i 4 SCIENTIFIC METHOD 



moves in a parabola, whose ordinate is as the tangent 

 squared. He therefore deduced that a projectile is such 

 a body moving in a parabola. This is a synthetic 

 deduction from cause to effect, from the forces acting 

 on a projectile to its consequent motion, when this 

 motion could not have been discovered empirically. 

 Again, Kepler's discovery that Mars moves in an ellipse 

 round the Sun in one of the foci, and so that the radius 

 vector from planet to sun describes equal areas in equal 

 times, is a deduction ; but in this case not causal, but 

 a pure deduction of simple facts. The observations of 

 the planet Mars, bequeathed by Tycho, and continued by 

 Kepler himself, gave him a great number of positions 

 successively occupied by Mars as they appeared. But 

 the confused dance of a planet as it appears to a spectator 

 from the earth could not by itself discover to him how 

 it moves in relation to the sun. He had to consider 

 in what curve a body occupying such positions moves ; 

 and this he could only do by the Greek laws of conic 

 sections, from which he deduced that it moves in an ellipse, 

 so that the radius vector to the sun in a focus describes 

 equal areas in equal times. As Laplace says in his 

 \ System of the World, 'Without the speculations of the 

 Greeks on the curves formed from the section of a cone 

 by a plane, these beautiful laws might have been still 

 unknown.' Kepler thus discovered that Mars occupies 

 positions such that it moves in an ellipse, not as Mill 

 thought, by a mere colligation of facts, for the facts did 

 not contain the curve round the sun ; nor, as Whewell 

 thought, by induction, for the curve is not a generaliza- 

 tion from the facts ; but by deduction in the following 

 form : 



The orbit of Mars has certain positions (by observa- 

 tion). 



