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Population of States, excluding Indians, not taxed, 1910.
Total, including Arizona and New Mexico.....
APPORTIONMENT OF REPRESENTATIVES
Ithaca, N. Y., December 21, 1910.
House of Representatives, Washington, D. C. SIR: In fulfillment of the agreement reached at our interview of December 15, 1910, I take pleasure in sending you herewith tables showing the apportionment of each number of Representatives from 390 to 440, inclusive, according to the results of the census of 1910 by a method which, Í believe, deserves the consideration of the Committee on the Census. I understand that you will have these tables printed and will give me an opportunity later to appear before the committee and explain the method by which they have been prepared.
The history of reports, debates, and votes upon apportionment seems to show a settled conviction in Congress that every major fraction gives a valid claim to an additional Representative. This conviction has controlled the final apportionment, I believe, on every occasion since and including the apportionment based on the census of 1840. It has been followed even when to follow it has entailed some departure from the method on which the computations were based, as happened in 1872 and 1901. The present method is based upon that conviction of Congress and seeks to facilitate action in conformity with it. An examination of Table 1 will show that an additional Representative is always assigned for every major fraction in the quotient and in no case is an additional Representative assigned for a minor fraction. Because of this feature I have called the present method in distinction from the usual method prescribed by Representative Vinton's amendment embodied in section 25 of the act of May 23, 1850, the method of major fractions.
The advantage just mentioned, however, was possessed also by Tables 2 and 3 of those submitted to your committee in December, 1900, and yet they received almost no attention. But they had not been so prepared as to apportion numbers of Representatives increasing regularly by one. On the contrary the ratio used as a divisor was changed arbitrarily and irrationally by 500 in each table. This change often made no change in the number of Representatives, once made a change of five, and many times a change of two or three. Your committee needs tables apportioning each number of Representatives within the limits to which its attention is likely to be confined.
The present tables conform to both requirements of the committee, as I conceive them, a regular series of tables each apportioning one more Representative than its predecessor, and the principle of the
major fraction, and that fact constitutes their only novel feature. If I am rightly informed, no series of tables has been prepared heretofore possessing both of these characteristics.
The results of this method are simple, but the method by which they have been reached is somewhat difficult to explain. If a ratio of 240,000 persons to each Representative be assumed arbitrarily as a starting point, that number divided into the constitutional population of each State and one Representative assigned for each whole number and each major fraction in the series of quotients a total of 383 Representatives is reached. If the ratio be then diminished by 10 to 239,990, no difference in the apportionment will result, but the decimal in each quotient will be slightly increased. The amount of this increase in each decimal will depend upon the population of the State in question, that of the largest States increasing most rapidly. If the ratio be further reduced to 239,980, 239,970, etc., the decimals continue to increase with each change of ratio, but with varying rapidity. It is a simple problem to compute in which State the decimal will first pass 0.500 and become a major fraction and at just what ratio the change will occur (see Table 2). In the present case the State whose decimal first reaches 0.500 is Illinois, and the corresponding ratio is 239,940 (see Table 3). Accordingly, Illinois is entitled to the next Representative, who might be called No. 384. The ratio of 239,940 has been called the boundary ratio. The next smaller boundary ratio is 239,615, at which point the decimal for Mississippi rises to 0.500, and that State therefore is entitled to Representative No. 385.
Any ratio between these two numbers, 239,940 and 239,615, will yield a table apportioning 384 Representatives; but the nearer the ratio is put to 239,940 the weaker becomes the admitted claim of Illinois to an additional Representative. A ratio of 239,935 gives a quotient for Illinois of 23.5005. So the nearer the ratio is put to 239,615 the stronger becomes the rejected claim of Mississippi to a Representative. The ratio of 239,617 divided into the constitutional population of Mississippi gives a quotient of 7.49994. In order to exclude such difficult cases the ratios for division have been fixed midway between the two boundary ratios; but it must be clearly understood that a table computed from any ratio whatever between the two boundary ratios and applying rigidly the fundamental principle of major fractions would yield precisely the same apportionment.
The method followed in finding these boundary ratios for the whole series of apportionable Representatives from 49 to 440 will be clear, I hope, to anyone who will examine Tables 2 and 3. If it is not, Í shall be glad to submit a further statement or to explain it fully when I appear before the committee.
Table 1.- Apportionment of each number of Representatives between 390 and 440,
inclusive, by method of major fractions.