Cavendish · 1798
Cavendish weighs the Earth
Across the months of August 1797 to May 1798, in the small purpose-built shed at the back of the garden of his Clapham Common house at the south-western edge of London, the painfully shy sixty-seven-year-old natural philosopher Henry Cavendish, the second son of Lord Charles Cavendish and grandson on the maternal side of the 2nd Duke of Kent, conducted the systematic series of seventeen torsion-balance measurements that became universally known ever since as the Cavendish Experiment: the first direct laboratory measurement of the gravitational force of attraction between two ordinary objects of known masses, and the foundational experimental result of modern gravitational physics. The torsion-balance apparatus (originally designed by the Reverend John Michell, the Cavendish family's late Cambridge friend and a fellow Royal Society Fellow, and bequeathed to Cavendish at Michell's death in 1793 with the working tools and the requirement to complete the apparatus and conduct the measurements) consisted of a six-foot wooden rod suspended horizontally at its midpoint by a fine steel torsion wire, with two two-inch lead spheres of approximately 1.6 pounds each at the rod's ends; two large twelve-inch lead spheres of approximately 350 pounds each were positioned by a separate suspension system close to the small spheres, and the gravitational attraction between the small spheres and the large spheres produced a small but measurable rotation of the suspended rod that could be observed through a telescope at the small angular-deflection scale Cavendish had marked on the rear wall of the shed. The seventeen measurements across the nine months gave a value for the average density of the Earth of approximately 5.48 times the density of water (the modern accepted value is 5.51), and on the strength of the geometry of the apparatus and the known radius of the Earth produced the first direct laboratory value for Newton's gravitational constant G of approximately 6.74 times ten to the minus eleven cubic metres per kilogram per second squared (the modern accepted value is 6.67). The Cavendish Experiment is the central single experimental measurement of late-eighteenth-century physics and the foundational laboratory result on which every subsequent value of the mass of the Sun, the Moon, the planets and the universe has been built.
An experiment is rarely conducted by a man who has gone to such lengths to avoid the presence of his own colleagues that he has had a back stairway built into his Clapham house so that his cook can deliver his meals to a small landing without his being seen by her. Henry Cavendish has, by the unanimous record of every contemporary acquaintance, been the most painfully shy senior scientific figure of the late eighteenth century. He has, across the same period, been the most precise experimental observer working in any English laboratory. The combination of the personal-and-scientific reticence is the central biographical fact of his career and the operational condition under which the central single experimental measurement of late-eighteenth-century physics was carried out across the months of August 1797 to May 1798 in the small shed at the back of his Clapham garden.
THE DUKE'S GRANDSON
Henry Cavendish was born at Nice in southern France on the tenth of October 1731, second son of Lord Charles Cavendish, the third son of the second Duke of Devonshire, and Lady Anne Grey, fourth daughter of the second Duke of Kent. His mother died when he was two; he was raised by his father at the family London townhouse on Great Marlborough Street and at the Devonshire estates at Chatsworth and Hardwick. He was schooled at the Hackney Academy under Newcome's grammar-school discipline from his eleventh year, took the place at Peterhouse College, Cambridge, in October 1749 at eighteen, left in 1753 without taking a degree (the standard arrangement for the senior English aristocratic undergraduates of the period, who were not required to take the religious-test-and-degree-formality of the standard Cambridge graduation), and from 1753 lived continuously in his father's London household as the lifelong scientific collaborator of his father's Royal Society research.
He inherited the substantial fortune from his maternal uncle Lord Kent in 1773 (the inheritance gave him a private income of approximately twelve thousand pounds per year, or roughly two and a half million pounds in modern money, the largest private income held by any working scientist of the late-eighteenth-century period) and from then took up an entirely independent scientific career on the strength of the private income. He acquired the Clapham Common house at the small village of Clapham, three miles south of London, in 1782 in his fifty-first year, and lived in the Clapham house with his small private laboratory at the back of the garden for the next twenty-eight years to his death in 1810.
THE MICHELL APPARATUS
The Reverend John Michell (1724 to 1793), rector of the small parish of Thornhill in Yorkshire, Fellow of Queens' College Cambridge, and Fellow of the Royal Society, was the central single English-language experimental natural-philosopher of the second half of the eighteenth century, and one of the small handful of Cavendish's actual personal friends. Michell had designed the torsion-balance apparatus across the late 1780s on the proposal to measure directly the gravitational attraction between two ordinary objects of known masses; the proposal would, if successful, give the first laboratory measurement of the mean density of the Earth (the standard derivation: from the gravitational attraction between the apparatus-masses, the geometry of the apparatus, and the known surface-gravity of the Earth, the mass of the Earth could be calculated; from the mass and the known volume of the Earth the mean density could be calculated).
Michell completed the apparatus design but had not begun the actual measurements at his death on the twenty-first of April 1793 in his sixty-ninth year. His will bequeathed the apparatus and the working tools to the Royal Society Council on the proposal that the Society select a Fellow to complete the work. The Royal Society Council, on the recommendation of Cavendish's late father Lord Charles Cavendish, made the formal offer to Cavendish on the strength of the Michell-Cavendish friendship and Cavendish's known precision-experimentalist competence. Cavendish accepted in 1794 in his sixty-third year.
THE SHED AT CLAPHAM
He set up the apparatus at the back of his Clapham garden across 1795 to 1797. The apparatus required a purpose-built ten-foot-by-ten-foot shed (the standard outdoor-laboratory dimension for the torsion-balance arrangement), specially-controlled temperature-and-air-current conditions (the small gravitational force the apparatus was attempting to measure was approximately one millionth the weight of the small lead spheres, and any air-current or temperature-gradient in the shed would produce a torsion-deflection of the apparatus larger than the gravitational deflection itself), and a precisely-machined torsion-wire that could deliver the required sensitivity at the small angular-deflection scale.
Cavendish solved the air-current problem by sealing the shed entirely (the standard practice of any subsequent experimentalist would have been to enter the shed to manipulate the apparatus and take the readings; Cavendish made the design-and-operational decision that the apparatus must be operated remotely from outside the shed, on the engineering principle that the experimentalist's own body heat would constitute the largest single uncontrolled-temperature source in the shed). He built the apparatus on a remote-operation system: the large twelve-inch suspension spheres were positioned by a system of ropes-and-pulleys that ran through the shed wall to the outside; the small angular-deflection of the torsion-rod was observed through a telescope sighted on the shed-wall scale through a small hole drilled in the shed wall.
The torsion-wire he selected was a silver-and-copper alloy of approximately one fortieth of an inch in diameter and forty inches in length, hand-drawn for the apparatus by a London precision-instrument-maker named Mr Wilson at one guinea per drawing. The wire's torsion-constant (the angular-deflection produced by a known torque) was calibrated against a small standard-weight pendulum across the spring of 1797.
THE SEVENTEEN MEASUREMENTS
Cavendish ran the seventeen measurements of the experiment between August 1797 and May 1798. Each measurement ran approximately three hours (the standard observational period for the torsion-rod to swing to maximum-deflection, oscillate around the equilibrium-position, and damp out to the new equilibrium under the gravitational force from the large spheres). The seventeen measurements were taken on three sets of paired-positioning of the large spheres (the small spheres deflected toward the large spheres, deflected away from the large spheres, and the null-position with no gravitational force); each set ran four-to-six repeated measurements at varying ambient-temperature-and-air-current conditions to calibrate the systematic uncertainties.
The mean result across the seventeen measurements gave the density of the Earth as 5.48 times the density of water, with an experimental uncertainty of approximately one percent. The result, when combined with the known volume of the Earth (from the Eratosthenes-and-Newton geometry), gave the mass of the Earth as approximately 6 times 10 to the 24th power kilograms (the modern accepted value is 5.97 times 10 to the 24th power kilograms). The Newtonian gravitational constant G, derived from the experiment as G equals (4 pi squared times the Earth's radius squared times the deflection) divided by (the Earth's mass times the period squared), came out at approximately 6.74 times 10 to the minus 11 cubic metres per kilogram per second squared (the modern accepted value is 6.67 times 10 to the minus 11). The Cavendish measurement of 1798 has been confirmed by every subsequent torsion-balance and atomic-recoil measurement across the next two hundred and twenty-seven years and stands within approximately one percent of the modern best-fit value.
THE PHILOSOPHICAL TRANSACTIONS
Cavendish reported the experimental result to the Royal Society in the paper Experiments to Determine the Density of the Earth in the Philosophical Transactions of the Royal Society of London for the year 1798, presented on the twenty-first of June 1798. The paper is on every modern syllabus of the foundational experimental results of late-eighteenth-century physics. It is the foundational experimental measurement of the gravitational mass-and-attraction of ordinary objects, and is the laboratory result on which every subsequent calculation of planetary masses, stellar masses and the mass of the universe rests.
Cavendish continued the laboratory-and-chemistry work at the Clapham house for the next twelve years to his death (his chemistry programme of the same period included the foundational measurement of the composition of water as hydrogen-and-oxygen in the molecular ratio of two-to-one, the foundational measurement of the composition of the atmosphere, and the first laboratory production of pure hydrogen gas). He died at the Clapham house on the twenty-fourth of February 1810 in his seventy-eighth year. The Cavendish-Devonshire family seventh Duke endowed the Cavendish Laboratory at the University of Cambridge in his memory in 1874, on the recommendation of James Clerk Maxwell. The Cavendish Laboratory has been the central single physical-research institution of Cambridge for the past hundred and fifty-one years and has produced thirty Nobel Prize-winning research programmes including the J. J. Thomson electron discovery of 1897 and the Cockcroft-Walton splitting of the atom of 1932. The Cavendish name in modern physics carries the weight of the Clapham shed of 1797 to 1798.