Length of the Seconds Pendulum. 247 



We have obtained a general expression for the distance in 

 question, as follows, namely, 



FO = /mr2 = /m ' mF 361. 



L xFG L x FF' 



But 



J* m m~F = f m mf?+ L X FP; 



whence, by substitution, 



-2 



_ fm-mF' + Lx FF' 

 L x FF -' 



that is, 



FO or FF' -J- F'O = ^^ t + FF 

 whence, 



' L x FF'' 



Thus, the distance of the centre of oscillation below the centre of 

 gravity is equal to the sum of all the parts multiplied by the squares 

 their respective distances from the axis drazvn through the centre of 

 gravity, divided by the product of the mass into the distance of the 

 centre of gravity from the axis of suspension. 



Now by multiplying both members of the above equation by 

 FF', and dividing both by F'O, we shall obtain, 



F'F=/~" 



L X OF 1 ' 



Accordingly, if we consider the body as inverted, and make O 

 the point of suspension, F will become the centre of oscillation, 

 since we have the same expression as before for the distance 

 of this point below the centre of gravity. 



We hence infer, that the point of suspension and centre of oscil- 

 lation are convertible, that is, either being made the point of suspen- 

 sion the other becomes the centre of oscillation. 





