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, there. fore, 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 constitu tional 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 ascer tained 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

right than it is by the bill. And both these propositions are equally true of a transfer to Delaware of the twenty-eighth member assigned by the bill to Pennsylvania, and to Missouri of the thirteenth member assigned to Kentucky. In other words, Vermont has, by her numbers, more right to six members than New York has to forty; Delaware, by her numbers, has more right to two members than Pennsylvania has to twenty-eight; and Missouri, by her numbers, has more right to three members than Kentucky has to thirteen. Without disturbing the proposed number of the House, the mere changing of these three members from and to the six States, respectively, would bring the representation of the whole six nearer to their due proportion, according to their respective numbers, than the bill in its present form makes it. In the face of this indisputable truth, how can it be said that the bill apportions members of Congress among those States according to their respective numbers, as near as may be?

The principle on which the proposed amendment is founded is an effectual corrective for these and all other equally great inequalities. It may be applied at all times, and in all cases, and its result will always be the nearest approach to perfect justice. It is equally simple and impartial. As a rule of apportionment, it is little other than a transcript of the words of the Constitution, and its results are mathematically certain. The Constitu tion, as the committee understand it, says, Representatives shall be apportioned among the States according to their respective numbers of people, as near as may be. The rule adopted by the committee says, out of the whole number of the House, that number shall be apportioned to each State which comes nearest to its exact right according to its number of people.

Where is the repugnancy between the Constitution and the rule? The arguments against the rule seem to assume, that there is a necessity of instituting some process, adopting some number as the ratio, or as that number of people which each member shall be understood to represent. But the committee see no occasion for any other process whatever, than simply the ascertainment of that quantum, out of the whole mass of the representative power, which each State may claim.

But it is said that, although a State may receive a number of Representatives which is something less than its exact pro

portion of representation, yet that it can in no case constitutionally receive more. How is this proposition proved? How is it shown that the Constitution is less perfectly fulfilled by allowing a State a small excess, than by subjecting her to a large deficiency? What the Constitution requires is the nearest practicable approach to precise justice. The rule is approximation; and we ought to approach, therefore, on whichever side we can approach nearest.

This

But there is a still more conclusive answer to be given to this suggestion. The whole number of Representatives of which the House is to be composed is, of necessity, limited. number, whatever it is, is that which is to be apportioned, and nothing else can be apportioned. This is the whole sum to be distributed. If, therefore, in making the apportionment, some States receive less than their just share, it must necessarily follow that some other States have received more than their just share. If there be one State in the Union with less than its right, some other State has more than its right; so that the argument, whatever be its force, applies to the bill in its present form, as strongly as it can ever apply to any bill.

But the objection most usually urged against the principle of the proposed amendment is, that it provides for the representation of fractions. Let this objection be examined and considered. Let it be ascertained, in the first place, what these fractions, or fractional numbers, or residuary numbers, really are, which it is said will be represented, should the amendment prevail.

A fraction is the broken part of some integral number. It is, therefore, a relative or derivative idea. It implies the previous existence of some fixed number, of which it is but a part or remainder. If there be no necessity for fixing or establishing such previous number, then the fraction resulting from it is itself not matter of necessity, but matter of choice or accident. Now, the argument which considers the plan proposed in the amendment as a representation of fractions, and therefore unconstitutional, assumes as its basis, that, according to the Constitution, every member of the House of Representatives represents, or ought to represent, the same, or nearly the same, number of constituents; that this number is to be regarded as an integer; and any thing less than this is therefore called a fraction, or a residu