way in which we can weigh and measure, submit the results to calculation, and draw from them conclusions which are formally quite legitimate, and still be all the time on the wrong track; then examine how we may be set upon the right road, and led to a new conclusion more plausible and more in harmony with the rest of our knowledge.
It has been discovered that the flea can leap two hundred times its length. Our admiration at this is changed to astonishment when it is demonstrated by calculation that, if nature had endowed the horse with a degree of strength similarly proportioned to his weight he would have been able to clear the Rocky Mountains at a bound, and that with a like effort a whale would be able to leap to a height of two hundred leagues. What can be more unassailable than these conclusions, founded on weight, measure, and calculation?
It is true that, if, instead of comparing the weights of the horse and the flea, we had compared their heights, we should have found that the horse's leap would not measure more than three hundred metres. Why is preference given to the weight? Because it is its whole body with its three dimensions and its density that the flea hurls to two hundred times its height, and it is the same feat of strength that we demand in vain of the horse. Calculations have also been made to show that, if a man could move with a speed proportioned to that of certain insects, he would be able to travel more than ten leagues in a minute, or sixty times as fast as a railroad-train.
The Amazon ants, going to battle, travel from two to two and a half metres a minute. The Amazons of antiquity, to be even with them, if we judge by the relative heights, should have traveled eight leagues an hour. We have, however, in this case, to compare the forces with which given masses move themselves, and should take account of weights or volumes. If we proceed by this rule, we shall obtain formidable numbers, that stagger the boldest imagination. The warlike inhabitants of the banks of the Thermodon would have to get over fifty thousand leagues in an hour. Yet, who can deny the truth of the observations, the rigor of the measurements, or the justice of the reasoning?
The authors of these interesting calculations have not had in mind only to make known some figures of comparison, good to store up, even if they are never used, but they have endeavored to set forth the idea that certain insects are much better endowed with powers of leaping and speed than the vertebrates, and especially than man. The persons who express this conclusion have failed to conform to the precept that they must not extract more from their facts than is rigorously contained in them, and are the victims of a scientific illusion, which is quite wide-spread, but not hard to dissipate. What is in question? It is the valuation of the labor necessary to raise a certain weight to a certain height. The labor increases in proportion to the weight and the height. When, then, two animals of different masses leap to