History of Dots Series: How Much Does the Earth Weigh? (1798)

JF Ptak Science Books     Post 1690 [Part of the History of Dots series: Weighing Earth's Biggest Dot--Itself.]

Archimedes said that given certain conditions and equipment that he could lift the Earth with a lever; he did not, however, have the necessaries to actually determine how much the whole thing "weighed", and would have to wait for  20 centuries  in the work of Henry Cavendish to have an answer. (Archimedes was a very busy man with an enormous list of contributions, and was perhaps the greatest physicist and mathematician of his age in the third century BCE, but he did not invent the lever--he did however  provide the mathematical understanding and formalization of how the thing worked in his "On the Equilibrium of Plane Figures".)

In this experiment,  "Experiments to determine the Density of the Earth", the results of which appeared in the Philosophical Transactions in 1798¹, the great and somewhat mysterious (and odd) Henry Cavendish determined to, of all things, weigh the Earth. (Well, really it was measuring the force of gravity and finding the gravitation constant G, which Cavendish referred to as the specific weight of the Earth.)  Now there are certain remarkable things to be achieved in the 18th century (like for example the discovery of oxygen by Scheele/Priestly), and of course the idea of measuring the weight of the Earth was a high intellectual achievement.  Cavendish set off to measure the force of attraction between large and small lead balls using as a basis for research parts of his dead friend John Michell's designs for a torsion balance (which he had created in 1783), and using of course Newton's laws showing that the force of gravity between two objects depends on their masses as well as the distance between them.  Michell had thought of the experiment years before but died before he could present; Cavendish carried on and up, and out. Mind he wasn't the first on the spot (Coloumb was there too slightly before Michell), or the first with the idea--he was the first to complete it, though, taking the difference in the measures on the very sensitive balance from a distance using a telescope so as to not disturb the readings. As a matter of fact this was the only method employed to conduct this experiment for nearly another hundred years, the results being confirmed by a number of scientists² over the coming decades.   It was a lovely idea, and  a fantastic piece of work. 

In his paper in the Philosophical Transactions, Cavendish described Michell and the instrumentation int he opening two paragraphs:

The instrument:

This is the test apparatus that Cavendish constructed following the original Michell plans--it was a big, solid instrument, as that horizontal piece suspended fro the rod (K) is six feet long, and those two spheres (W) attached to its ends are 350-pounds apiece.  The smaller sphere is located in the box to the side of the large sphere, as so:

 

 

“Henry Cavendish had fitful habits of publication that did not at all reveal the universal scope of his natural philosophy. He wrote no books and fewer than twenty articles in a career of nearly fifty years. Only one major paper was theoretical, a study of electricity in 1771; the remainder of his major papers were carefully delimited experimental inquiries, the most important of which were those on pneumatic chemistry in 1766 and 1783–1788, on freezing temperatures in 1783–1788, and on the density of the earth in 1798.” (D.S.B. III:155).

 

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Notes:

1.  A copy of the first German edition of this work is available at our blog's bookstore:  "Versuche über die Dichtigkeit der Erde zu Bestimmen." Halle, Rengerschen Buchhandlung, 1799, and published  in Annalen der Physik, herausgegeben von Ludwig Wilhelm Gilbert, band. 2, erstes stück.  120pp in this section, 488pp overall in in the entire volume, with 9 plates.  Cavendish's paper occupies pp 1-62, with two plates  (the torsion balance of Michell shown on the plates).

The entire Cavendish paper can be found here:  Cavendish, Henry (1798). "Experiments to Determine the Density of the Earth". In MacKenzie, A. S.. Scientific Memoirs Vol.9: The Laws of Gravitation. American Book Co.. 1900. pp. 59–105 Online copy of Cavendish's 1798 paper, and other early measurements of gravitational constant.

2.  The experiment was in fact repeated numerous times, including that by Reich (1838), Baily (1843), Cornu & Baille (1878), among others, and it wasn't until 1895--the year of Roentgen's epochal discovery--that Cavenidsh's accuracy was exceeded by the work of C.V. Boys.