84. If throughout a certain space (which need not be continuous, and which may extend to infinity)
and in all the bounding surfaces
and at infinite distances within the space (if such there are)
then throughout the space
86. If throughout a certain space (which need not be continuous, and which may extend to infinity)
and in all the bounding surfaces the normal components of and are equal, and at infinite distances within the space (if such there are) where denotes the distance from some fixed origin,—then throughout the space
and in each continuous part of which the space consists
86. If throughout any continuous space (or in all space)
and |
and in any finite part of that space, or in any finite surface in or bounding it,
then throughout the whole space
For, since we may set making the space acyclic (if necessary) by diaphragms. Then in the whole space is single-valued and and in a part of the space, or in a surface in or bounding it, Hence throughout the space
87. If throughout an aperiphractic[1] space contained within finite boundaries but not necessarily continuous
and |
and in all the bounding surfaces the tangential components of and are equal, then throughout the space
It is evidently sufficient to prove this proposition for a continuous space. Setting we have for the whole space,
- ↑ If a space encloses within itself another space, it is called periphractict, otherwise aperiphractic.