A field of force thus arises from an attitude of mind. If we do not take our coordinate-system to be something different from that which it really is, there is no field of force. If we do not regard our rotating axes as though they were non-rotating, there is no centrifugal force. Coordinates for which the natural geometry is \[ ds^{2} = - dx_{1}^{2} - dx_{2}^{2} - dx_{3}^{2} + dx_{4}^{2} \] are called Galilean coordinates. They are the same as those we have hitherto \index{Coordinate-systems!Galilean}% \index{Galilean coordinates}% called ordinary rectangular coordinates and time (the velocity of light being unity). Since this geometry is familiar to us, and enters largely into current conceptions of space, time and mechanics, we usually choose Galilean geometry when we have to ascribe an abstract geometry. Or we may use slight modifications of it, e.g.\ substitute polar for rectangular coordinates. It has been shown in \SecRef{4} that when the $g$'s are constants, coordinates can be chosen so that Galilean geometry is actually the natural geometry. There is then no need to introduce a field of force in order to enjoy our accustomed outlook; and if we deliberately choose non-Galilean coordinates and attribute to them abstract Galilean geometry, we recognise the artificial character of the field of force introduced to compensate the discrepancy. But in the more general case it is not possible to make the reduction of \SecRef{4} accurately throughout the region explored by our experiments; and no Galilean coordinates exist. In that case it has been usual to select some system (preferably an approximation to a Galilean system) and ascribe to it the abstract geometry of the Galilean system. The field of force so introduced is called ``Gravitation.'' \index{Gravitation}% \PageSep{39} It should be noticed that the rectangular coordinates and time in current \index{Time!extended meaning}% use can scarcely be regarded as a close approximation to the Galilean system, since the powerful force of terrestrial gravitation is needed to compensate the error. The naming of coordinates (e.g.\ time) usually follows the \emph{abstract geometry} attributed to the system. In general the natural geometry is of some complicated kind for which no detailed nomenclature is recognised. Thus when we call a coordinate~$t$ the ``time,'' we may either mean that it fulfils the observational conditions discussed in \SecRef{4}, or we may mean that any departure from those conditions will be ascribed to the interference of a field of force. In the latter case ``time'' is an arbitrary name, useful because it fixes a consequential nomenclature of velocity, acceleration, etc.