EINSTEIN'S LAW OF GRAVITATION 239 



ine any world-line simpler than that of a particle of 

 matter left to itself; we shall therefore call it a "straight" 

 line. Our experience is that two particles of matter at- 

 tract one another. Expressed in terms of world-lines, 

 this means that, if the world-lines of two isolated particles 

 come near each other, the lines, instead of being straight, 

 will be deflected or bent in towards each other. The 

 world-line of any one particle is therefore deformed ; and 

 we have just seen that a deformation is the equivalent of 

 a mathematical transformation. In other words, for any 

 one particle it is possible to replace the effect of a gravi- 

 tational field at any instant by a mathematical transforma- 

 tion of axes. The statement that this is always possible 

 for any particle at any instant is Einstein's famous "Prin- 

 ciple of Equivalence." 



Let us rest for a moment, while I call attention to a most 

 interesting coincidence, not to be thought of as an inter- 

 section of world-lines. It is said that Newton's thoughts 

 were directed to the observation of gravitational phe- 

 nomena by an apple falling on his head ; from this striking 

 event he passed by natural steps to a consideration of the 

 universality of gravitation. Einstein in describing his 

 mental process in the evolution of his law of gravitation 

 says that his attention was called to a new point of view 

 by discussing his experiences with a man whose fall from 

 a high building he had just witnessed. The man fortu- 

 nately suffered no serious injuries and assured Einstein 

 that in the course of his fall he had not been conscious in 

 the least of any pull downward on his body. In mathe- 

 matical language, with reference to axes moving with the 

 man the force of gravity had disappeared. This is a case 

 where by the transfer of the axes from the earth itself to 

 the man, the force of the gravitational field is annulled. 

 The converse change of axes from the falling man to a 

 point on the earth could be considered as introducing the 

 force of gravity into the equations of motion. Another 

 illustration of the introduction into our equations of a 



