32 MR. J. Y. BUCHANAN ON THE 



Four weighings of the hydrometer by replacement with standard weights were 

 made in air. The weights found were : — 



180-7141 grams. 

 180-7137 „ 

 180-7136 „ 

 180-7137 „ 



Mean = 180-7138 „ 



As the hydrometer floats without added weights in distilled water with only a 

 part of the stem exposed, we take its weight in air, 1807138 grams, as expressing, to 

 first approximation, its volume in cubic centimetres. The correction for net buoyancy, 

 that is, the difference between the weight of air displaced by the hydrometer and 

 that displaced by the weights, is (taking dry air at G'lS" C. and 741 mm.) 0"1961 gram, 

 whence the first approximation to the weight in vacuo of the instrument is 

 1807138 + 0-1961 = 180-9099 grams. 



It was found that by the addition of 1*698 gram to the weight of the hydrometer 

 it floated totally immersed in distilled water at 6*15° C. ; that is, if the weight were 

 diminished ever so little the top of the stem became exposed, and if it were increased 

 ever so little the instrument began to sink to the bottom. 



Taking now the first approximation to the weight in vacuo, 180"9099 grams, and 

 adding r6980 gram, we have the sura 182*6079 grams. This is the first approximation 

 to the weight in vacuo of the mass of distilled water which is displaced by the whole 

 hydrometer at a temperature of 6*15° C. Taking the volume of 1 kilogram of water 

 at 6"15° C. to be 1000*034 cubic centimetres, we find the volume of the hydrometer 

 at 6*15° C. to be 182*6139 c.c. ; and this is the volume of air which it displaces at 

 6*15° C. We have found that 1 litre of the air in the balance-room at the time 

 weighed 1*2288 gram. Therefoi'e the exact weight of the air displaced by the 

 hydrometer when being weighed was 182*6139 x 00012288 = 0*22439 gram, and 

 taking the weights as consisting of brass of the density 8*38, we find the weight of 

 air displaced by them to be 0*02650 gram, whence the net buoyancy = 0* 19789 

 gram, and the true weight in vacuo of the hydrometer is 180*7138 + 0*1979 

 - 180*9117 grams. 



The weight in vacuo was determined on two other days, namely 24th April and 

 2nd June 1894; on each of these days four determinations were made of the weight 

 in air, which on the first of these days weighed 1*2081 gram per litre, and on the 

 second 1*2037 gram per litre. The weights in vacuo deduced from these observations 

 were 180*9109 and 180*9113 grams respectively. The mean of the three determina- 

 tions is 180*9113 grams, which is accepted as the final value of the weight in vacuo of 

 hydrometer No. 17. The weights of the other hydrometers, Nos. 21 and 3, were 

 determined in the same way ; the particulars are collected in the following table : — 



