ATaiiualrryPi92im"}        An  Epoch-Making  Discovery.  31 
tive  determinations  are  predicated  upon  some  prearranged  method  of 
synchronizing  our  clocks ;  otherwise  conceptions  of  simultaneity  and 
equal  duration  can  have  no  definite  and  invariable  meaning. 
The  influence  of  the  gravitational  field  prevents  the  application 
of  the  special  theory  of  relativity  to  any  but  systems  at  rest  or 
moving  uniformly  and  rectilinearly. 
The  mathematical  development  of  the  theory  presupposes  the 
introduction  of  the  time  factor  as  a  fourth  coordinate  and  calling 
the  new  and  complex  curve  thus  produced  the  World-line  of  a  given 
point.  The  final  formulation  of  the  Einstein  Law  is  expressed  as 
follows :  "The  world-line  of  a  material  point  is  a  geodetic  line  in 
the  space  time  continuum."  The  time  factor  is  not  introduced 
simply  as  such,  but  as  ct  —  x4  in  which  c  denotes  the  velocity  of 
light. 
The  statement  that  every  motion  is  relative  may  be  looked  upon 
as  another  way  of  expressing  the  view  that  space  and  time  have  no 
physical  objectivity.  Space  and  time  are  not  measurable  in  the 
abstract.  They  constitute  the  framework  which  we  fill  up  with 
physical  events,  both  spatial  and  chronological. 
We  gain  our  knowledge  of  both  space  and  time  by  direct  ex- 
perience, so  in  our  everyday  life  we  shall  continue  to  deal  with 
them  as  heretofore.  To  the  physicist  and  astronomer,  however, 
new  fields  of  research  are  already  opening  and  it  is  not  too  much  to 
expect  the  future  to  bring  us  into  closer  harmony  and  a  more  nearly 
correct  understanding  of  electrodynamics  and  gravitational  law 
with  a  realization,  perhaps,  that  matter  after  all  is  but  one  of  the 
manifestations  of  energy. 
One  comfort  for  the  average  student  of  mathematics  is  found 
in  the  assertion  that  "Euclidean  geometry  is  to  remain  valid  for 
infinitely  small  portions"  which  includes  those  within  the  ken  of  our 
ordinary  daily  life.  The  trouble  with  the  whole  subject  at  present 
lies  in  the  fact  that  Einstein  enthusiasts  are  presuming  to  "prove 
the  unprovable"  and  to  make  assertions  to  the  effect  that  there  is 
such  a  thing  as  "finite  space  without  boundaries." 
Students  of  philosophy  who  remember  the  speculations  of  Kant 
in  his  "Subjectivity  of  Time  and  Space"  and  Locke  in  his  "Essay  on 
Human  Understanding,"  and  Leibnitz,  the  originator  of  differential 
calculus,  will  enjoy  the  spiritual  exhilaration  of  cleaning  out  the 
cobwebs  of  the  mental  attic,  by  reading  one  of  the  works  which 
have  recently  been  published  in  which  the  subject  is  discussed  with  a 
