MECHANICS. 131 



of suspension, divided by the sum of the products 

 of each body into the simple power of its distance 

 from that centre. 



If the bodies be A, B, C, D, &c. and their distances 

 from the centre of suspension a, b, c, d, &c. and x 

 the distance of the centre of oscillation from the 

 same point, then 



Aa 2 + B6 2 + C6' 2 +p^ 2 

 Aa+Bi+Cc+Dd 



This value of x is deduced from D^ALEMBERT'S prin- 

 ciple, 120. 



x is also the length of the simple pendulum, isochro- 

 nous with the compound, or vibrating in the same 

 time. 



If any of the bodies are above the point of suspen- 

 sion, their distances from that point are accounted 

 negative. 



206. If a cylinder, of which the altitude is a, 

 and the radius r, be suspended from its vertex, the 

 distance of the centre of oscillation from the ver- 



. 2 a r* 



tex is . 



3 2a 



If the radius r =z 0, so that the cylinder coincides 

 with a straight rod of inconsiderable thickness, 



52 a 



the distance of the centre of oscillation is -^- 



o 



207. If 



