IvAMBEiRT: CONSTITUTION OF* THE EARTH 125 



traction, and from this the mean density of the whole mass of the 

 earth comes out as 5.5 or 5.6. There are several steps in the 

 determination of this mean density. We start with the equation 

 that expresses Newton's law of attraction 



where mx and m^ are the masses of two bodies, preferably homo- 

 geneous spheres ; r is the distance between the centers of gravity 

 of the bodies, the linear dimensions of which are supposed to be 

 infinitesimal compared with r, unless the bodies be homogeneous 

 spheres ; / is the force with which these two bodies attract each 

 other; and k is the so-called gravitation constant. The first 

 step in determining the earth's mean density is to determine k 

 by a laboratory experiment. All quantities that occur in equa- 

 tion (i) are measured under laboratory conditions, and k is 

 thus deduced. One form of the experiment, in which we observe 

 the deflection of a torsion balance caused by the near approach 

 of a large mass, is known as Cavendish's experiment. In the 

 second step we use the same equation, with k now supposed 

 known, to determine the mass of the earth. If mi be taken to 

 represent this mass and Wo the mass of another body near the 

 earth's surface, then r is very nearly the earth's mean radius a. 

 The force of attraction equals nitg where g is the acceleration of 

 gravity, so that 



ni2g = — ^, — (2) 



which gives us nn in terms of known quantities. When the earth's 

 mass is known, its mean density is computed from its known di- 

 mensions. 



Since the surface density is less than the mean density, some- 

 where below the surface the density must exceed the mean. 

 Just how that density is distributed from center to surface is a 

 matter for hypothesis. One hypothesis often made is due to 

 Legendre"' and is based on the idea of the compression of the mat- 



* The law to which this hypothesis leads is often called Laplace's law of density. 

 Legendre and Laplace reached the same result from different starting points. See 

 ToDHUNTER, History of the theories of aUraction and figure of the earth, 2: 117 and 



