!6o STATICS. [262. 



262. It will be shown later (Art. 273) that the attraction of 

 .a homogeneous sphere on* an external point is the same as if 

 the mass of the sphere were concentrated at its centre. Thus, 

 if m be the mass of. the earth (here assumed as a homogeneous 

 sphere), the attraction it exerts on a mass I situated at a point 

 P above its surface, at the distance OP = r from the centre O, is 

 ^Km/r*', and this is also the acceleration j that it would cause 

 in any mass m' at P. 



Now for points P near the earth's surface this acceleration j 

 is known from experiments; it is the acceleration of gravity, 

 usually denoted by g. As the radius of the earth, ^=6.37 x io 8 

 centimetres, and its mean density /o = 5f, are also known, the 



value of the constant K can be found from the formula 



i 



m 



or *:= 



With -=980 we find in C.G.S. units 



K = - - - - = o.ooo ooo 0648. 

 1.543* I0 ' 



This, then, is the force in dynes with which two masses of i 

 gramme each would attract each other if concentrated at two 

 points i centimetre apart. 



263. Exercises. 



(1) Show that the value of K in the F.P.S. system is - - 



9.8 x io 8 



(2) When the units are so selected as to make the constant K equa 

 T to i, they are called astronomical units. Show that the astronomica 



unit of mass, i.e. a mass which when concentrated at a point produces 

 unit acceleration at unit distance, is= I/K. 



264. Let a mass or a system of masses be given, and let it be 

 required to determine the attraction at any point P (Art. 261) 

 produced by it. The given masses may consist of discrete par- 

 ticles, or they may be continuous of one, two, or three dimen- 

 sions. Continuous masses must be resolved into elernents; the 



j 



