To find the circumference of a latitude \(\theta\) degrees south on Earth, you can use the following formula:

1. Understanding Latitude Circles:

At latitude \(\theta\) degrees south, the Earth's surface forms a circle with a radius that is smaller than the Earth's radius \(R\). The radius of this circle is \(R \cos \theta\), where \(R\) is the radius of the Earth.

2. Calculate the Circumference:

The circumference \(C\) of a circle is given by:

\[
C = 2 \pi \times \text{radius}
\]

For the latitude circle:

\[
\text{radius} = R \cos \theta
\]

Therefore, the circumference \(C\) is:

\[
C = 2 \pi \times R \cos \theta
\]

So, the correct answer is:

B. \(2 \pi R \cos \theta\)