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. $2\pi R\cos \theta$