ANALYSIS OF QUANTITATIVE PHENOMENA. 395 



When a pendulum cannot be made to swing uniformly, 

 as in experiments upon the force of gravity, it becomes 

 requisite to resort to the third method, and a correction 

 is introduced, calculated on theoretical grounds from 

 the amount of the observed change in the length of 

 vibration. 



It has been mentioned that the apparent expansion 

 of a liquid by heat, when contained in a thermometer tube 

 or other vessel, is the difference between the real ex 

 pansion of the liquid and that of the containing vessel. The 

 effects can be accurately distinguished provided that we 

 can learn the real expansion by heat of any one convenient 

 liquid ; for by observing the apparent expansion of the 

 same liquid in any required vessel we can by difference 

 learn the amount of expansion of the vessel due to any 

 given change of temperature. When we once know the 

 change of dimensions of the vessel, we can of course- 

 determine the absolute expansion of any other liquid 

 tested in it. Thus it became an all-important object in 

 scientific research to measure with accuracy the absolute 

 dilatation by heat of some one liquid, and mercury owing 

 to several circumstances was by far the most suitable. 

 Dulong and Petit devised a beautiful mode of effecting 

 this by simply avoiding altogether the effect of the 

 change of size of the vessel. Two upright tubes full of 

 mercury were connected by a fine tube at the bottom, 

 and were maintained at two different temperatures. As 

 mercury was free to flow from one tube to the other 

 by the connecting tube, the two columns necessarily 

 exerted equal pressures by the principles of hydrostatics. 

 Hence it was only necessary to measure very accurately 

 by a cathetometer the difference of level of the surfaces 

 of the two columns of mercury, to learn the difference of 

 length of columns of equal hydrostatic pressure, which at 

 once gives the difference of density of the mercury, and 



