# R Dataset / Package HistData / Cavendish

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## Visual Summaries

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Documentation

On this Picostat.com statistics page, you will find information about the Cavendish data set which pertains to Cavendish's Determinations of the Density of the Earth. The Cavendish data set is found in the HistData R package. You can load the Cavendish data set in R by issuing the following command at the console data("Cavendish"). This will load the data into a variable called Cavendish. If R says the Cavendish data set is not found, you can try installing the package by issuing this command install.packages("HistData") and then attempt to reload the data. If you need to download R, you can go to the R project website. You can download a CSV (comma separated values) version of the Cavendish R data set. The size of this file is about 447 bytes.

## Cavendish's Determinations of the Density of the Earth

### Description

Henry Cavendish carried out a series of experiments in 1798 to determine the mean density of the earth, as an indirect means to calculate the gravitational constant, G, in Newton's formula for the force (f) of gravitational attraction, f = G m M / r^2 between two bodies of mass m and M.

Stigler (1977) used these data to illustrate properties of robust estimators with real, historical data. For these data sets, he found that trimmed means performed as well or better than more elaborate robust estimators.

### Usage

data(Cavendish)

### Format

A data frame with 29 observations on the following 3 variables.

density

Cavendish's 29 determinations of the mean density of the earth

density2

same as density, with the third value (4.88) replaced by 5.88

density3

same as density, omitting the the first 6 observations

### Details

Density values (D) of the earth are given as relative to that of water. If the earth is regarded as a sphere of radius R, Newton's law can be expressed as G D = 3 g / (4 π R), where g=9.806 m/s^2 is the acceleration due to gravity; so G is proportional to 1/D.

density contains Cavendish's measurements as analyzed, where he treated the value 4.88 as if it were 5.88. density2 corrects this. Cavendish also changed his experimental apparatus after the sixth determination, using a stiffer wire in the torsion balance. density3 replaces the first 6 values with NA.

The modern "true" value of D is taken as 5.517. The gravitational constant can be expressed as G = 6.674 * 10^-11 m^3/kg/s^2.

### Source

Kyle Siegrist, "Virtual Laboratories in Probability and Statistics", http://www.math.uah.edu/stat/data/Cavendish.html

Stephen M. Stigler (1977), "Do robust estimators work with real data?", Annals of Statistics, 5, 1055-1098

### References

Cavendish, H. (1798). Experiments to determine the density of the earth. Philosophical Transactions of the Royal Society of London, 88 (Part II), 469-527. Reprinted in A. S. Mackenzie (ed.), The Laws of Gravitation, 1900, New York: American.

Brownlee, K. A. (1965). Statistical theory and methodology in science and engineering, NY: Wiley, p. 520.

### Examples

data(Cavendish)
summary(Cavendish)
boxplot(Cavendish, ylab='Density', xlab='Data set')
abline(h=5.517, col="red", lwd=2)# trimmed means
sapply(Cavendish, mean, trim=.1, na.rm=TRUE)# express in terms of G
G <- function(D, g=9.806, R=6371) 3*g / (4 * pi * R * D)

boxplot(10^5 * G(Cavendish), ylab='~ Gravitational constant (G)', xlab='Data set')
abline(h=10^5 * G(5.517), col="red", lwd=2)
--

Dataset imported from https://www.r-project.org.

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