240 CONTEMPORARY SCIENCE 



force by means of a change of axes is furnished by the 

 ordinary treatment of a body in uniform rotation about 

 an axis. For instance, in the case of a so-called conical 

 pendulum, that is, the motion of a bob suspended from 

 a fixed point by a string, which is so set in motion that 

 the bob describes a horizontal circle and the string there- 

 fore describes a circular cone, if we transfer our axes 

 from the earth and have them rotate around the vertical 

 line through the fixed point with the same angular veloc- 

 ity as the bob, it is necessary to introduce into our equa- 

 tions of motion a fictitious "force" called the centrifugal 

 force. No one ever thinks of this force other than as a 

 mathematical quantity introduced into the equations for 

 the sake of simplicity of treatment ; no physical meaning 

 is attached to it. Why should there be to any other so- 

 called "force," which, like centrifugal force, is independ- 

 ent of the nature of the matter? Again, here on the earth 

 our sensation of weight is interpreted mathematically by 

 combining expressions for centrifugal force and gravity; 

 we have no distinct sensation for either separately. Why 

 then is there any difference in the essence of the two? 

 Why not consider them both as brought into our equations 

 by the agency of mathematical transformations? This is 

 Einstein's point of view. 



Granting, then, the principle of equivalence, we can so 

 choose axes at any point at any instant that the gravita- 

 tional field will disappear; these axes are therefore of 

 what are called the "Galilean" type, the simplest possible. 

 Consider, that is, an observer in a box, or compartment, 

 which is falling with the acceleration of the gravitational 

 field at that point. He would not be conscious of the field. 

 If there were a projectile fired off in this compartment, 

 the observer would describe its path as being straight. In 

 this space the infinitesimal interval between two space- 

 time points would then be given by the formula 



ds 2 = dx\ + dx\ 



