744 THE POPULAR SCIENCE MONTHLY. 



it to the beginning of the nineteenth century. Alexander von Hum- 

 bohlt relates that he and Sir Humphry Davy were several times in- 

 vited by Captain Symmes to join an expedition into the interior of 

 the earth, which was represented as a hollow sphere having a large 

 opening at the eighty-second parallel of north latitude. The idea of 

 the existence of a hollow space within the earth was set at rest by the 

 measurement of the average density of the planet, and the contrary view 

 was advanced that the globe is a mass of great specific gravity. The 

 constituency of this mass, whether it is fluid or solid, with only local 

 bubble-like spaces, filled with fluid matter, has not been determined ; 

 but the calculations that have been made contradict the theory of a 

 wholly fluid interior. 



Several- methods have been adopted for ascertaining the mean den- 

 sity of the earth, to the older of which a more accurate method has 

 been added within a few years. An account of the methods hitherto 

 adopted, and the results obtained by them, is here given. 



DETEKMTNATIOlSr FROM THE DeFLECTIOK OF THE PlUMB-LiNE. 



I^ewton first suggested that the specific gravity of the earth could be 

 ascertained by means of the plumb-line, but he made no eflort to apply 

 his suggestion. The thought was a sequence of his law of gravitation, 

 on which all the methods that have been employed have been based. 

 That law declares that all bodies exert an attractive force upon each 

 other in direct proportion to their masses and in inverse proportion to 

 the square of the distance of their centers of gravity from each other. 

 Accordingly, a body hanging by a line, which over a level surface 

 would be drawn by the earth's attraction into a direction with refer- 

 ence to its point of suspension, the prolongation of the line of which 

 would pass through the center of the earth that is, would be per- 

 pendicular, or i^lumb would be attracted and turned away from the 

 perpendicular by a mass like a mountain in the neighborhood. If, now, 

 the amount of this diversion and the size of the mass exercising the 

 deflecting influence were known, then the mass of the earth, and from 

 this in connection with the shape and size of the earth, its mean den- 

 sity, could be computed. The diversion of the plummet from its per- 

 pendicular direction is, however, too minute to make a direct measure- 

 ment possible, and the following method has, therefore, been adopted : 

 In Fig. 1, let K L be a part of the surface of the earth, and G an 

 isolated mountain. A plumb-line at the point A, at the foot of the 

 mountain, and one at B, several miles from it, would take such direc- 

 tions in case the earth were a perfect sphere that the prolongation of 

 the lines would intersect each other at the center of the earth, and 

 form the angle x, with the sides C Z and C Z", Z and Z" representing 

 the zeniths at A and B. The zenith-distance v, of any suitable fixed 

 star S, in the neighborhood of Z, may be easily obtained by direct 

 measurement. Let also the zenith-distance of the same star at the 

 point B, which is equivalent to the angle ^^, be determined. The lines 



