. Their value is dependent on the observer’s reference system and on the geometrical character of the surface observed. The curves being arbitrary, the formula is appropriate for any reference system, or even if the observer does not know exactly what his reference system is. (The Fabric observer does not know what his space and time partitioning actually is because he is in a gravitational field). It is the g’s which disclose the geometry of an observer’s partitions, and their values also contain a reflection of the character of the region observed.
We find s by direct exploration with a moving ship (
is found by direct exploration with a freely moving particle);
,
are the observed length and breadth measurement differences which we have to relate to s. By making sufficient observations in a small area and referring them to the general formula we can find the values of the g’s for the observer’s particular reference system. Different values for g’s will be found if the observer changes his reference system, but there is a limitation to the values so obtainable owing to the part played by the surface itself, which is diffidently expressing its intrinsic geometrical character in the g’s in each observation.