This section is from the book "The Constitutional Law Of The United States", by Westel Woodbury Willoughby. Also available from Amazon: Constitutional Law.
In the first Congress representatives were apportioned among the States according to a rough estimate as to their respective populations. Since that time new apportionments have been based upon the figures of the decennial censuses.
5 Principles of Constitutional Law, edition of 1898. p. 292. The state courts have very generally held that reasonable registration and other laws for the protection of the ballot against fraud, intimidation, ignorance, etc., are not unconstitutional under the state Constitution as adding to the qualifications laid down. Cf. Cooley, Const. Lim., 7th ed., Ch. XVIII.
The first apportionment bill passed by. Congress was vetoed by President Washington as unconstitutional in that it provided for a representative for each thirty thousand of population, the minimum fixed by the Constitution, and also an additional number to the States having the largest fractions left over after the division was made.6
Until 1842 fractions of populations left over by the dividing of the populations of the several States by the number selected for determining the number of representatives, went unrepresented. Since that time, however, where these fractions have exceeded a half of the ratio number, an additional representative has been allowed.
 
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