"The first member of the clause of the constitution above cited, is express - that representatives shall be apportioned among the several states according to their respective numbers; that is to say, they shall be apportioned by some common ratio, for proportion and ratio are equivalent words; and it is the definition of proportion among numbers, that they have a ratio common to all, or, in other words, a common divisor. Now, trial will show that there is no common ratio, or divisor, which, applied to the numbers of each state, will give to them the number of representatives allotted in this bill; for, trying the several ratios of 29, 30, 31, 32, 33, the allotments would be as follows:

"It will be said, that, though for taxes there may always be found a divisor, which will apportion them among the states according to numbers exactly, without leaving any remainder; yet, for representatives, there can be no such common ratio, or divisor, which, applied to the several numbers, will divide them exactly, without a remainder or fraction. I answer, then, that taxes must be divided exactly, and representatives as nearly as the nearest ratio will admit, and the fractions must be neglected; because the constitution wills, absolutely, that there be an apportionment, or common ratio; and if any fractions result from the operation, it has left them unprovided for. In fact, it could not but foresee that such fractions would result, and it meant to submit to them. It knew they would be in favor of one part of the Union at one time, and of another part of it at another, so as, in the end, to balance occasional inequalities. But, instead of such a single common ratio, or uniform divisor, as prescribed by the constitution, the bill has applied two ratios, at least, to the different states to wit, that of 30,026 to the seven following: Rhode Island, New York, Pennsylvania, Maryland, Virginia, Kentucky, and Georgia; and that of 27,770 to the eight others; namely, Vermont, New Hampshire, Massachusetts, Connecticut, New Jersey, Delaware, North Carolina, and South Carolina. As follows:

"Another member of the clause of the constitution, which has been cited, says, 'the number of representatives shall not exceed one for every 30,000, but each state shall have, at least, one representative. ' This last phrase proves that it had in contemplation, that all fractions, or numbers below the common ratio, were to be unrepresented; and it provides specially, that in the case of a state whose whole number shall be below the common ratio, one representative shall be given to it. This is the single instance where it allows representation to any smaller number than the common ratio, and, by providing specially for it in this, shows it was understood, that, without special provision, the smaller number would, in this ease, be involved in the general principle.

"The first phrase of the above citation, that 'the number of representatives shall not exceed one for every 30,000,' is violated by this bill, which has given to eight states a number exceeding one for every 30,000, to wit, one for every 27,770.

"In answer to this, it is said, that this phrase may mean either the thirty thousands in each slate, or the thirty thousands in the whole Union; and that, in the latter case, it serves only to find the amount of the whole representation, which, in the present state of population, is one hundred and twenty members. Suppose the phrase might bear both meanings, which will common sense apply to it? Which did the universal understanding of our country apply to it? Which did the senate and representatives apply to it during the pendency of the first bill, and even till an advanced stage of this second bill, when an ingenious gentleman found out the doctrine of fractions - a doctrine so difficult and inobvious, as to be rejected, at first sight, by the very persons who afterwards became its most zealous advocates? The phrase stands in the midst of a number of others, every one of which relates to states in their separate capacity. Will not plain common sense, then, understand it, like the rest of its context, to relate to states in their separate capacities?

"But if the phrase of one for 30,000, is only meant to give the aggregate of representatives, and not at all to influence their apportionment among the states, then the one hundred and twenty being once found, in order to apportion them, we must recur to the former rule, which does it according to the numbers of the respective states; and we must take the nearest common divisor as the ratio of distribution, that is to say, that divisor, which, applied to every state, gives to them such numbers as, added together, come nearest to 120. This nearest common ratio will be found to be 28,858, and will distribute 119 of the 120 members, leaving only a single residuary one. It will be found, too, to place 96,648 fractional numbers in the eight northernmost states, and 105,582, in the southernmost. The following table shows it:

"Where a phrase is susceptible of two meanings, we ought certainly to adopt that which will bring upon us the fewest inconveniences. Let us weigh those resulting from both constructions.

"From that giving to each state a member for every 30,000 in that state, results the single inconvenience, that there may be large fractions unrepresented. But it being a mere hazard on which states this will fall, hazard will equalize it in the long run.

"From the other, results exactly the same inconvenience. A thousand cases may be imagined to prove it Take one; suppose eight of the states had 45,000 inhabitants each, and the other seven 44,999 each, that is to say, each one less than each of the others, the aggregate would be 674,993, and the number of representatives, at one for 30,000 of the aggregate, would be 22. Then, after giving one member to each state, distribute the seven residuary members among the seven highest fractions; and, though the difference of population be only an unit, the representation would be the double. Here a single inhabitant the more would count as 30,000. Nor is this case imaginable only; it will resemble the real one, whenever the fractions happen to be pretty equal through the whole states. The numbers of our census happen, by accident, to give the fractions all very small or very great, so as to produce the strongest case of inequality that could possibly have occurred, and which may newer occur again. The probability is, that the fractions will generally descend gradually from 39,999 to 1. The inconvenience, then, of large unrepresented fractions attends both constructions; and, while the most obvious construction is liable to no other, that of the bill incurs many and grievous ones.

"2. The bill does not say, that it has given the residuary representatives to the greatest fractions; though, in fact, it has done so. It seems to have avoided establishing that into a rule, lest it might not suit on another occasion. Perhaps it may be found the next time more convenient to distribute them among, the smaller states; at another time among the larger states; at other times. according to any other crotchet, which ingenuity may invent, and the combination of the day give strength to carry; or they may do it arbitrarily, by open bargain and cabal. In short, this construction introduces into congress a scramble, or a vendue for the surplus members. It generates waste of time, hot blood, and may, at some time, when the passions are high, extend a disagreement between the two houses, to the perpetual loss of the thing, as happens now in Pennsylvania assembly: whereas the other construction reduces the apportionment always to an arithmetical operation, about which no two men can possibly differ.

"3. It leaves in full force the violation of the precept which declares, that representatives shall be apportioned among the states according to their numbers, that is, by some common ratio.

"Viewing this bill either as a violation of the constitution, or as giving an inconvenient exposition to its words, is it a case wherein the president ought to interpose his negative? I think it is.

"1. The non-user of his negative begins already to excite a belief, that no president will ever venture to use it; and, consequently, has begotten a desire to raise up barriers in the state legislatures against congress throwing off the control of the constitution.

"2. It can ever be used more pleasingly to the public, than in the protection of the constitution.

"3. No invasions of the constitution are so fundamentally dangerous, as the tricks played on their own numbers, apportionment, and other circumstances respecting themselves, and affecting their legal qualifications to legislate. for the Union.

"4. The majorities, by which this bill has been carried, (to wit, of one in the senate, and two in the house of representatives,) show how divided the opinions were there.

"5. The whole of both houses admit the constitution will bear the other exposition; whereas the minorities in both deny it will hear that of the bill.

"6. The application of any one ratio is intelligible to the people, and will, therefore, be approved; whereas the complex operations of this bill will never be comprehended by them; awl, though they may acquiesce, they cannot approve, what they do not understand."

Mr. Webster's report on the same subject, in the senate in April, 1832, presents the leading arguments on the other side.

"This bill, like all laws on the same subject, must be regarded, as of an interesting and delicate nature. It respects the distribution of political power among the states of the Union. It is to determine the number of voices, which, for ten years to come, each state is to possess in the popular branch of the legislature. In the opinion of the committee, there can be few or no questions, which it is more desirable should be settled on just, fair, and satisfactory principles, than this; and, availing themselves of the benefit of the discussion, which the bill has already undergone in the senate, they have given to it a renewed and anxious consideration. The result is, that, in their opinion, the bill ought to be amended. Seeing the difficulties, which belong to the whole subject, they are fully convinced, that the hill has been framed and passed in the other house, with the sincerest desire to overcome those difficulties, and to enact a law, which should do as much justice as possible to all the states. But the committee are constrained to say, that this object appears to them not to have been obtained. The unequal operation of the bill on some of the states, should it become a law, seems to the committee most manifest; and they cannot but express a doubt, whether its actual apportionment of the representative power among the several states can be considered, as conformable to the spirit of the constitution. The bill provides, that, from and after the third of March, 1833, the house of representatives shall be composed of members, elected agreeably to a ratio of one representative for every forty-seven thousand and seven hundred persons in each state, computed according to the rule prescribed by the constitution. The addition of the seven hundred to the forty-seven thousand, in the composition of this ratio, produces no effect whatever in regard to the constitution of the house. It neither adds to, nor takes from, the number of members assigned to any state. Its only effect is, a reduction of the apparent amount of the fractions, as they are usually called, or residuary numbers, alter the application of the ratio. For all other purposes, the result is precisely the same, as if the ratio had been 47,000.

"As it seems generally admitted, that inequalities do exist in this bill, and that injurious consequences will arise from its operation, which it would be desirable to avert, if any proper means of averting them, without producing others equally injurious, could be found, the committee do not think it necessary to go into a full and particular statement of these consequences. They will content themselves with presenting a few examples only of these results, and such as they find it most difficult to reconcile with justice, and the spirit of the constitution.

"In exhibiting, these examples, the committee must necessarily speak of particular states; but it is hardly necessary to say, that they speak of them as examples only, and with the most perfect respect, not only for the states themselves, but for all those, who represent them here.

"Although the bill does not commence by fixing the whole number of the proposed house of representatives, yet the process adopted by it brings out the number of two hundred and forty members. Of these two hundred and forty members, forty are assigned to the state of New York, that is to say, precisely one sixth part of the whole. This assignment would seem to require, that New York should contain one sixth part of the whole population of the United States; and would be bound to pay one sixth part of all her direct taxes. Yet neither of these is the case. The whole representative population of the United Stares is 11,929,005; that of New York is 1,918,623, which is less than one sixth of the whole, by nearly 70,000. Of a direct tax of two hundred and forty thousand dollars, New York would pay only $38.59. But if, instead of comparing the numbers assigned to New York with the whole numbers of the house, we compare her with other states, the inequality is still more evident and striking.

"To the state of Vermont, the bill assigns five members. It gives, therefore, eight times as many representatives to New York, as to Vermont; but the population of New York is not equal to eight times the population of Vermont, by more than three hundred thousand. Vermont has five members only for 280,657 persons. If the same proportion were to be applied to New York, it would reduce the number of her members from forty to thirty-four - making a difference more than equal to the whole representation of Vermont, and more than sufficient to overcome her whole power in the house of representatives.

"A disproportion, almost equally striking, is manifested, if we compare New York with Alabama. The population of Alabama is 262,208; for this, she is allowed five members. The rule of proportion, which gives to her but five members for her number, would give to New York but thirty-six for her number. Yet New York receives forty. As compared with Alabama, then, New York has an excess of representation equal to four fifths of the whole representation of Alabama; and this excess itself will give her, of course, as much weight in the house, as the whole delegation of Alabama, within a single vote. Can it be said, then, that representatives are apportioned to these states according to their respective numbers?

"The ratio assumed by the bill, it will be perceived, leaves large fractions, so called, or residuary numbers, in several of the small states, to the manifest loss of a part of their just proportion of representative power. Such is the operation of the ratio, in this respect, that New York, with a population less than that of New England by thirty or thirty-five thousand, has yet two more members, than all the New England states; and there are seven states in the Union, whose members amount to the number of 123, being a clear majority of the whole house, whose aggregate fractions altogether amount only to fifty-three thousand; while Vermont and New Jersey, having together but eleven members, have a joint fraction of seventy-five thousand.

"Pennsylvania by the bill will have, as it happens, just as many members as Vermont, New Hampshire, Massachusetts, and New Jersey; but her population is not equal to theirs by a hundred and thirty thousand; and the reason of this advantage, derived to her from the provisions of the bill, is, that her fraction, or residuum, is twelve thousand only, while theirs is a hundred and forty-four.

"But the subject is capable of being presented in a more exact and mathematical form. The house is to consist of two hundred and forty members. Now the precise proportion of power, out of the whole mass represented by the numbers two hundred and forty, which New York would be entitled to according to her population, is 38.59; that is to say, she would be entitled to thirty-eight members, and would have a residuum, or fraction; and, even if a member were given her for that fraction, she would still have but thirty-nine; but the bill gives her forty.

"These are a part, and but a part, of those results produced by the bill in its present form, which the committee cannot bring themselves to approve. While it is not to be denied, that, under any rule of apportionment, some degree of relative inequality must always exist, the committee cannot believe, that the senate will sanction inequality and injustice to the extent, in which they exist in this bill, if they can be avoided. But recollecting the opinions, which had been expressed in the discussions of the senate, the committee have diligently sought to learn, whether there was not some other number, which might be taken for a ratio, the application of which would work out more justice sad equality. In this pursuit the committee have not been successful. There are, it is true, other numbers, the adoption of which would relieve many of the states, which suffer under the present; but this relief would be obtained only by shifting the pressure on to other States, thus creating new grounds of complaint in other quarters. The number forty-four thousand has been generally spoken of, as the most acceptable substitute for forty-seven thousand seven hundred; but should this be adopted, great relative inequality would fall on several states, and, among them, on some of the new and growing states, whose relative disproportion, thus already great, would be constantly increasing. The committee, therefore, are of opinion, that the bill should be altered in the mode of apportionment. They think, that the process, which begins by assuming a ratio, should be abandoned, and that the bill ought to be framed on the principle of the amendment, which has been the main subject of discussion before the senate. The fairness of the principle of this amendment, and the general equity of its results, compared with those, which flow from the other process, seem plain and undeniable. The main question has been, whether the principle itself be constitutional; and this question the committee proceeded to examine, respectfully asking of those, who have doubted its constitutional propriety, to deem the question of so much importance, as to justify a second reflection.

"The words of the constitution are, 'representatives and direct taxes shall be apportioned among the several states, which may be included within this Union, according to their respective numbers, which shall be determined by adding to the whole number of free persons, including those bound to service for a term of years, and excluding Indians, three fifths of all other persons. The actual enumeration shall be made within three years after the first 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 fractional parts of the smallest coins, and the smallest denomination of money of account, yet, by the usual subdivisions of the coin, and of tim denomination of money, the apportionment of taxes is capable of being made so exact, that tire 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 arising. 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 greatest 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 tale. 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 [heir 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, viz. 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, it becomes, when each process has been carried through, not matter of opinion, but matter of mathematical certainty. If the whole population 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 hills, if either, apportions the representatives according to the number of 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 inequality. 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 240 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 two hundred and forty members, the exact mathematical proportion, to which her numbers entitle the state of New York, is 38.59; it is certain, therefore, that thirty-nine 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 number? 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 tony 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 two hundred sad forty, 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 two hundred and forty, 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. Secondly, 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 of the twenty-eighth member assigned by the bill to Pennsylvania, to Delaware, and of the thirteenth member assigned to Kentucky, to Missouri; 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 each 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 these members among those states, according to their respective number, at 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 constitution, 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 proportion 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.

"But there is still a 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. This 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 state 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 hill 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 lint a part, or remainder. If there be no necessity for fixing or establishing such previous number, then the fraction, resulting from it, is itself no matter of necessity, but matter of choice or of 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 n fraction, or a residuum, and cannot be entitled to a representative. But all this is not the provision of the constitution of the United States. That constitution contemplates no integer, or any common number for the constituents of a member of the house of representatives. It goes not at all into these subdivisions of the population of a state. It provides for the apportionment of representatives among the several states, according to their respective numbers, and stops there. It makes no provision for the representation of districts, of states, or for the representation of any portion or the people of a state, less than the whole. It says nothing of ratios or of constituent numbers. All these things it leaves to state legislation. The right, which each state possesses to its own due portion of the representative power, is a state right, strictly; it belongs to the state, as a state; and it is to be used and exercised, as the state may see fit, subject only to the constitutional qualifications of electors. In fact, the states do make, and always have made, different provisions for the exercise of this power. In some, a single member is chosen for a certain defined district; in others, two or three members are chosen for the same district; and, in some again, as New Hampshire, Rhode Island, Connecticut, New Jersey, and Georgia, the whole representation of the state is exerted, as a joint, undivided representation. In these last- mentioned states, every member of the house of representatives has for his constituents all the people of the state; and all the people of those states are consequently represented in that branch of congress. If the bill before the senate should pass into a law, in its present form, whatever injustice it might do to any of those states, it would not be correct to say of them, nevertheless, that any portion of their people was unrepresented. The well-founded objection would be, as to some of them at least, that they were not adequately, competently, fairly represented; that they had not as many voices and as many votes in the house of representatives, as they were entitled to. This would be the objection. There would be no unrepresented fractions; but the state, as a state, as a whole would be deprived of some part of its just rights.

"On the other hand, if the bill should pass, as it is now proposed to be amended, there would be no representation of fractions in any state; for a fraction supposes a division and a remainder. All, that could justly be said, would be, that some of these states, as states, possessed a portion of legislative power, a little larger than their exact right; as it must be admitted, that, should the bill pass unamended, they would posses, of that power, much less than that exact right. The same remarks are substantially true, if applied to those states, which adopt the district system, as most of them do. In Missouri, for example, there will be no fraction unrepresented, should the bill become a law in its present form; nor any member for a fraction, should the amendment prevail; because the mode of apportionment, which assigns to each state that number, which is nearest to its exact right, applies no assumed ratios, makes no subdivisions, and, of course, produces no fractions. In the one case, or in the other, the state, as a state, will have something more, or something less, than its exact proportion of representative power; but she will part out this power among her own people, in either case, in such mode, as she may choose, or exercise it altogether, as an entire representation of the people of the state.

"Whether the subdivision of the representative power within any state, if there be a subdivision, be equal or unequal, or fairly or unfairly made, congress cannot know, and has no authority to inquire. It is enough, that the state presents her own representation on the floor of congress in the mode she chooses to present it. If a state were to give to one portion of her territory a representative for every twenty-five thousand persons, and to the rest a representative only for every fifty thousand, it would be an act of unjust legislation, doubtless, but it would be wholly beyond redress by any power in congress; because the constitution has left all this to the state itself.

"These considerations, it is thought, may show, that the constitution has not, by any implication, or necessary construction, enjoined that, which it certainly has not ordained in terms, viz. that every member of the house shall be supposed to represent the same number of constituents; and therefore, that the assumption of a ratio, as representing the common number of constituents, is not called for by the constitution. All that congress is at liberty to do, as it would seem, is to divide the whole representative power of the Union into twenty-four parts, assigning one part to each state, as near as practicable, according to its right, and leaving all subsequent arrangement, and all subdivisions, to the state itself.

"If the view thus taken of the rights of the states, and the duties of congress, be the correct view, then the plan proposed in the amendment is, in no just sense, a representation of fractions. But suppose it was otherwise; suppose a direct division were made for allowing a representative to every state, in whose population, it being first divided by a Common ratio, there should be found a fraction exceeding half the amount, of that ratio, what constitutional objection could be fairly urged against such a provision? Let it be always remembered, that the case here supposed provides only for a fraction exceeding the moiety of the ratio; for the committee admit, at once, that the representation of fractions, less than a moiety, is unconstitutional; because, should a member be allowed to a state for such a fraction, it would be certain, that her representation would not be so near her exact right, as it was before. But the allowance of n member for a major fraction is a direct approximation towards justice and quality. There appears to the committee to be nothing, either in the letter or the spirit of the constitution, opposed to such a mode of apportionment. On the contrary, it seems entirely consistent with the very object, which the constitution contemplated, and well calculated to accomplish it. The argument commonly urged against it is, that it is necessary to apply some one common divisor, and to abide by its results.

"If, by this, it be meant, that there must be some common rule, or common measure, applicable, and applied impartially to all the states, it is quite true. But, if that which is intended, be, that the population of each state must be divided by a fixed ratio, and all resulting fractions, great or small, disregarded, this is but to take for granted the very thing in controversy. The question is, whether it be unconstitutional to make approximation to equality, by allowing representatives for major fractions. The affirmative of this question is, indeed, denied; but iris not disproved, by saying, that we must abide by the operation of division, by an assumed ratio, and disregard fractions. The question still remains, as it was before; anti it is still to be shown, what there is in the constitution, which rejects approximation, as the rule of apportionment. But suppose it to be necessary to find a divisor, and to abide its results. What is a divisor? Not necessarily a simple number. It may be composed of a whole number and a fraction; it may itself be the result of a previous process; it may be any thing, in short, which produces accurate and uniform division: whatever does this, is a common rule, a common standard, or, if the word be important, a common divisor. The committee refer, on this part of the case, to some observations by Professor Dean, with a table, both of which accompany this report.

"As it is not improbable, that opinion has been a good deal influenced on this subject by what took place on the passing of the first act, making an apportionment of representatives among the states, the committee have examined and considered that precedent. If it be in point to the present case, it is certainly entitled to very great weight; but if it be of questionable application, the text of the constitution, even if it were doubtful, could not be explained by a doubtful commentary. In the opinion of the committee, it is only necessary, that what was said on that occasion should be understood in connection with the subject matter then under consideration; and, in order to see what that subject matter really was, the committee think it necessary to state, shortly, the case.

"The two houses of congress passed a bill, after the first enumeration of the people, providing for a house of representatives, which should consist of one hundred and twenty members. The bill expressed no rule or principle, by which these members were assigned to the several states. It merely said, that New Hampshire should have five members, Massachusetts ten, and so on; going through all the states, and assigning the whole number of one hundred and twenty. Now, by the census, then recently taken, it appeared, that the whole representative population of the United States was 3,615,920; and it was evidently the wish of congress to make the house as numerous, as the constitution would allow. But the constitution has said, that there should not be more than one member for every thirty thousand persons. This prohibition was, of course, to be obeyed; but did the constitution mean, that no states should have more than one member for every thirty thousand persons? or did it only mean, that the whole house, as compared with the whole population of the United States, should not contain more than one member for every thirty thousand persons? If this last were the true construction, then the bill, in that particular, was right; if the first were the true construction, then it was wrong; because so many members could not be assigned to the states, without giving to some o! them more members than one for every thirty thousand. In fact, the bill did propose to do this in regard to several states.

"President Washington adopted that construction of the constitution, which applied its prohibition to each state individually. He thought, that no state could, constitutionally, receive more than one member for every thirty thousand of her own population. On this, therefore, his main objection to the bill was founded. That objection he states in these words:

"The constitution has also provided, that the number of representatives shall not exceed one for every thirty thousand; which restriction is, by the context, and by fair and obvious construction, to be applied to the separate and respective numbers of the states; and the bill has allotted to eight of the states more than one for every thirty thousand.'

"It is now necessary to see what there was further objectionable in this bill. The number of one hundred and twelve members was all that could be divided among the states, without giving to some of them more than one member fur thirty thousand inhabitants. Therefore, having allotted these one hundred and twelve, there still remained eight of the one hundred and twenty to be assigned; and these eight the bill assigned to the states having the largest fractions. Some of these fractions were large, and some were small. No regard was paid to fractions over a moiety of the ratio, any more than to fractions under it. There was no rule laid down, stating what fractions should entitle the states, to whom they might happen to fall, or in whose population they might happen to be found, to a representative therefor. The assignment was net made on the principle, that each state should have a member for a fraction greater than half the ratio; or that all the states should have a member for a fraction, in all cases where the allowance of such member would bring her representation nearer to its exact proportion than its disallowance. There was no common measure, or common rule, adopted, but the assignment was matter of arbitrary discretion. A member was allowed to New Hampshire for example, for a fraction of less than one half the ratio, thus placing her representation further from her exact proportion, than it was without such additional member; while a member was refused to Georgia, whose case closely resembled that of New Hampshire, both having what were thought large fractions, but both still under a moiety of the ratio, and distinguished from each other only by a very slight difference of absolute numbers. The committee have already fully expressed their opinion on such a mode of apportionment.

"In regard to this character of the bill. President Washington said: 'The constitution has prescribed, that representatives shall be apportioned among the several states according to their respective numbers; and there is no one proportion, or divisor, which, applied to the respective numbers of the states, will yield the number and allotment of representatives proposed by the bill.'

"This was all undoubtedly true, and was, in the judgment of the committee, a decisive objection against the bill. It is nevertheless to be observed, that the other objection completely covered the whole ground. There could, in that bill, be no allowance for a fraction, great or small; because congress had taken for the ratio the lowest number allowed by the constitution, viz. thirty thousand. Whatever fraction a state might have less than that ratio, no member could be allowed for it. It is scarcely necessary to observe, that no such objection applies to the amendment now proposed. No state should the amendment prevail, will have a greater number of members than one for every thirty thousand; nor is it likely, that that objection will ever again occur. The whole force of the precedent, whatever it be, in its application to the present case is drawn from the other objection. And what is the true import of that objection? Does it mean any thing more than, that the apportionment was not made on a common rule or principle, applicable, and applied alike to all the states?

"President Washington's words are, 'there is no one proportion or divisor, which, applied to the respective numbers of the states, will yield the number and allotment of representatives proposed by the bill. '

"If, then, he could have found a common proportion, it would have removed this objection. He required a proportion or divisor. These words he evidently uses, as explanatory of each other. He meant by divisor, therefore, no more than by proportion. What he sought was, some common and equal rule, by which the allotment had been made among the several states; he did not find such common rule; and on that ground, he thought the bill objectionable.

"In the opinion of the committee, no such objection applies to the amendment recommended by them. That amendment gives a rule, plain, simple, just, uniform, and of universal application. The rule has been frequently stated. It may be clearly expressed in either of two ways. Let the rule be, that the whole number of the proposed house shall be apportioned among the several states according to their respective numbers, giving to each state that number of members, which comes nearest to her exact mathematical part or proportion; or, let the rule be, that the population of each state shall be divided by a common divisor, and that, in addition to the number of members resulting from such division, a member shall be allowed to each state, whose fraction exceeds a moiety of the divisor.

"Either of these is it seems to the committee, a fair and just rule, capable of uniform application, and operating with entire impartiality. There is no want of a common proportion, or a common divisor; there is nothing left to arbitrary discretion. If the rule, in either of these forms, be adopted, it can never be doubtful how every member of any proposed number for a house of representatives ought to be assigned. Nothing will be left in the discretion of congress; the right of each state will be a mathematical right, easily ascertained, about which there can be neither doubt nor difficulty; and, in the application of the rule, there will be no room for preference, partiality, or injustice. In any case, in all time to come, it will do all, that human means can do, to allot to every state in the Union its proper and just proportion of representative power. And it is because or this, its capability of constant application, as well as because of its impartiality and justice, that the committee are earnest in recommending its adoption to congress. If it shall be adopted, they believe it will remove a cause of uneasiness and dissatisfaction, recurring, or liable to recur, with every new census, and place the rights of the states, in this respect, on a fixed basis, of which none can with reason complain. It is true, that there may be some numbers assumed for the composition of the house of representatives, to which, if the rule were applied, the result might give a member to the house more than was proposed. But it will be always easy to correct this, by altering the proposed number by adding one to it, or taking one from it; so that this can be considered no objection to the rule.

"The committee, in conclusion, cannot admit, that it is sufficient reason for rejecting this mode of apportionment, that a different process has heretofore prevailed. The truth is, the errors and inequalities of that process were at first not obvious and startling. But they have gone on increasing; they are greatly augmented and accumulated every new census; and it is of the very nature of the process itself, that its unjust results must grow greater and greater in proportion as the population of the country enlarges. What was objectionable, though tolerable yesterday, becomes intolerable tomorrow. A change, the committee are persuaded, must come, or the whole just balance and proportion of representative power among the states will be disturbed and broken up."

Mr. Everett also made a very able speech on the same subject, in which he pressed some additional arguments with great force on the same side.