Discovery therefore, which has labor for its condition, is the principle of the progress of science.  Under what form does a discovery present itself to the mind of its author?  As a supposition, or, which is the same thing, as an hypothesis.  Hypothesis is the sole process by which progress in science is effected.  If we supposed nothing, we should know nothing.  In vain should we look at the sky and the earth to all eternity, our eye would never read the laws of astronomy in the stars of heaven, nor the laws of life upon the bark of trees or in the entrails of animals.  This is true even of mathematics.  The contemplation, prolonged indefinitely, of the series of numbers, or of the forms of space, would produce neither arithmetic nor geometry, if the human mind did not suppose relations between the numbers and the lines, which it can only demonstrate after it has supposed them.  The conditions are very clearly seen which have prepared and made possible a fruitful supposition, but the hypothesis does not itself follow of any necessity.  It appears like a flash of light passing suddenly through the mind.

The carpenter’s saw opens a plank from end to end on the sole conditions of labor and time; but the discovery of truth preserves always a sudden and unforeseen character.  Archimedes leaps from a bath and rushes through the streets of Syracuse, crying out, “I have found it!” Why?  The flash of genius has visited him unexpectedly.  Pythagoras discovers a geometrical theorem; and he offers, it is said, a sacrifice to the gods, in testimony of his gratitude.  He thought therefore, according to the fine remark of Malebranche, that labor and attention are a silent prayer which we address to the Master of truth:  the labor is a prayer, and the discovery is an answer granted to it.

When this wholly spontaneous character of discovery is not recognized, and when it is thought that the observation of facts naturally produces their explanation, it must needs be granted that a discovery is confirmed by the very fact that it is made.  But this is by no means the case.  Hypothesis does not carry on its brow, at the moment of its birth, the certain sign of its truth.  A flash of light crosses the mind of the savant; but he must enter on a course, often a long course, of study, in order to know whether it is a true light, or a momentary glare.  Every supposition suggested by observation must be confirmed by its agreement with the data of experience.  Let us listen to a great discoverer—­ Kepler.  He is giving an account of the discovery of one of the laws which have immortalized his name.