Mr. KITCHELL said, gentlemen seemed to be mistaken; they were continually alluding to the law passed yesterday. There was not a word about two troops of horse yesterday. All we then said, was, that we would not say there should not be two troops of horse; the Message of the PRESIDENT did not say that two troops should be mounted, nor do I say, said Mr. K., that horse are not necessary; I think some are necessary; but the inquiry seemed to be, now, whether the House were to vote for more. Mr. W. SMITH said, the gentleman's observations were very extraordinary; he surely could not have attended to the subject, to say that the House had not passed the law authorizing two troops of horse. We have a law in force, said he, to ascertain and fix the Military Establishment, in which we authorize the PRESIDENT to employ the two troops of dragoons, to serve either on horse or foot at his discretion. The bill we sent up yesterday does not repeal that law, and yet gentlemen would now come forward to oppose the appropriation, and determine they shall act on foot. He could not think with what propriety the restriction could be made as the gentleman from Massachusetts wishes, nor could he think how the gentleman from Jersey had attended. Should we now say they should be at our direction, and that we would not grant money without? This would be strange conduct--an assumption of power which he hoped the House would never arrogate. Mr. KITCHELL said his meaning was, that the horse were not established yesterday, but before. Mr. HARTLEY said it appeared, from good testimony, that the troops were requisite to save the people on the frontiers from the depredations of the Indians; he thought, therefore, that they having been established before, the House were bound to make the appropriation to give effect, or show the great inconsistency. Mr. NICHOLAS said it was not his intention to vote for these men at all; but if they must have them, perhaps it would be most economical to equip them. With respect to their power of withholding the appropriation, he had no doubt; and though they had yesterday passed a law establishing two companies of cavalry, it was in the power of that House, of the Senate, or of the PRESIDENT, to refuse an appropriation. This was the sense of the constitution. When the bill came before the House, he should give his negative to the additional horse; for, if they were always to keep up the same number of men, whether in war or peace, except two-thirds of both Houses were found to oppose the will of the PRESIDENT, they might bid adieu to all restraint upon Executive power, and count upon a military Government, if ever an Executive should be found whose will it should be to make it so. If these were to be kept up, he would still say the House had better go to $100,000 expense to mount them on horse-back.