VII 



PRINCIPLE OF ARCHIMEDES 



column is longer than the balancing column of the other. If 

 water is used in one of the tubes, you can determine the relative 

 density of the other liquid as below. 



Density of spirit : density of water : : water column : spirit 

 column. 



Therefore relative density of spirit = ae o . 



spirit column 



Hare's Apparatus for Determination of Relative Densities. 

 A convenient arrangement to use instead of a U-tube to deter- 

 mine the relative densities is represented in Fig. 45, and is known 

 as Hare's apparatus. Two straight glass 

 tubes are connected at the top by a three- 

 way junction, upon the unconnected*end 

 of which a piece of india-rubber tubing is 

 placed. The lower ends of the tubes dip 

 into beakers containing the liquids the 

 relative densities of which have to be 

 determined. By applying suction to the 

 free end of the rubber tube, the two 

 liquids are drawn up the glass tubes, and 

 the heights of the liquid columns above 

 the level of liquids in the beakers will be 

 inversely proportional to the relative 

 densities of the liquids employed. The 

 principle is thus precisely the same as 

 that of the U-tube, but by using the form 

 of apparatus here described, the relative 

 densities of liquids which mix can be more 



conveniently found than by the ordinary (J-tube in which the 

 liquids have to be poured. 



Results of Accurate Determinations of Relative Densities. 

 When exact determinations of relative densities are made, it is 

 necessary to take into consideration the fact that the density of 

 water varies with the temperature, for reasons which will be 

 understood later. The following table shows the relative 

 densities of a number of solids and liquids : 



Fio. 45. Hare's Method 

 of Determining Densit y. 



