In 1798, Cavendish reported his results for the density of the Earth in this manuscript. He used a torsion pendulum to measure the gravitational force between two lead spheres. Comparing this to the weight of the spheres and knowing the radius of the Earth allowed him to calculate the density of the Earth. This was a very difficult experiment which he attempted 30 times over 3 years.
Cavendish recorded some 30 values for the density of the Earth for each of the times he ran his experiment (this file). While the values are reasonably close they all differ and are a nice example of experimental error. We will study this variance of these results with the following steps:
- Make a histogram of the measured densities.
- Determine the mean and standard deviation of the densities.
- Over plot a Gaussian distribution with the mean and standard deviation you have found on top of the histogram.
What final answer for the Earth’s density might you give based on your plots? Does the distribution of values look like a Gaussian? Over what range?
