y of the water employed; and their
mode of computing the temperature correction is proved erroneous; and
their favorite natural reference of a quadrant of the earth is not
found a scientific feature capable of serving the purpose they have been
employing it for; and even their own sons show some dislike to adopt it
fully, and adhere to as much of the ancient system as they can."[327]

But coming down to more practical and every-day calculations, in which
money is invested, how very erroneous are the calculations of our best
engineers, and how fatal their results. Nineteen serious errors were
discovered in an edition of _Taylor's Logarithms_, printed in 1796; some
of which might have led to the most dangerous results in calculating a
ship's place, and were current for thirty-six years. In 1832 the
_Nautical Almanac_ published a correction which was itself erroneous by
one second, and a new correction was necessary the next year. But in
making this correction a _new error was committed of ten degrees_.[328]
Who knows how many ships were run ashore by that error?

Nor can our American mathematicians boast of superior infallibility to
the French or British. In computing the experiments which were made at
Lowell (for a new turbine wheel), it was found that when the gate was
fully open, the quantity of water discharged through the guides was
_seventy per cent. of the theoretical discharge_. (An error of thirty
per cent.) The effect of the wheel during these experiments was
eighty-one and a half per cent. of the power expended; but when the gate
was half open the effect was sixty-seven per cent. of the power, while
the discharge through the guides eleven per cent. more than the
theoretical discharge. But when the opening of the gate was still
further reduced to one-fourth of the full opening, the effect was also
reduced to forty-five per cent. of the power, while the discharging
velocity was raised to _forty-nine per cent. more than that given by
the theory_.[329] An unscientific man would hardly call that good
guessing; but it was the best result of labored and expensive scientific
calculation. No wonder the _London Mechanics' Magazine_ says: "More can
be learned in this way (testing engines in the workshop) in half an
hour, than can be derived from the theoretical instructions, however
good, in a year." So much for the infallibility of a mathematical
demonstration. In regard even to the very limited circle of our
relations