§ 339. There yet remain two practical questions of no inconsiderable importance, connected with the 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.

§ 340. 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.

§ 338. It remains only to take notice of two qualifi-. cations of the general principle of representation, which are engrafted on the clause. One is, that each state shall have at least one representative; the other is that already quoted, that the number of representatives shall not exceed one for every 30,000. The former was indispensable in order to secure to each state a just representation in each branch of the legislature; which, as the powers of each branch were not exactly co-extensive, and especially, as the power of originating taxation was exclusively vested in the house of representatives, was indispensable to preserve the equality of the small states, and to reconcile them to a surrender of their sovereignty. This proviso was omitted in the first draft of the constitution, though proposed in one of the preceding resolutions. But it was adopted without resistance, when the draft passed under the solemn discussion of the convention. The other was a matter of more controversy. The original limitation proposed was 40,000; and it was not until the very last day of the session of the convention, that the number was reduced to 30,000. The object of fixing some limitation was to prevent the future existence of a very numerous and unwieldy house of representatives. The friends of a national government had no fears, that the body would ever become too small for real, effective, protecting service. The danger was, that from the natural impulses of the popular will, and the desire of ambitious candidates to attain office, the number would be soon swollen to an unreasonable size, so that it would at once generate, and combine factions, obstruct deliberations, and introduce and perpetuate turbulent and rash counsels.

§ 339. There yet remain two practical questions of no inconsiderable importance, connected with the 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, 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.

§ 340. 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.

§ 341. But the difficulty is far otherwise in regard to representatives. Here, there can be no subdivision of the unit; each state must be entitled to an entire representative, and a fraction of a representative is incapable of apportionment. Yet it will be perceived at once, that it is scarcely possible, and certainly is wholly improbable, that the relative numbers in each state should bear such an exact proportion to the aggregate, that there should exist a common divisor for all, which should leave no fraction in any state. Such a case never yet has existed; and in all human probability it never will. Every common divisor, hitherto applied, has left a fraction greater, or smaller in every state; and what has been in the past must continue to be for the future. Assume the whole population to be three, or six, or nine, or twelve millions, or any other number; if you follow the injunctions of the constitution, and attempt to apportion the representatives according to the numbers in each state, it will be found to be absolutely impossible. The theory, however true, becomes practically false in its application. Each state may have assigned a relative proportion of representatives up to a given number, the whole being divisible by some common divisor; but the fraction of population belonging to each beyond that point is left unprovided for. So that the apportionment is, at best, only an approximation to the rule laid down by the constitution, and not a strict compliance with the rule. The fraction in one state may be ten times as great, as that in another; and so may differ in each state in any assignable mathematical proportion. What then is to be done? Is the constitution to be wholly disregarded on this point? Or is it to be followed out in its true spirit, though unavoidably differing from the letter, by

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the nearest approximation to it? presentative can be assigned to one state beyond its relative proportion to the whole population, it is equally true, that it can be assigned to all, that are in a similar predicament. If a fraction admits of representation in any case, what prohibits the application of the rule to all fractions? The only constitutional limitation seems to be, that no state shall have more than one representative for every thirty thousand persons. Subject to this, the truest rule seems to be, that the apportionment ought to be the nearest practical approximation to the terms of the constitution; and the rule ought to be such, that it shall always work the same way in regard to all the states, and be as little open to cavil, or controversy, or abuse, as possible.

§ 342. But it may be asked, what are the first steps to be taken in order to arrive at a constitutional apportionment? Plainly, by taking the aggregate of population in all the states, (according to the constitutional rule,) and then ascertain the relative proportion of the population of each state to the population of the whole. This is necessarily so in regard to direct taxes; and there is no reason to say, that it can, or ought to be otherwise in regard to representatives; for that would be to contravene the very injunctions of the constitution, which require the like rule of apportionment in each case. In the one, the apportionment may be run down below unity; in the other, it cannot. But this does not change the nature of the rule, but only the extent of its application.

§ 343. The next clause of the second section of the first article, is: "When vacancies happen in the repre"sentation of any state, the executive authority thereof "shall issue writs of election to fill such vacancies."