158 



MR J. Y. BUCHANAN ON THE 



be iv-^. Then the weight of the liquid displaced by the hydrometer is (W + Wj) 

 grams (true), and the specific gravity of the liquid at the fixed temperature is 



W + i^i 



Q 





Fig. 6. 



, . We may repeat this operation, with different added weights, 



VV *T" t^i 



as often as we please, and it is evident that at each operation we obtain 

 a perfectly independent determination of the specific gravity of the 

 liquid referred to that of distilled water of the same temperature as 

 unity. 



Experiment No. 3. — While continuing to work in the vacuum, let 

 us allow air to enter and fill the hydrometer, after which the top of 

 the stem is closed air-tight by a cover without weight. We now weigh 

 the hydrometer, and find its weight to be (W + a) grams (true). 



Let it be immersed in distilled water of the fixed temperature. 

 Being heavier than before, by a, the weight of air which it contains, 

 it will sink in the water until its surface cuts the stem in a line a 

 little above C, say C ; therefore (W + a) grams (true) is the weight of 

 the water displaced by the part of the hydrometer below C Let the 

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

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

 top until the surface of the liquid cuts the stem at C ; let this added 

 weight be tv' grams (true), w' will be a little greater than was w in 

 the first experiment by the difi'erence between the weights of the small 

 cylinder CC of water and of liquid respectively, and the specific gravity 



of the liquid will be given by the ratio 



W + a + w' 

 W + a ' 



which must be 



equal to — ^ — , as in the first experiment. 



Experiment No. 4. — 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' ; if the water is now replaced in the cylinder 

 by the experimental liquid, then we shall have to add a weight iv^', a 

 little greater than w^ in experiment 2, and the specific gravity of the 



liquid will be given by .^^ -, and it will be the same as in the 



^ 6 / W + a + Wi 



former experiments. 



Let us now return to the experimental conditions in which the 



hydrometer full of air floats in vacuo at C in water, and, with the added weight 



w', Sit C in the liquid. 



Experiment No. 5. — Let air be admitted generally, and let it be of the same 



density as that in the hydrometer, so that we are experimenting in air instead of in 



a vacuum. The hydrometer is still closed by the cover without weight ; and, as 



