748 THE POPULAR SCIENCE MONTHLY, 



rod, on vrliich a perpendicular beam of light is made to fall, indicates, 

 by means of a graduated circle engraved upon it, the most minute 

 horizontal deflections of the balance. Two leaden balls. A'" and K\ are 

 brought within a suitable distance of the balls a and b, exercise an 

 attractive force upon, them, and cause an horizontal deflection of the 

 balance, in a direction opposed to the torsion force of the cord, the 

 value of which may be ascertained by measurement. From this value 

 is computed the force of the attraction which the leaden masses Iv 

 and K' exercise upon a and b. Since the masses of the four balls, 

 their relative distances from each other, and the amount of the 

 attraction exerted upon them by the earth (which is given by the 

 absolute weight of the balls), are all measurable, the ratio of the mass 

 of the earth to the masses of the balls /r and K' can be calculated, 

 and from this, by the process already given, the mean density of 

 the earth. 



The results obtained by this method have a considerable degree of 

 trustworthiness, for clear determinations are obtained in which errors 

 are possible only in a small degree. The method was used by Caven- 

 dish in 1T98, whose calculations gave 5*48, by Reich in Freiberg in 

 1837, who obtained 5*44, and by Baily in 1842, who obtained 5*6747. 

 Reich repeated his experiments with improved apparatus between 1847 

 and 1850, using tin balls instead of leaden ones, and twisted copper 

 wires or double iron w^ires instead of cord, and obtained 5*5756, a 

 value which is often written briefly as 5*58. Hutton calculated the 

 specific gravity of the earth from Cavendish's observations at 5*32, and 

 E. Schmidt at 5.52. 



Determination by Means of the Two-Akmed Balance. The 

 idea of using the balance as means of measuring the mean density of 

 the earth originated with the physicist Jolly, who suggested its appli- 

 cation to this purpose in describing some improvements he had made 

 in the instrument to increase its sensitiveness. The application was 

 made by II. Poynting, in Manchester, v\dio adopted the following 

 method : Instead of a scale, he attached a weight {b Fig. 4), of 452*92 

 grammes to the end of a rod six feet in length, to which he opposed a 

 counter-weight in the scale at the other end of the balance ; a ball, C, 

 weighing 154*220*6 grammes was brought to a position joerpendicularly 

 under b, when the mutual attraction of the two bodies occasioned a 

 disturbance of the balance to the amount of 0*01 of a milligramme. 

 The weight of the two mutually attracting bodies and the amount of 

 attraction exerted upon them by the earth being known, and the dis- 

 tance apart of their centers of gravity having been carefully measured, 

 Poynting calculated the mean density of our planet at 5*69, with a 

 ]^)robable error of 0*15. 



The approximate agreement of the results obtained by these four 

 methods authorizes us to conclude that the masses of the interior of 

 the earth possess a great density. If we consider, with Alexander von 



