SPECIFIC GEAVITY AND DISPLACEMENT OF SOME SALINE SOLUTIONS. 159 



the density of the air within and without the instrument is the same, there is no 

 cause for disturbance of equilibrium between the two masses of air, and they will 

 not interfere with each other. 



The external air, admitted generally, reaches only to the surface of the water or 

 liquid and cannot interfere with the immersed portion of the hydrometer. The stem, 

 however, is now surrounded by a medium of given density, whereas, before, it was 

 surrounded by one of insensible density. The exposed stem displaces its own volume 

 of the air, and the downward vertical pressure which it exerts on the immersed portion 

 of the hydrometer is diminished by the weight of this volume of air. The whole of 

 its vertical pressure is exerted on the immersed part of the hydrometer below the 

 line C. As this pressure is diminished by the weight of the air displaced by the stem, 

 the hydrometer will rise and will float a little higher ; let it cut the stem at the line C", 

 which is situated a little lower than C but higher than C. 



We have then the proportion : — 



The volume of the cylinder : that of the cylinder : : the volume of the exposed : the volume of the air in 

 C'C" C'C stem the hydrometer. 



The total vertical pressure exerted by the hydrometer when floating in the distilled 

 water is now W + a — s, and the stem cuts the water at C". s is the weight of the air 

 displaced by the exposed portion of the stem. 



Let the distilled water be now replaced by the same experimental liquid as before, 

 and let the hydrometer be immersed in it, and let weights be added to the top of the 

 stem until the surface of the liquid cuts the stem at C" ; let this added weight be w" 

 grams (true), w" will be a little less than was w' in Experiment No. 3, and the 

 specific gravity of the liquid is given by the ratio 



W + a + w" — s 

 W + a-s ' 

 which must be equal to 



W + a + w' 

 W + a ' 



as in the third experiment, and also equal to — = — , as in the first experiment. 



Experiment No. 6. — Similarly, if the hydrometer be now immersed in the distilled 

 water with weight u^, then the surface of the water will cut the stem at D", a little 

 lower than D', but higher than D. If the water in the cylinder is now replaced by the 

 same experimental liquid, then we shall have to add a weight w\, a little less than 

 w\ in Experiment No. 4, and the specific gravity of the liquid will be given by the ratio 



W + a + io'\ - s 

 W + a + Wj - s ' 



and it will be the same as in the former experiments. 



§ 82. The above suggested experiments will be best understood by reference to a 

 specific instance of the use of the instrument. 



