1900.] on Recent Studies in Gravitation. 279 



sun. But in this weighing our standard weight is not the pound or 

 kilogramme of terrestrial weighings, hut 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 2 , while the earth itself falls towards 

 the sun, 92 million miles away, with a velocity increasing by about 

 |- inch / sec 2 , 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 kilo- 

 grammes, 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 weigh- 

 able 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, page 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. 



Newton also considered the possibility of measuring the attrac- 

 tion 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 ^-inch, through 

 that ^-incb. But he made a very great mistake in his arithmetic, for 

 while his result gave about 1 month the actual time would only be 

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

 ments would have been beyond the power of even Professor Boys. 

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

 but I confess that there is something not altogether unpleasing in 

 the mistake even of a Newton. His faulty 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 to Chimborazo, one of the Andes peaks, 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 



