out a relative error four times as big as a
stockbroker's commission, he must needs be dreadfully out in his attempt to
predict the time of passage of the moon. Now, what is the fact? His error
is less than a second of time, and the moon takes 27 days odd to revolve.
That is to say, setting out with 10s. in 100l. of error in his
circumference, he gets within the fifth part of a farthing in 100l. in
predicting the moon's transit. Now we cannot think that the respect in
which mathematical science is held is great enough--though we find it not
small--to make this go down. That respect is founded upon a notion that
right ends are got by right means: it will hardly be credited that the
truth can be got to farthings out of data which are wrong by shillings.
Even the celebrated Hamilton[207] of Edinburgh, who held that in
mathematics there was no way of going wrong, was fully impressed with the
belief that this was because error was avoided from the beginning. He never
went so far as to say that a mathematician who begins wrong must end right
somehow.

"There is always a difficulty about the mode in which the thinking man of
common life is to deal with subjects he has not studied to a professional
extent. He must form opinions on matters theological, political, legal,
medical, and social. If he can make up his mind to choose a guide, there
is, of course, no perplexity: but on all the subjects mentioned the
direction-posts point different ways. Now why should he not form his
opinion upon an abstract mathematical question? Why not conclude that, as
to the circle, it is possible Mr. James Smith may be the man, just {112} as
Adam Smith[208] was the man of things then to come, or Luther, or Galileo?
It is true that there is an unanimity among mathematicians which prevails
in no other class: but this makes the chance of their all being wrong only
different in degree. And more than this, is it not generally thought among
us that priests and physicians were never so much wrong as when there was
most appearance of unanimity among them? To the preceding questions we see
no answer except this, that the individual inquirer may as rationally
decide a mathematical question for himself as a theological or a medical
question, so soon as he can put himself into a position in mathematics,
level with that in which he stands in theology or medicine. The every-day
thought and reading of common life have a certain resemblance to the
thought and read