316 THE PRINCIPLES OF SCIENCE. [CHAP 



of the pendulum as regards the centre of suspension. 

 Huyghens discovered that the centres of suspension 

 and oscillation are interchangeable, and 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 

 determining 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 pendulums were swung. Even if such 

 corrections were rendered unnecessary by operating in a 

 vacuum, other difficult questions remain. 2 Gauss' mode of 

 comparing the vibrations of a wire pendulum when sus- 

 pended at two different lengths is open to equal or greater 

 practical difficulties. Thus it is found that the pendulum 

 standard cannot compete in accuracy and certainty with 

 the simple bar standard, and the method would only be 

 useful as an accessory mode of restoring the bar standard 

 if at any time again destroyed. 



Unit of Density. 



Before we can measure the phenomena of nature, we 

 require a third independent unit, which shall enable us to 

 define the quantity of matter occupying any given space. 

 All the changes of nature, as we shall see, are probably so 

 many manifestations of energy ; but energy requires some 

 substratum or material machinery of molecules, in and by 

 which it may be manifested. Observation shows that, as 

 regards force, there may be two modes of variation of 

 matter. As Newton says in the first definition of the 

 Principia, " the quantity of matter is the measure of the 

 same, arising from its density and bulk conjunctly." 



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

 8 Grant's Histoi-y of Physical Astronomy, p. 156. 



