As Fred Hoyle has observed, most readers assume a preface is written first and thus
contains the author’s hopes and aspirations. In reality most prefaces are written after the fact and
contain the authors' views of his accomplishments. So it is in this case and I am forced to observe
that my own perception of the subject has deepened and sharpened the considerable respect I
have always had for the virial theorem. A corollary aspect of this expanded perspective is an
awareness of how much remains to be done. Thus by no means can I claim to have prepared here
a complete and exhaustive discussion of the virial theorem; rather this effort should be viewed as
a guided introduction, punctuated by a few examples. I can only hope that the reader will
proceed with the attitude that this constitutes not an end in itself, but an establishment of a point
of view that is useful in comprehending some of the aspects of the universe.