it.] MODERN SCIENCE 335 



traversed on the movable straight line to the time employed 

 in traversing it, that is, if we are able to indicate the po- 

 sition of the movable point, on the straight line which it 

 traverses, at any moment whatever of its course. This 

 relation is just what we call the equation of the curve. To 

 substitute an equation for a figure consists, therefore, in 

 seeing the actual position of the moving points in the tra- 

 cing of the curve at any moment whatever, instead of re- 

 garding this tracing all at once, gathered up in the unique 

 moment when the curve has reached its finished state. 



Such, then, was the directing idea of the reform by which 

 both the science of nature and mathematics, which serves 

 as its instrument, were renewed. Modern science is the 

 daughter of astronomy; it has come down from heaven 

 to earth along the inclined plane of Galileo, for it is through 

 Galileo that Newton and his successors are connected with 

 Kepler. Now, how did the astronomical problem present 

 itself to Kepler? The question was, knowing the respective 

 positions of the planets at a given moment, how to calculate 

 their positions at any other moment. So the same question 

 presented itself, henceforth, for every material system. 

 Each material point became a rudimentary planet, and the 

 main question, the ideal problem whose solution would 

 yield the key to all the others was, the positions of these 

 elements at a particular moment being given, how to de- 

 termine their relative positions at any moment. No doubt 

 the problem cannot be put in these precise terms except 

 in very simple cases, for a schematized reality; for we 

 never know the respective positions of the real elements 

 of matter, supposing there are real elements; and, even if 

 we knew them at a given moment, the calculation of their 

 positions at another moment would generally require a 

 mathematical effort surpassing human powers. But it is 

 enough for us to know that these elements might be known, 



