170 THE LIMITATIONS OF SCIENCE 



Now our measurements of length are usually made 

 under the condition that we, clocks, and rods are all 

 moving with the earth and so relatively at rest. Our 

 measurements of length of bodies on the earth are 

 thus different from those which would be made on the 

 same bodies by an observer if he could be stationed 

 with his clocks in the moon. Also if an object on the 

 earth is measured while it is moving with respect to 

 the observer, it will appear to have a different length 

 from that which it has when relatively at rest. Thus 

 the dimensions of a body are dependent on its velocity, 

 and Newtonian mechanics, which assumes the con- 

 trary, must be modified when applied to bodies in 

 motion. 



Professor Einstein then derives a set of equations 

 which will express the dimensions of a moving body 

 as they appear to a stationary observer. These show 

 that the length of every body moving with a velocity, 

 v, is diminished in the direction of its motion by the 

 fraction 



and that its dimensions at right angles to its mo- 

 tion remain unchanged. Thus a sphere in motion 

 becomes an ellipsoid flattened in the direction of 

 its motion by an amount equal to the above frac- 

 tion. It is proper to say, that this effect is quite 

 inappreciable at ordinary velocities. This is true even 



