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Hereditary Genius
383
interval of 6.5 is very generally adhered to. Now, then, let us see
what the numbers in the classes would have been by theory if,
starting either from 2.5 (a little lower than 2.6, as we agreed it ought
to be) above the average, or from 4, below it, we construct a series
of classes, according to Quetelet's grades, having a common interval
of 6.5. Column VIII. shows what these classes would be; Column
IX. shows the corresponding figures taken directly from Quetelet's N,
and Column X. gives the difference between these figures, which are
so closely accordant with the entries in Column IV., as to place it
beyond all doubt that the errors in the Greenwich observations are
strictly governed by the law of a deviation from an average.
It remains that I should say a very few words on the principle of the
law of deviation from an average, or, as it is commonly called, the
law of Errors of Observations, due to La Place. Every variable event
depends on a number of variable causes, and each of these, owing to
the very fact of its variability, depends upon other variables, and so on
step after step, till one knows not where to stop. Also, by the very
fact of each of these causes being a variable event, it has a mean
value, and, therefore, it is (I am merely altering the phrase), an even
chance in any case, that the event should be greater or less than the
mean. Now, it is asserted to be a matter of secondary moment to
busy ourselves in respect to these minute causes, further than as to
the probability of their exceeding or falling short of their several mean
values, and the chance of a larger or smaller number of them doing
so, in any given case, resembles the chance, well known to
calculators, of the results that would be met with when making a
draw out of an urn containing an equal quantity of black and white
balls in enormous numbers. Each ball that is drawn out has an equal
chance of being black or white, just as each subordinate event has an
equal chance
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