or difficulty are submitted to all the Heads of departments composing the cabinet; sometimes by the President's consulting them separately and successively, as they happen to call on him; but in the greatest cases, by calling them together, discussing the subject maturely, and finally taking the vote, in which the President counts himself but as one. So that in all important cases the executive is, in fact, a directory, which certainly the President might control; but of this there was never an example, either in the first or the present administration. I have heard, indeed, that my predecessor sometimes decided things against his council. * * * * * I adopted in the present case the mode of separate consultation. The opinion of each member, taken separately, was that the addition of a third negotiator was not at this time advisable. For the present therefore, the question must rest. Mr. Bowdoin, we know, is anxious to come home, and is detained only by the delicacy of not deserting his post. In the existing temper between him and his colleague, it would certainly be better that one of them should make an opening for re-composing the commission more harmoniously. I salute you with affection and respect. TO GEORGE HAY. WASHINGTON, June 12, 1807.