+-------------+-------------------+
| Cavendish   | R Documentation   |
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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 Ï€ 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.xhtml <http://www.math.uah.edu/stat/data/Cavendish.xhtml>`_

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)

