He was the original inventor of the torsion balance, which afterwards became so famous in the hands of its second inventor Coulomb. Michell described it in his proposal of a method for obtaining the mean density of the earth. He did not live to put his method into practice; but this was done by Henry Cavendish, who made, by means of Michell’s apparatus, the celebrated determination that now goes by the name of Cavendish’s experiment (Phil. Trans., 1708). His most important geological essay was that entitled Conjectures concerning the Cause and Observations upon the Phaenomena of Earthquakes (Phil. Trans., li. 1760), which showed a remarkable knowledge of the strata in various parts of England and abroad. Michell’s other contributions to science are: “Observations on the Comet of January 1760 at Cambridge, Phil. Trans. (1760); “A Recommendation of Hadley’s Quadrant for Surveying,” ibid. (1765); “Proposal of a Method for measuring Degrees of Longitude upon Parallels of the Equator,” ibid. (1766); “An Inquiry into the Probable Parallax and Magnitude of the Fixed Stars,” ibid. (1767); “On the Twinkling of the Fixed Stars,” ibid. His name appears fourth in the Tripos list for 1748–1749; and in 1755 he was moderator in that examination. He became M.A. in 1752, and B.D. in 1761. He was a fellow of his college, and was appointed Woodwardian professor of geology in 1762, and in 1767 rector of Thornhill in Yorkshire, where he died on the 29th of April 1793. He was  ​ elected a fellow of the Royal Society in the same year as Henry Cavendish (1760). In 1750 he published at Cambridge a work of some eighty pages entitled A Treatise of Artificial Magnets , in which is shown an easy and expeditious method of making them superior to the best natural ones . Besides the description of the method of magnetization which still bears his name, this work contains a variety of accurate magnetic observations, and is distinguished by a lucid exposition of the nature of magnetic induction. He was the original inventor of the torsion balance, which afterwards became so famous in the hands of its second inventor Coulomb. Michell described it in his proposal of a method for obtaining the mean density of the earth. He did not live to put his method into practice; but this was done by Henry Cavendish, who made, by means of Michell’s apparatus, the celebrated determination that now goes by the name of Cavendish’s experiment ( Phil. Trans. , 1708).

This was probably due to local irregularities in the strata which could not be directly detected. All the experiments to determine Δ by the attraction of natural masses are open to the serious objection that we cannot determine the distribution of density in the neighbourhood with any approach to accuracy. The experiments with artificial masses next to be described give much more consistent results, and the experiments with natural masses are now only of use in showing the existence of irregularities in the earth’s superficial strata when they give results deviating largely from the accepted value. II. Determination of the Attraction between two Artificial Masses. Fig. 2.—Cavendish’s Apparatus. h h, torsion rod hung by wire l g,; x, x, attracted balls hung from its ends; WW, attracting masses. Cavendish’s Experiment (Phil. Trans., 1798, p. 469).—This celebrated experiment was planned by the Rev. John Michell. He completed an apparatus for it but did not live to begin work with it. After Michell’s death the apparatus came into the possession of Henry Cavendish, who largely reconstructed it, but still adhered to Michell’s plan, and in 1797–1798 he carried out the experiment. In fact, astronomy gives us the product GM, but neither G nor M. For example, the acceleration of the earth towards the sun is about 0·6 cm/sec. 2 at a distance from it about 15 × 10 12 cm. The acceleration of the moon towards the earth is about 0·27 cm/sec. 2 at a distance from it about 4 × 10 10 cm. If S is the mass of the sun and E the mass of the earth we have 0·6＝GS/(15 × 10 12 ) 2 and 0·27＝GE/(4 × 10 10 ) 2 giving us GS and GE, and the ratio S/E＝300,000 roughly; but we do not obtain either S or E in The aim of the experiments to be described here may be regarded either as the determination of the mass of the earth in grammes, most conveniently expressed by its mass ÷ its volume, that is by its “mean density” Δ , or the determination of the “gravitation constant” G. Corresponding to these two aspects of the problem there are two modes of attack. Suppose that a body of mass m is suspended at the earth’s surface where it is pulled with a force w vertically downwards by the earth—its weight. {\displaystyle \Delta ={\tfrac {3}{4}}{\frac {g}{\text{G}}}\cdot {\frac {1}{\pi {\text{R}}}}.} Experiments of the first class in which the pull of a known mass is compared with the pull of the earth may be termed experiments on the mean density of the earth, while experiments of the second class in which the pull between two known masses is directly measured may be termed experiments on the gravitation constant. We shall, however, adopt a slightly different classification for the purpose of describing methods of experiment, viz:— 1. Comparison of the earth pull on a body with the pull of a natural mass as in the Schiehallion experiment. 2. Determination of the attraction between two artificial masses as in Cavendish’s experiment. 3. Comparison of the earth pull on a body with the pull of an artificial mass as in experiments with the common balance. It is interesting to note that the possibility of gravitation experiments of this kind was first considered by Newton, and in both of the forms (1) and (2). In the System of the World (3rd ed., 1737, p. 40) he calculates that the deviation by a hemispherical mountain, of the earth’s density and with radius 3 m., on a plumb-line at its side will be less than 2 minutes. From these examples it will be realized that in gravitation experiments extraordinary precautions must be adopted to eliminate disturbing forces which may easily rise to be comparable with the forces to be measured. We shall not attempt to give an account of these precautions, but only seek to set forth the general principles of the different experiments which have been made. I. Comparison of the Earth Pull with that of a Natural Mass . Bouguer’s Experiments .—The earliest experiments were made by Pierre Bouguer about 1740, and they are recorded in his Figure de la terre (1749). They were of two kinds. Boys having found that it is possible to draw quartz fibres of practically any degree of fineness, of great strength and true in their elasticity, determined to repeat the Cavendish experiment, using his newly invented fibres for the suspension of the torsion rod. He began by an inquiry as to the best dimensions for the apparatus. He saw that if the period of vibration is kept constant, that is, if the moment of inertia I is kept proportional to the torsion couple per radian μ , then the deflection remains the same however the linear dimensions are altered so long as they are all altered in the same proportion. But the moment of the attracting force is halved only, so that the deflection against one-fourth torsion is doubled. In Cavendish’s arrangement there would be an early limit to the advantage in reduction of rod in that the mass opposite one ball would begin seriously to attract the other ball. But Boys avoided this difficulty by suspending the balls from the ends of the torsion rod at different levels and by placing the attracting masses at these different levels. Fig. 3 represents diagrammatically a vertical section of the arrangement used on a scale of about 1/10. The torsion rod was a small rectangular mirror about 2·4 cm. wide hung by a quartz fibre about 4·3 cm. long. The simple pendulum would be set swinging by the varying attraction and from its amplitude after a known number of swings of the outside pendulums G could be found. III. Comparison of the Earth Pull on a body with the Pull of an Artificial Mass by Means of the Common Balance. The principle of the method is as follows:—Suppose a sphere of mass m and weight w to be hung by a wire from one arm of a balance. Let the mass of the earth be E and its radius be R. Then w = GE m R 2 {\displaystyle \textstyle w={\frac {{\text{GE}}m}{{\text{R}}^{2}}}} . Now introduce beneath m a sphere of mass M and let d be the distance of its centre from that of m .