The Constitution has declared that “Representatives & direct taxes shall be apportioned among the several states according to their respective numbers,” that “the number of representatives shall not exceed one for every 30,000, but each state shall have at least one representative; & until such enumeration shall be made, the state of New Hampshire shall be entitled to chuse 3. Massachusets &c.[”]

The bill for apportioning representatives among the several states, without explaining any principle at all, which may shew it’s conformity with the constitution, or guide future apportionments, says that New-Hampshire shall have three members, Massachusets 16. &c. we are therefore to find by experiment what has been the principle of the bill, to do which it is proper to state the federal or representable numbers of each state, and the members allotted to them by the bill. they are as follows.

It happens that this representation, whether tried as between great & small states, or as between North & South, yeilds, in the present instance, a tolerably just result, and consequently could not be objected to on that ground, if it were obtained by the process prescribed in the Constitution. but if obtained by any process out of that, it becomes arbitrary, & inadmissible.

The Ist 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, & ratio, are equivalent words; & 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 shew 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:

Then the bill reverses the Constitutional precept, because, by it, “representatives are not apportioned among the several states according to their respective numbers.”

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, & 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; & 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, & it meant to submit to them. it knew they would be in favor of one part of the union at one time, & of another 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 R. Island, N. York, Pennsylvania, Maryland, Virginia, Kentuckey & Georgia, and that of 27,770 to the eight others, namely Vermont, N. Hampshire, Massachusets, Connecticut[,] N. Jersey, Delaware, N. Carolina, & S. Carolina, as follows:

and if two ratios may be applied, then 15 may, & the distribution become arbitrary, instead of being apportioned to numbers.

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; & 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, shews it was understood that, without special provision, the smaller number would, in this case, 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 8. 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 state, or the thirty thousands in the whole union, & that in the latter case it serves only to find the amount of the whole representation: which, in the present state of population, is 120 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 & Representatives apply to it during the pendency of the first bill, & even till an advanced stage of this second bill, when an ingenious gentleman found out the doctrine of fractions, a doctrine so difficult & inobvious, as to be rejected at first sight by the very persons who afterwards became it’s 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 it’s 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, & not at all to influence their apportionment among the states, then the 120 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 28,658. 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 8. Northernmost states, & 105,582 in the 7. Southernmost. the following table shews it:

Whatever may have been the intention, the effect of rejecting the nearest divisor, (which leaves but one residuary member) And adopting a distant one (which leaves eight) is merely to take a member from New York & Pensylvania each, & give them to Vermont & New Hampshire.

But it will be said, “this is giving more than one for 30,000.” true: but has it not been just said that the one for 30,000 is prescribed only to fix the aggregate number, and that we are not to mind it when we come to apportion them among the states? that for this we must recur to the former rule which distributes them according to the numbers in each state? besides does not the bill itself apportion among 7. of the states by the ratio of 27,770? which is much more than one for 30,000.

Where a phrase is susceptible of two meanings, we ought certainly to adopt that which will bring upon us the fewest inconveniencies. 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 8 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. & 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 7. residuary members among the 7. highest fractions, & tho’ 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, & which may never occur again. the probability is that the fractions will generally descend gradually from 29,999 to 1. the inconvenience then of large unrepresented fractions attends both constructions: & while the most obvious construction is liable to no other, that of the bill incurs many & grievous ones.

1. if you permit the large fraction in one state to chuse a representative for one of the small fractions in another state, you take from the latter it’s election, which constitutes real representation, and substitute a virtual representation of the disfranchised fractions: and the tendency of the doctrine of virtual representation has been too well discussed & appreciated by reasoning & resistance, on a former great occasion, to need developement now.

2. the bill does not say that it has given the residuary representatives to the greatest fractions; tho’ 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 among the larger states; at other times according to any other crotchet which ingenuity may invent, & the combinations of the day give strength to carry; or they may do it arbitrarily, by open bargain & cabal. in short this construction introduces into Congress a scramble, or a vendue, for the surplus members, it generates waste of time, hot-blood, & 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 the Pensylvania assembly: whereas the other construction reduces the apportionment always to an arithmetical operation, about which no two men can ever 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 i.e. by some common ratio.

Viewing this bill either as a violation of the constitution, or as giving an inconvenient exposition to it’s 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: & consequently has begotten a desire to raise up barriers in the state legislatures against Congress throwing off the controul of the constitution.

2. it can never 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, & other circumstances respecting themselves, & affecting their legal qualifications to legislate for the Union.

4. The majorities by which this bill has been carried (to wit of 1. in the Senate, and 2. in the Representatives) shew 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 bear that of the bill.

6. the application of any one ratio is intelligible to the people, & will therefore be approved: whereas the complex operations of this bill will never be comprehended by them, & tho’ they may acquiesce, they cannot approve what they do not understand.