for a Convertible Pendulum, 35 



the other. Hence, if we adjust a pendulum so as that its 

 oscillations on two opposed knife-edges be performed in equal 

 times, the distance between those edges will be the true length 

 of the corresponding simple pendulum. 



It is my object in this paper, to shew how advantage may 

 best be taken of this beautiful proposition. 



If the knife-edge of a pendulum be conceived to turn round 

 horizontally, without changing its distance from the centre of 

 gravity, the time of oscillation will change ; there being in the 

 general case, one direction in which the time of oscillation is 

 a maximum, and another exactly at right angles, in which it 

 is a minimum. Should it happen that the two axes of motion 

 are not accurately in the same vertical plane, the measurement 

 will, on this account, be erroneous, unless care have been 

 taken so to form the instrument as that its times of oscilla- 

 tion may be alike in all directions. 



Referring all the parts of the pendulum to rectangular axes 

 passing through the centre of gravity, and putting z in the 

 vertical direction ; let I be the length of the simple pendu- 

 lum, X the distance of the axis of motion from the centre of 

 gravity, and & the inclination of that axis to x (supposed to be 

 an axis of greatest or least motion), then have we according 

 to the well-known laws of oscillation 



(/- X) X . 2 w = 2 . w ,:;2 + sin ^- 2 . w a;2 + cos ^^ 2 . ^ ^^ 

 so that the times of oscillation will be alike in all directions if 

 2 . w a;^ = 2 . w j/^. 



Several years ago I drew the attention of the Society to 

 the importance of attending to this circumstance in construct- 

 ing the pendulums of clocks: the flat bobs in common use 

 exhibit the worst possible form for the load of a pendulum. 



Supposing this condition attended to, the above equatioa 

 becomes 



(/- X) X . 2 w = 2 . w ^2 4. 2 . w a;2 . 

 or if we put 



2.wa;2 + 2.w5;2 = P.2w. 

 (/-X)X=P. 



in which equation P is constant for the same mass of matter. 



Although the proposition be quite true, that the point of 

 suspension and the centre of oscillation are interchangeubley 



