162 MR J. Y. BUCHANAN" ON THE 



The scale reading would therefore be 32*10 millimetres, and as the two readings 

 are such that the difference on the millimetre scale is imperceptible, they are taken 

 as identical. 



The final weight is therefore : — 



Shot + glass + air + added weight 



= W + a + M;'=136'69884 + 0-13592 + 23-28170 = 160-11649 grams. 

 Correction for non-immersed portion of stem ^s = — 0'00109 



&' 



W + a + it;'-s=:160-11540 



o -n -^ 160-11540 T.T^,ni.. 



Specific gravity = ^^^^^^^ = 1 1701 44. 



C" is then the final position at which the surfaces of the water and of the 

 experimental liquid cut the stem when the added weight is nothing for water and 

 w' for the experimental liquid, and the experiment is made in air. The effective 

 downward vertical pressures are represented by the true weights W + a — s and 

 W + a + w' -s respectively. 



It should be noted that in the example here given the value of the weight added 

 to the stem of the hydrometer to cause it to float at C" = 32 09 mm. is so very nearly 

 the same as that which caused it to float at C'=32-2 mm., that no alteration has 

 been made in the value of this weight, and we have, therefore, used the symbol tv' in 

 this first experiment instead of w", as given in Experiment No. 5. 



We have imagined that the open hydrometer was actually weighed in a vacuum, 

 when it contained no air. In practice the hydrometer is weighed full of air and in air. 

 When to this weight we apply the vacuum correction, that is, the weight of air displaced 

 by the whole hydrometer and closed with its weightless cover, we obtain the value of 

 W + a which is the working weight in vacuo of the hydrometer. In this expression, 

 for any particular load, W is constant, it is the sum of the weights of glass and shot 

 alone. The weight of air, a, contained in it will vary with the density of the atmosphere 

 at the time. 



§ 83. The open hydrometer consists of G^ grams (true) of glass and L,, grams (true) 

 of shot and A,, grams (true) of air, as when weighed in vacuo. In order to obtain these 

 constants, we first weigh the glass instrument empty as it comes from the glass-blower, 

 and find that it weighs G grams in air of given density. Taking the specific gravity 



G 



of the glass to be 2-5, we obtain -^ as the volume (in cubic centimetres) of the glass. 



z 



C 

 The weight of -^ cubic centimetres of air of the given density is a^ grams, and when 



added to G gives the weight in vacuo of the glass of the instrument : 



Go = G + Ug, 



Similarly, the weight of the sliot added as load is found to be L grams in air, and 



