16 SCIENTIFIC METHOD 



for the force of impact by Sir Christopher Wren's ex- 

 periments before the Royal Society, which proved that, 

 if one body impinge upon another, and by its force 

 change the motion of the other, that first body also, 

 because of the equality of the mutual pressure, will 

 undergo an equal change in its own motion towards the 

 contrary part. Newton repeats Wren's experiments, and, 

 having added fresh instances from magnetism and other 

 attractions, extended the law from impact to all forces, 

 and induced it in the universal form, action and reaction 

 are always equal and opposite. Thus did Newton finally 

 establish the main principles of dynamical mechanics by 

 the empirical method of Bacon. But he went beyond 

 induction, which never could have discovered the im- 

 perceptible link between the sun and its planets. The 

 sequel is deduction ; and even under the head of Axioms 

 he immediately uses the third law, as induced from 

 impact, to deduce that the whole momentum of bodies 

 acting reciprocally on one another, together with the 

 state of their centre of gravity, is conserved. So true 

 is it that ; induction leading to deduction is the most 

 fruitful method of natural science. 



In the first book of the Principia Newton, starting 

 from the general laws of motion, proceeds to deduce a 

 great number of derivative laws in dynamical mechanics. 

 Two of these laws require special notice here : the first, 

 that every body, which moves in a curve, and by a 

 radius drawn to a point describes about that point areas 

 proportional to the times, is urged by a centripetal force 

 to that point ; and the second, that the centripetal forces 

 of bodies, which by equable motion describe different 

 circles, are to one another as the squares of the arcs 

 described in equal times applied to the radii of the 

 circles ; while by a further corollary, if the squares of the 



