XT.J ANALYSIS OF QUANTITATIVE PHENOMENA. 341 



At the Paris Observatory a clock has been placed in the 

 caves beneath the building, where there is no appreciable 

 difference between the summer and winter temperature. 



To avoid the effect of unequal oscillations Huyghens 

 made his beautiful investigations, which resulted in the 

 discovery that a pendulum, of which the centre of oscilla- 

 tion moved upon a cycloidal path, would be perfectly 

 isochronous, whatever the variation in the length of oscilla- 

 tions. m But though a pendulum may be easily rendered in 

 some degree cycloidal by the use of a steel suspension 

 spring, it is found that the mechanical arrangements re- 

 quisite to produce a truly cycloidal motion introduce more 

 error than they remove. Hence astronomers seek to 

 reduce the error to the smallest amount by maintaining 

 their clock pendulums in uniform movement; in fact, 

 while a clock is in good order and has the same weights, 

 there need be little change in the length of oscillation. 

 When a pendulum cannot be made to swing uniformly, as 

 in experiments upon the force of gravity, it becomes re- 

 quisite 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 expansion 

 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 deter- 

 mine 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 tine tube at the bottom, and were maintained at two 



