48 OR A VITATION. 



we leave behind us particles of matter whose attraction 

 partly counterbalances that of the rest of the earth. 



104. Ail Example. Consider the earth's radius 

 to be 4,000 miles, and the earth's density to be uniform. 

 At the centre, a body, whose weight at the surface is 

 100 pounds, would be attracted in every direction 

 with equal force. The resultant of these equal and oppo- 

 site forces would be zero, and the body would have no 

 weight. At 1,000 miles from the centre, one fourth of the 

 distance to the surface, it would weigh 25 pounds, one- 

 fourth the surface weight ; at 2,000 miles from the centre, 

 50 pounds ; at 3,000 miles from the centre, 75 pounds ; at 

 4,000 miles from the centre, or the surface distance, it 

 would weigh 100 pounds or the full surface weight. If 

 carried up still further, the weight will decrease according 

 to the square of the distance. At an elevation of 4,000 

 miles above the surface (8,000 miles from the centre) it 

 will weigh 25 pounds, or one-fourth the surface weight. 



105. Law of Weight. Bodies weigh most at 

 the surface of the eaHh. Below the surface, the 

 weight decreases as the distance to the centre de- 

 creases. Above the surface, the weight decreases as 

 the square of the distance from the centre in- 

 creases. 



106. Formulas for Gravity Problems. 



Representing the surface weight by W and the surface dis- 

 tance (4,000 miles) by D, the other weight by w 9 and the 

 other distance from the earth's centre by d, the above law 

 may be algebraically expressed as follows: 



Below the earth's surface : w : W : : d : D. 



Above the earth's surface : w : W : : D 2 : d 2 . 



