meeting of the Congress of the United States, and within every subsequent term of ten years, in such manner as they shall by law direct. The number of Representatives shall not exceed one for every thirty thousand, but each State shall have at least one Representative."

There would seem to be little difficulty in understanding these provisions. The terms used are designed, doubtless, to be received in no peculiar or technical sense, but according to their common and popular acceptation. To apportion is to distribute by right measure, to set off in just parts, to assign in due and proper proportion. These clauses of the Constitution respect not only the portions of power, but the portions of the public burden, also, which should fall to the several States; and the same language is applied to both. Representatives are to be apportioned among the States according to their respective numbers, and direct taxes are to be apportioned by the same rule. The end aimed at is, that representation and taxation should go hand in hand; that each State should be represented in the same extent to which it is made subject to the public charges by direct taxation. But between the apportionment of Representatives and the apportionment of taxes, there necessarily exists one essential difference. Representation founded on numbers must have some limit, and being, from its nature, a thing not capable of indefinite subdivision, it cannot be made precisely equal. A tax, indeed, cannot always, or often, be apportioned with perfect exactness; as in other matters of account, there will be frac tional parts of the smallest coins, and the smallest denomination of money of account; yet, by the usual subdivisions of the coin, and of the denominations of money, the apportionment of taxes is capable of being made so exact, that the inequality becomes minute and invisible. But representation cannot be thus divided. Of representation, there can be nothing less than one Representative; nor, by our Constitution, more Representatives than one for every thirty thousand. It is quite obvious, therefore, that the apportionment of representative power can never be precise and perfect. There must always exist some degree of inequality. Those who framed and those who adopted the Constitution were, of course, fully acquainted with this necessary operation of the provision. In the Senate, the States are entitled to a fixed number of Senators; and therefore, in regard to their representation in that body, there is no consequential

or incidental inequality. But, being represented in the House of Representatives according to their respective numbers of people, it is unavoidable that, in assigning to each State its number of members, the exact proportion of each, out of a given number, cannot always or often be expressed in whole numbers; that is to say, it will not often be found that there belongs to a State exactly one tenth, or one twentieth, or one thirtieth of the whole House; and therefore no number of Representatives will exactly correspond with the right of such State, or the precise share of representation which belongs to it, according to its population.

The Constitution, therefore, must be understood, not as enjoining an absolute relative equality, because that would be demanding an impossibility, but as requiring of Congress to make the apportionment of Representatives among the several States according to their respective numbers, as near as may be. That which cannot be done perfectly must be done in a manner as near perfection as can be. If exactness cannot, from the nature of things, be attained, then the nearest practicable approach to exactness ought to be made.

Congress is not absolved from all rule merely because the rule of perfect justice cannot be applied. In such a case, approximation becomes a rule; it takes the place of that other rule, which would be preferable, but which is found inapplicable, and becomes itself an obligation of binding force. The nearest approximation to exact truth or exact right, when that exact truth or that exact right cannot itself be reached, prevails in other cases, not as matter of discretion, but as an intelligible and definite rule, dictated by justice and conforming to the common sense of mankind; a rule of no less binding force in cases to which it is applicable, and no more to be departed from, than any other rule or obligation.

The committee understand the Constitution as they would have understood it if it had said, in so many words, that Representatives should be apportioned among the States according to their respective numbers, as near as may be. If this be not its true meaning, then it has either given, on this most delicate and important subject, a rule which is always impracticable, or else it has given no rule at all; because, if the rule be that Representatives shall be apportioned exactly according to numbers, it is

impracticable in every case; and if, for this reason, that cannot be the rule, then there is no rule whatever, unless the rule be that they shall be apportioned as near as may be.

This construction, indeed, which the committee adopt, has not, to their knowledge, been denied; and they proceed in the discussion of the question before the Senate, taking for granted that such is the true and undeniable meaning of the Constitution.

The next thing to be observed is, that the Constitution prescribes no particular process by which this apportionment is to be wrought out. It has plainly described the end to be accomplished, namely, the nearest approach to relative equality of representation among the States; and whatever accomplishes this end, and nothing else, is the true process. In truth, if, without any process whatever, whether elaborate or easy, Congress could perceive the exact proportion of representative power rightfully belonging to each State, it would perfectly fulfil its duty by conferring that portion on each, without reference to any process whatever. It would be enough that the proper end had been attained. And it is to be remarked, further, that, whether this end be attained best by one process or by another, becomes, when each process has been carried through, not matter of opinion, but matter of mathematical certainty. If the whole popu lation of the United States, the population of each State, and the proposed number of the House of Representatives, be all given, then, between two bills apportioning the members among the several States, it can be told with absolute certainty which bill assigns to any and every State the number nearest to the exact proportion of that State; in other words, which of the two bills, if either, apportions the Representatives according to the numbers in the States, respectively, as near as may be. If, therefore, a particular process of apportionment be adopted, and objection be made to the injustice or inequality of its result, it is surely no answer to such objection to say, that the inequality necessarily results from the nature of the process. Before such answer could avail, it would be necessary to show, either that the Constitution prescribes such process, and makes it necessary, or that there is no other mode of proceeding which would produce less inequality and less injustice. If inequality, which might have otherwise been avoided, be produced by a given

process, then that process is a wrong one. It is not suited to the case, and should be rejected.

Nor do the committee perceive how it can be matter of constitutional propriety or validity, or in any way a constitutional question, whether the process which may be applied to the case be simple or compound, one process or many processes; since, in the end, it may always be seen whether the result be that which has been aimed at, namely, the nearest practicable approach to precise justice and relative equality. The committee, indeed, are of opinion, in this case, that the simplest and most obvious way of proceeding is also the true and constitutional way. To them it appears, that, in carrying into effect this part of the Constitution, the first thing naturally to be done is to decide on the whole number of which the House is to be composed; as when, under the same clause of the Constitution, a tax is to be apportioned among the States, the amount of the whole tax is, in the first place, to be settled.

When the whole number of the proposed House is thus ascertained and fixed, it becomes the entire representative power of all the people in the Union. It is then a very simple matter to ascertain how much of this representative power each State is entitled to by its numbers. If, for example, the House is to contain two hundred and forty members, then the number 240 expresses the representative power of all the States; and a plain calculation readily shows how much of this power belongs to each State. This portion, it is true, will not always, nor often, be expressed in whole numbers, but it may always be precisely exhibited by a decimal form of expression. If the portion of any State be seldom or never one exact tenth, one exact fifteenth, or one exact twentieth, it will still always be capable of precise decimal expression, as one tenth and two hundredths, one twelfth and four hundredths, one fifteenth and six hundredths, and so on. And the exact portion of the State, being thus decimally expressed, will always show, to mathematical certainty, what integral number comes nearest to such exact portion. For example, in a House consisting of 240 members, the exact mathematical proportion to which her numbers entitle the State of New York is 38.59; it is certain, therefore, that 39 is the integral or whole number nearest to her exact proportion of the representative power of the Union. Why, then, should she not

have thirty-nine? and why should she have forty? She is not quite entitled to thirty-nine; that number is something more than her right. But allowing her thirty-nine, from the necessity of giving her whole numbers, and because that is the nearest whole number, is not the Constitution fully obeyed when she has received the thirty-ninth member? Is not her proper number of Representatives then apportioned to her, as near as may be? And is not the Constitution disregarded when the bill goes further, and gives her a fortieth member? For what is such a fortieth member given? Not for her absolute numbers, for her absolute numbers do not entitle her to thirty-nine. Not for the sake of apportioning her members to her numbers as near as may be, because thirty-nine is a nearer apportionment of members to numbers than forty. But it is given, say the advocates of the bill, because the process which has been adopted gives it. The answer is, No such process is enjoined by the Constitution.

The case of New York may be compared, or contrasted, with that of Missouri. The exact proportion of Missouri, in a general representation of 240, is two and six tenths; that is to say, it comes nearer to three members than to two, yet it is confined to two. But why is not Missouri entitled to that number of Representatives which comes nearest to her exact proportion? Is the Constitution fulfilled as to her, while that number is withheld, and while, at the same time, in another State, not only is that nearest number given, but an additional member given also? Is it an answer with which the people of Missouri ought to be satisfied, when it is said that this obvious injustice is the necessary result of the process adopted by the bill? May they not say with propriety, that, since three is the nearest whole number to their exact right, to that number they are entitled, and the process which deprives them of it must be a wrong process? A similar comparison might be made between New York and Vermont. The exact proportion to which Vermont is entitled, in a representation of 240, is 5.646. Her nearest whole number, therefore, would be six. Now two things are undeniably true; first, that to take away the fortieth member from New York would bring her representation nearer to her exact proportion than it stands by leaving her that fortieth member; second, that giving the member thus taken from New York to Vermont would bring her representation nearer to her exact