57, or 89.3. Which means that we may reasonably
expect the number of deaths not to vary from 1000 by more than 89,
_i.e._, they will be between 1090 and 910. It will be seen that this
number is in very satisfactory agreement with 88.5 given by the rougher
calculation based on my own experiments.
To come to the question of sampling. Consider a powder of uniform
fineness and fine enough to pass through an 80 sieve. For purposes of
calculation this may be assumed to be made up of particles of about
one-eighth of a millimetre across (say roughly 1/200 of an inch); cubed,
this gives the content as about 1/500 (strictly 1/512) of a cubic m.m.
Now one cubic m.m. of water weighs 1 milligram; therefore 500 such
particles if they have the specific gravity of water weigh 1 milligram,
and otherwise weigh 1 milligram multiplied by the sp. gr.: 500 particles
of ruby silver (Pyrargyrite)[129] will weigh 5.8 milligrams and will
contain nearly 3.5 milligrams of silver.
Now suppose a portion of 3.2667 grams (1/10 Assay Ton) of silver ore to
contain 500 such particles of ruby silver and no other material carrying
silver: such an ore would contain 35 ozs. of silver to the ton. But the
limits of variation on 500 particles would be 28[130] multiplied by the
square root of 5, or 62 particles. Thus the limit of sampling error
would amount to just one-eighth of the silver present, or say to rather
more than 4 ozs.
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