62 OUTLINES OF NATURAL PHILOSOPHY. 



113. To find the centre of gravity of any number 

 of bodies placed in the same straight line at given 

 distances from one another. 



The centre of gravity is found by Art. 110. 



If the bodies are A, B, C, D, and their distances 

 from a given point in the straight line in which 

 they are supposed to be placed, a, 6, c, d, the dis- 

 tance of their centre of gravity from the same point, 

 A a + B b + C c + D d 



is 



A+B+C+D 



If the bodies are on different sides of the point to which 

 their distances are referred, the distances on the one 

 side being accounted affirmative, those on the op- 

 posite must be accounted negative. 



114. Any number of bodies being given in posi- 

 tion, to find their centre of gravity. 



a. The bodies must be referred to three planes given 

 in position, cutting one another at right angles, one 

 of them horizontal, and, of course, the other two 

 vertical. 



Let the bodies be A, B, C, and D, their distances 

 from the given horizontal plane , &, c, d; their 

 distances from one of the vertical planes a', 6', c', d' ; 

 and from the other a", 6," c ', d" ; then if we take 



Aa + B6 + Cc + Dd 

 a? = - A + B-f C+D - ' centre of gravity 



of 



