SPECIFIC GRAVITY AND DISPLACEMENT OF SOME SALINE SOLUTIONS. 27 



gravity, at the rate of 1 "2 milligram per cubic centimetre of stem so immersed in air. 

 This upward pressure lifts the hydrometer until it displaces a weight of water less than 

 it did in vacuo by the weight of air which the exposed stem displaces after air has 

 been admitted. 



Therefore, in ordinary laboratory practice, when the hydrometer floats in the liquid 

 at any line C on the stem, the true weight of the liquid so displaced is equal to the true 

 weight in vacuo of the hydrometer less the weight of the air displaced by the exposed 

 portion of the stem. 



If s be the weight of the air displaced by the exposed portion of the stem, and W, 

 as before, be the weight in vacuo of the instrument, the effective vertical pressure 

 exercised by the hydrometer when floating in equilibrium on the water is 



H = (W-s), 



and this is the measure of its displacement in distilled water of temperature T under 

 existing atmospheric conditions. 



§ 10. In instruments of the pattern, fig. 3, § 80, which I construct for use in dilute saline 

 solutions I aim at a displacement of 180 grams distilled water. The stem is made from 

 tubing selected with the greatest care so as to secure uniformity of calibre. Its total length 

 is about 130 millimetres, and its external diameter is such that a length of 10 centimetres 

 displaces something less than a cubic centimetre. This condition is satisfied if the 

 glass-blower selects a suitable piece of tube having an external diameter of 3 to 3 '5 

 millimetres by the callipers. If the diameter of the tube is exactly 3'56825 millimetres 

 and its section circular, 10 centimetres of it will displace at 4° C. 1 cubic centimetre. 

 The graduated portion of the stem occupies a length of 10 centimetres, which is divided 

 into millimetres numbered at every centimetre from below upwards: 0, 1, 2, . . . 10. 

 The zero is about 1 centimetre above the junction of the stem with the body, and the 

 highest division, numbered 10, is found at a distance of about 2 centimetres below the 

 top of the stem. The total length of the instrument should not exceed 33 centimetres. 



If the hydrometer floats in distilled water of temperature T so that the surface of 

 the water cuts the stem at 5 millimetres above the zero of the scale (I express this 

 shortly by saying, the hydrometer floats at 5), and the weight of air so displaced by 

 the exposed stem is s^, then the true weight of water so displaced is 



The other conditions remaining the same, let the distilled water in the cylinder be 

 replaced by a saline solution at temperature T. Let the hydrometer be floated in it ; 

 the surface of the liquid will cut the stem or the body of the instrument at a lower 

 level than the 5th millimetre on the scale. In order to immerse the instrument exactly 

 to the 5th millimetre, we have to place a certain weight on the top of the stem. Let 

 its weight in vacuo be w^ grams. Then the weight of liquid displaced by the system is 



H'j = W - s^ + W5 - dw^, 



where dw^ is the weight of the air displaced by the small added weight iv^. 



