HEAT. 



The pinch-cock being closed, hot water is poured into one tube, and 

 cold water, to about the same level, into the other. On now opening the 

 pinch-cock, it is found that the level of the hot water is quite appreciably 

 higher than the level of the cold, since it takes a longer column of 

 lighter hot water to balance a given column of heavier cold water. In 

 fact, if h, ti be the heights, p, p the densities, we have, on equating the 

 hydrostatic pressures at the bottom, 



lip = h'p', 

 But if Y, V be the volumes of equal masses of densities /o, p' t 



Hence 



V V 



Vh' 



Hot 



Cold 



so that we can express the expanded volume in terms of the original volume 

 Though water serves very well for an illustration of the method, 

 mercury has been chosen as the liquid on which 

 to make exact experiments for the following 

 reasons : it is easily obtained pure ; it expands 

 nearly regularly as the temperature increases, when 

 this is indicated either by the mercury-glass scale 

 or the air scale ; it has a high boiling-point (about 

 356 0.) ; it does not evaporate much until the 

 temperature is approaching 200 ; it does not wet 

 the vessel in which it is placed, if this be glass, 

 so that its level may be read with great accuracy ; 

 and its great specific gravity renders it especially 

 suitable for gauging vessels, when its expansion 

 has been found. 



The first experiments of this kind with mercury 

 were made by Dulong and Petit, who employed 



FiG.21. U- u $ y ro- arrangement exactly similar in principle to that 



meter, with hot and & . ' 



cold water. represented in iig. 21. Ihe two tubes were 



enclosed, the hot one in an oil-bath, and the cold 



one in a vessel filled with melting ice, the upper ends rising above the 

 enclosing vessels, and the upper levels of the mercury being just visible 

 when the height was measured. The connecting cross-tube at the bottom 

 was of very fine bore, so as to prevent circulation from one tube to the 

 other when the temperatures were steady. An air- thermometer was 

 used to give the temperature of the hot vessel. 



If H and H are the two heights, hot and cold, and p and p are the 

 respective densities, 



But if a volume Y at expands to V (1 + A t ) at <, since the mass is 

 the same at each temperature, 



or 

 Hence 



H 



