ANNUAL ADDRESS OF THE PRESIDENT. LXI 
These results show the extreme difficulty of determining the exact 
mass of a given volume of water. The discordance between the 
different observers amounts to more than one part in a thousand, 
while good weighings are exact to one part in eight or ten millions. 
Without doubt two weights can be compared at least a thousand 
times more accurately than either of them can be reproduced by 
weighing a specified volume of water, and for that reason the kilo- 
gram, like the English pound, can now be regarded only as an ar- 
bitrary standard of which copies must be taken by direct compari- 
son. As already stated, the kilogram is equivalent to 15432°54874 
English troy grains, or about two pounds three ounces avoirdupois. 
In consequence of the circumstance that the mass of a body is not 
affected either by temperature or flexure, weighing is an easier pro- 
cess than measuring ; but in order to obtain precise results many 
precautions are necessary. Imagine a balance with a block of wood 
tied to its right-hand pan and accurately counterpoised by lead 
weights in its left-hand pan. If with things so arranged the bal- 
ance were immersed in water the equilibrium would be instantly 
destroyed and to restore it all the weights would have to be re- 
moved from the left-hand pan, and some of them would have to be 
placed in the right-hand pan to overcome the buoyancy of the wood. 
The atmosphere behaves precisely as the water does, and although 
its effect is minute enough to be neglected in ordinary business 
affairs, it must be taken into account when scientific accuracy is 
desired. To that end the weighing must either be made in a vacuum, 
or the difference of the buoyant effect of the air upon the substances 
in the two pans must be computed and allowed for. As very few 
vacuum balances exist, the latter method is usually employed. The 
data necessary for the computation are the latitude of the place 
where the weighing is made and its altitude above the sea level; 
the weights, specific gravities, and coefficients of expansion of each 
of the substances in the two pans; the temperature of the air, its 
barometric pressure, and the pressure, both of the aqueous vapor, 
and of the carbonic anhydride, contained in it. 
Judging from the adjustment of the pile de Charlemagne, and 
the Exchequer troy weights of Queen Elizabeth, the accuracy at- 
tained in weighing gold and silver at the mints during the four- 
teenth, fifteenth, and sixteenth centuries must have been about one 
part in ten thousand. The balance which Mr. Harris of the Lon- 
