370 THE PRINCIPLES OF SCIENCE. 



serious character than the theoretical ones. The length 

 of a pendulum is not the ordinary length of the instru- 

 ment, which might be greatly varied, without affecting 

 the duration of a vibration, but the distance from the 

 centre of suspension to the centre of oscillation. There is 

 no direct means of determining this centre, which depends 

 upon the average momentum of all the particles of the 

 pendulum as regards the centre of suspension. Huyghens 

 discovered that the centres of suspension and oscillation 

 are interchangeable, and Captain Kater pointed out that 

 if a pendulum vibrates with exactly the same rapidity 

 when suspended from two different points, the distance 

 between these points is the true length of the equivalent 

 simple pendulum 1 ". But the practical difficulties in em- 

 ploying Kater's reversible pendulum are considerable, and 

 questions regarding the disturbance of the air, the force 

 of gravity or even the interference of electrical attractions 

 have to be entertained. It has been shown that all the 

 experiments made under the authority of government for 

 establishing the ratio between the standard yard and the 

 seconds' pendulum, were vitiated by an error in the correc- 

 tions for the resisting, adherent or buoyant power of the 

 air in which the pendulum swung. Even if such correc- 

 tions were rendered unnecessary by operating in a vacuum, 

 other difficult questions remain 8 . Gauss' mode of com- 

 paring the vibrations of a wire pendulum when suspended 

 at two different lengths is open to equal or greater practi- 

 cal difficulties. Thus it is found that the pendulum 

 standard cannot compete in accuracy arid certainty with 

 the simple bar standard, and the method would only be 

 useful as an accessory mode of 'restoring the bar standards 

 if at any time again destroyed. 



r Kater's ' Treatise on Mechanics;' Cabinet Cyclopaedia, p. 154. 

 B Grant's ' History of Physical Astronomy/ p. 156. 



