The Apportionment clause in Article I, Section 2 may have been the first constitutional clause invalidly amended (see Statute vs Constitutional Amendment).
Article I, Section 2
(as it reads today; it was affected by Amendments XIV and XVI):
"Representatives shall be apportioned among the several States
which may be included within this Union,
according to their respective Numbers,
which shall be the whole number of Persons, excluding Indians not taxed. 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…"
Apportionment and districting schemes have been used as a party prize for most of our history. But the freeze came with the Reapportionment Act of 1929 (ch 28, 46 Stat. 21, 2 USC Section 2a; updating Pub. L. 62-5 (1911)). Thisstatute froze membership in the House of Representatives at 435 for all time, based on the 1910 population, and created Representatives at large with odd-sized districts, ending population-based apportionment and invalidly amending Article I, Section 2.
Reapportionment statutes since have continued this, claiming to balance representation among large and small states although two-factor districting would balance state sizes more effectively (see Redistricting Without Gerrymandering) and without violating the Constitution.
There's only so much one Representative can do well. When a state's population increases its number of Representatives must increase. When the number of Representatives is fixed but population grows we have less representation every decade, reducing our consent and ability to ordain and establish government a little more with every reapportionment. Representation by population doesn’t mean reducing representation when population increases.
Up to a point, this might be expected with a large population, but the Constitution's original floor ratio was 1 to 30,000, and it is now (in 2014) 1:600,000+. We have less than 1/20 the representation we used to have.
And it gets worse...
Rrius (own work)' public domain via Wikimedia Commons
Image, Studio Under the Bed