there food and rest. When set at liberty he finds his way back to it with the constancy of the magnetic needle turning to the pole.
The horse knows perfectly the road back to his home. If in the course of a drive the reins are let to fall loose on his neck he will take this opportunity of returning to his stable. With the help of an excel- lent memory he knows the comparative length of the roads to be fol- lowed, and chooses without hesitation the shortest.
Suppose that the same horse is taken into a country of which he is ignorant. After a stay of some hours in a stable he develops the same attachment for his new home which he showed for the former. If in the first drive he is left to his instinct to find his way back it has been ascertained that he will follow the same road, reversed, by which he came, even if it is not the shortest.
Third. The carrier pigeon when set loose within a short radius of its home will return to its cote by the shortest way. If it is set at liberty some hundreds of miles from its home it follows in its return very exactly the line of the railroad by which it came. We need no further proof of this than the following fact.
In the season of the conventions of pigeon fanciers the inhabitants of Bapaume remarked the flight every Sunday of numerous bands of pigeons returning to their homes in the north of France, or in Belgium. We can not claim that Bapaume is exactly on the straight line that connects the different points from which the pigeons were let loose to their dovecotes scattered throughout the region of the north, from Dunkerque to Mézières. It was not merely choice that thousands of pigeons should pass every Sunday over the little city. Bapaume is only an insignificant point in the very extended zone which separates Belgium from the center of France. Moreover, from similar observations made at Amiens, at Arras, and all along the line of the route from Paris to Brussels, it was proven that the pigeons retraced in a contrary direction the road by which they had been taken to the place of release.
We might cite any number of observations of the same sort. For example, the employees of the Orleans railway have often told us of the passage to Arthenay, to Étampes, or to Juvisy of Belgian pigeons released at Poitiers, Angouléme, and Bordeaux.
We have deduced from these facts the following hypothesis, which we will call the "law of retracement." The instinct of orientation from a distance is a faculty which all animals possess in different degrees, of retracing a route over which they have once passed.
IV.
In the study of mathematics the method is often employed of considering a proposition as demonstrated, then stating it in the form of a problem and studying out the consequences. We will use this method here. Let us admit that the hypothetical law stated above has been
