clause of the constitution now under consideration. One is, what are to be deemed direct taxes within the meaning of the clause. The other is, in what manner the apportionment of representatives is to be made. The first will naturally come under review in examining the powers of congress, and the constitutional limitations upon those powers; and may, therefore, for the present, be passed over. The other was a subject of much discussion at the time, when the first apportionment was before congress after the first census was taken; and has been recently revived with new and increased interest and ability. It deserves, therefore, a very deliberate examination.
§ 675. The language of the constitution is, that "representatives and direct taxes shall be apportioned among the several states, &c. according to their respective numbers;" and at the first view it would not seem to involve the slightest difficulty. A moment's reflection will dissipate the illusion, and teach us, that there is a difficulty intrinsic in the very nature of the subject. In regard to direct taxes, the natural course would be to assume a particular sum to be raised, as three millions of dollars; and to apportion it among the states according to their relative numbers. But even here, there will always be a very small fractional amount incapable of exact distribution, since the numbers in each state will never exactly coincide with any common divisor, or give an exact aliquot part for each state without any remainder. But, as the amount may be carried through a long series of descending money fractions, it may be ultimately reduced to the smallest fraction of any existing, or even imaginary coin.
