200 RECENT STUDIES IN" GRAVITATION. 



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 kilogram of 

 terrestrial weighings, but the mass of the sun. 



For instance, from the fact that a body at the earth's surface. 4,000 

 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. 

 92,00!). 000 miles away, w T ith a velocity increasing 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 <l X mass acting, hut does not tell us 

 the value of (I nor of the mass acting in terms of our terrestrial 

 standards. 



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

 grams, or to find (i. 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, 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 

 locks 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 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 one-fourth 

 inch, through that one-fourth inch. But he made a very great mis- 

 take in his arithmetic, for while his result gave about one month, the 

 actual time would only be about five and one-half minutes. Had his 

 value been right, gravitational experiments 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 some- 

 thing not altogether unpleasing in the mistake even of a New ton. 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 honor 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 



