EXPANSION OF LIQUIDS. 



37 



, = (l + G)(l+rcA). 

 1+nX 



Then 



Whence A is determined. 



Matthiessen's Hydrostatic Method. Matthiessen* determined 

 the expansion of water by a hydrostatic method. For 

 this purpose the linear expansion of a glass rod was 

 measured, and its volume expansion was deduced. A 

 piece of the rod was then cut off and weighed in water 

 at different temperatures. The loss of weight gave the 

 weight of a volume of water equal to that of the glass, 

 and since the expansion of the glass was known that of 

 the water could be determined. 



Matthiessen also applied the method to find the 

 expansion of mercury when that of water had been 

 determined, weighing a small bucket containing mercury 

 in water at different temperatures. He obtained results 

 very close to those of Regnault. Later he applied the 

 method to other metals. 



The Expansion Of Water. Researches on the 

 expansion of water have been made by many experi- 

 menters using one or other of the methods already 

 described, that with the dilatometer giving, probably, 

 the best results. By some the dilatometer has been 

 modified so as to have a constant internal capacity. 

 As usually employed, the rise of the water in the dilato- 

 meter shows only the so-called apparent expansion the 

 excess of expansion of water over the containing vessel. 

 But the expansion of mercury is about seven times that 

 of glass, so that if about i of the bulb of the dilatometer 

 is filled with mercury, the internal capacity is constant, 

 and the rise of the water shows its 

 true expansion. Though interest- 

 ing, this modification probably does not give such 

 accurate determinations as the simple instrument 

 used in the ordinary way. 



All the methods concur in showing that water 

 has a point of maximum density at about 4 0., 

 and that the volume is nearly equal for tempera- 

 tures equidistant on the two sides of this point. 

 But since the rate of change of volume is very 

 small near the maximum density, it is exceedingly 

 difficult to determine the exact position of the 

 point. 



Hope's Apparatus. The existence of a maximum 

 density may be shown by Hope's apparatus, which 

 consists of a cylindrical vessel of tin, surrounded 

 midway by a gallery. The vessel is filled with water, and two thermo- 

 meters are inserted, one near the top, the other near the bottom, as 



* Phil. Trans., clvi., 1866, pp. 231-248, "On the Expansion of Water and 

 Mercury." 



2(J _ 

 meter. 



FIG. 27. Hope's 



Apparatus. 



