Describe the replication of $DNA$ and provide experimental proof for it.

(N/A) In addition to the double helical structure of $DNA$, Watson and Crick also proposed a scheme for $DNA$ replication.
Their original statement is as follows:
$(i)$ It has not escaped our notice that the specific pairing we have postulated immediately suggests a possible copying mechanism for the genetic material (Watson and Crick, $1953$).
$(ii)$ The scheme suggested that the two strands would separate and act as templates for the synthesis of new complementary strands.
$(iii)$ After the completion of replication, each $DNA$ molecule would have one parental and one newly synthesized strand.
$(iv)$ This scheme was termed as semiconservative $DNA$ replication.
It is proven that $DNA$ replicates semiconservatively. This was shown first in $Escherichia coli$ and subsequently in higher organisms, such as plants and human cells.
Mathew Meselson and Franklin Stahl performed the following experiment in $1958$:
$(i)$ They grew $E. coli$ in a medium containing $^{15}NH_4Cl$ ($^{15}N$ is the heavy isotope of nitrogen) as the only nitrogen source for many generations. The result was that $^{15}N$ was incorporated into newly synthesized $DNA$ (as well as other nitrogen-containing compounds).
$(ii)$ They then transferred the cells into a medium with normal $^{14}NH_4Cl$ and took samples at various definite time intervals as the cells multiplied. The extracted $DNA$ was centrifuged in a cesium chloride $(CsCl)$ density gradient to measure the densities of $DNA$.
$(iii)$ The $DNA$ extracted from the culture after one generation ($20$ minutes) had a hybrid or intermediate density. The $DNA$ extracted from the culture after another generation ($40$ minutes) was composed of equal amounts of this hybrid $DNA$ and of 'light' $DNA$.