August 23, 1900] 



NATURE 



403 



RECENT STUDIES IN GRAVITATION.^ 



THE studies in gravitation which I am to describe to you this 

 evening will perhaps fall into better order if I rapidly run 

 over the well beaten track which leads to those studies, the 

 track first laid down by Newton, based on astronomical 

 observations, and only made firmer and broader by every later 

 observation. 



- I may remind you, then, that ihe motion of the planets round 

 the sun in ellipses, each marking out the area of its orbit at a 

 constant rate, and each having a year proportional to the 

 square root of the cube of its mean distance from the sun, 

 implies that there is a force on each planet exactly proportional 

 to its mass, directed towards, and inversely as the square of its 

 distance from the sun. The lines of force radiate out from the 

 sun on all sides equally, and always grasp any matter with a 

 force proportional to its mass, whatever planet that matter 

 belongs to. 



If we assume that action and reaction are equal and opposite, 

 then each planet acts on the sun with a force proportional to its 

 own mass ; and if, further, we suppose that these forces are 

 merely the sum totals of the forces due to every particle of 

 matter in the bodies acting, we are led straight to the law of 

 gravitation, that the force between two masses Mj M^ is always 

 proportional to the product of the masses divided by the square 

 of the distance r between them, or is equal to 



G X M, X M, 



and the constant multiplier G is the constant of gravitation. 



Since the force is always proportional to the mass acted on, ^ 

 and produces the same change of velocity whatever that mass 

 may be, the change of velocity tells us nothing about the mass 

 in which it takes place, but only about the mass which is pulling. 

 If, however, we compare the accelerations due to different 

 pulling bodies, as for instance that of the sun pulling the earth 

 with that of the earth pulling the moon, or if we compare 

 changes in motion due to the different planets pulling each 

 other, then we can compare their masses and weigh them, one 

 against another and each against the sun. But in this weighing 

 our standard weight is not the pound or kilogramme of terres- 

 trial weighings, but the mass of the sun. 



For instance, from the fact that a body at the earth's surface, 

 4000 miles, on the average, from the mass of the earth, falls 

 with a velocity increasing by 32 ft. /sec.^ while the earth falls • 

 towards the sun, 92 million miles away, with a velocity increas- 

 ing by about | inch /sec. -, we can at once show that the mass 

 of the sun is 300,000 times that of the earth. In other words, 

 astronomical observation gives us only the acceleration, the 

 product of G X mass acting, but does not tell us the value of 

 G nor of the mass acting, in terms of our terrestrial standards. 



To weigh the sun, the planets, or the earth, in pounds or 

 kilogrammes, or to find G, we must descend from the heavenly 

 bodies to earthly matter and either compare the pull of a 

 weighable mass on some body with the pull of the earth on it, 

 or else choose two weighable masses and find the pull between 

 them. 



All this was clearly seen by Newton, and was set forth in his 

 " System of the World " (third edition, p. 41). 



He saw that a mountain mass might be used, and weighed 

 against the earth by finding how much it deflected the plumb 

 line at its base. The density of the mountain could be found 

 from specimens of the rocks composing it, and the distance of 

 its parts from the plumb line by a survey. The deflection of the 

 vertical would then give the mass of the earth. 



Ne.vton also considered the possiVjility of measuring the 

 attraction between two weighable masses, and calculated how 

 long it would take a sphere a foot in diameter, of the 

 earth's mean density, to draw another equal sphere, with their 

 surfaces separated by J-inch, through that J-inch. But he made 

 a very great mistake in his arithmetic, for while his result gave 

 about one month, the actual time would only be about 

 5i minutes. Had his value been right, gravitational experi- 

 ments would have l)een beyond the power of even Prof. Boys. 

 Some doubt has been thrown on Newton's authorship of this 

 mistake, but I confess that there is something not altogether 

 unpleasing even in the mistake of a Newton. His faulty 



1 A discourse delivered at the Royal Institution of Great Britain on 

 Friday, February 23, by Prof. John H. Poynting, F.R.S. 



arithmetic showed that there was one quality which he shared 

 with the rest of mankind. 



Not long after Newton's death the mountain experiment was 

 actually tried, and in two ways. The honour of making these 

 first experiments on gravitation belongs to Bouguer, whose 

 splendid work in thus breaking new ground does not appear to 

 me to have received the credit due to it. 



One of his plans consisted in measuring the deflection of the 

 plumb line due lo Chimborazo, one of the Andes peak.s, by 

 finding the distance of a star on the meridian from the zenith, 

 first at a station on the south side of the mountain, where the 

 vertical was deflected, and then at a station to the west, where 

 the mountain attraction was nearly inconsiderable, so that the 

 actual nearly coincided with the geographical vertical. The 

 difference in zenith distances gave the mountain deflection. 

 It is not surprising that, working in snowstorms at one station, 

 and in sandstorms at the other, Bouguer obtained a very in- 

 correct result. But at least he showed the possibility of such 

 work, and since his time many experiments have been carried 

 out on his lines under more favourable conditions. Now, how- 

 ever, I think it is generally recognised that the difficulty of 

 estimating the mass of a mountain from mere surface chips is 

 insurmountable, and it is admitted that the experiment should 

 be turned the other way about and regarded as an attempt to 

 measure the mass of the mountains from the density of the earth 

 known by other experiments. 



These other experiments are on the line indicated by Newton 

 in his calculations of the attraction of two spheres. The first 

 was carried out by Cavendish. 



In the apparatus (Fig. l) he used two lead balls, b b, each 2" 

 in diameter. These were hung at the end of a horizontal rod 6' 

 long, the torsion rod, and this was hung up by a long wire from 

 its middle point. Two large attracting spheres of lead, w w, 

 each 12" in diameter, were brought clo.se to the balls on opposite 

 sides so that their attractions on the balls con.spired to twist 

 the torsion rod round the same way, and the angle of twist was 

 measured. The force could be reckoned in terms of this angle 

 by setting the rod vibrating to and fro and finding the time of 

 vibration, and the force came out to less than 1/3000 of a grain. 

 Knowing M, Mg and r the distance between them and the force 

 G Ml y[.2lr-, of course Cavendish's result gives o, or knowing 

 the attraction of a big sphere on a ball, and knowing the 

 attraction of the earth on the same ball, that is, its weight, the 

 experiment gives the mass of the earth in terms of that of the 

 big sphere, and so its mean density. This experiment has often 

 been repeated, but I do not think it is too much to say that 

 no advance was made in exactness till we come to quite recent 

 work. 



By far the most remarkable recent study in gravitation is Prof. 

 Boys' beautiful form of the Cavendish experiment, a research 

 which stands out as a model in beauty of design and in exactness 

 of execution (Fig. 2). But as Prof. Boys has described his ex- 

 periment already in this theatre (Proc. A\I., xiv. Part ii. 1894, 

 p. 353), it is not necessary for me to more than refer to it. It 

 is enough to say that he made the great discovery, obvious 



NO. ]6c8, \OL. 62] 



