THE THEORY OF RELATIVITY* 

 By Andrew H. Patterson 



The idea of Relativity is not new. It was presented by the old 

 philosophers, and has been a constant part of philosophical doctrine to 

 this day. AH of our knowledge is relative. Especially is this true of 

 our knowledge of time and space. We know time only at a certain 

 place ; we observe the position of a point only at a certain time. To 

 say that an observation or measurement was made at a given time is 

 useless and meaningless until we have stated the place, — Greenwich or 

 Washington or Tokio, — to which the time is referred. Places of stars 

 in \he Nautical Almanac are given only for the epoch, or time, stated 

 at the head of the page, and corrections must be applied for later 

 dates. It is quite true to say that we do not kuow the exact place of a 

 star unless we know the exact time. Important dates in Assyrian 

 history have been fixed because of the record of a total eclipse of the 

 sun which was seen in the streets of the city of Nineveh at half -past 

 nine on a certain morning of a certain month of a certain year in the 

 reign of Jeroboam the Second. By calculating when this eclipse must 

 have occurred at that particular place at that time of the morning, 

 we at once link up the Assyrian era to our own, and can translate their 

 time into ours. Time without position in space has no more inde- 

 pendent existence than the direction "vertically upwards", for ex- 

 ample, which changes with every point on the earth's surface. 



But to fix the place of a point we need a system of axes to which 

 we can refer its position by means of co-ordinates. The latitude and 

 longitude of a ship are the two co-ordinates which fix its position on 

 the surface of the ocean. If the point is to be fixed in space, three 

 co-ordinates are needed, and if we can conceive of a four-dimensional 

 space, four co-ordinates will be necessary to specify the position of any 

 point therein. 



It is immaterial whether we choose rectangular axes, or oblique 

 axes, or whether we use polar co-ordinates or some other system, pro- 

 vided that the position of the point arrived at by any system is the 

 same. Again, we can transform the co-ordinates of a point in one sys- 

 tem of axes into its co-ordinates in another system of axes by appro- 

 priate mathematical operations, and since a line is a series of points, 



* Presidential Address, delivered before the North Carolina Academy of Science, at the 

 North Carolina State College of Agriculture and Engineering, Raleigh, April 30, 1920. 



[19 ] 



