THE COMMON HYDROMETER. 77 



suspended from the hook, and then its weight is determined. 

 It is then weighed in water, and thus its loss of weight is 

 ascertained, which is the weight of a portion of water equal 

 in volume to the body. 



37. The Common Hydrometer. The name hydrom- 

 eter is given to a class of instruments used for determining 

 the specific gravities of liquids by observing either the 

 depths to which they sink in the liquids or the weights re- 

 quired to make them sink to a given depth. These 

 instruments depend upon the principle that the 

 weight of a floating body is equal to the weight of 

 the fluid which it displaces. 



The common hydrometer is usually made of 

 glass, and consists of a straight stem ending in two 

 hollow spheres, B and C, the lower one being 

 loaded so as to keep the instrument in a vertical 

 position when floating in the liquid. There are no 

 weights used with the instrument ; but the stem Fig- 27 

 is graduated, so as to enable the operator to ascer- 

 tain the specific gravity of a liquid by the depth to which 

 the instrument sinks in it. 



Let k = the area of a section of the stem, v = the vol- 

 ume, and 10 = the weight of the hydrometer. When the 

 hydrometer floats in a liquid whose specific gravity is s, let 

 the level D of the stem be in the surface ; and when it 

 floats in a liquid whose specific gravity is s', let the level E 

 be in the surface. Then (Art. 34, Rem.) we have for the 

 weights of the liquid displaced in the first and second cases, 

 respectively, 



10 = s (v &-AD), 



w 8 ' (v &-AE); 



but the weight of the liquid displaced in each case is the 

 same, since each is equal to the weight of the instrument. 



