To the best of our knowledge, no book on this subject has been
published since Deltheirs excellent little brochure Probability geometriques
of 1926) NQt only does no book exist in English, but most textbooks
on probability completely ignore applications in the geometrical field.
The reason, we suppose, is that by 1900 the set of beautiful results
obtained by Morgan Crofton and others seemed to have exhausted the
subject.
In the last twenty years a large number of problems have arisen
which require for their solution all that was discovered in the past about
geometrical probabilities and a great deal more besides. The subject,
in fact, has been reborn. A glance through the examples in this book
will illustrate the breadth of the field of current application: astronomy,
atomic physics, biology, crystallography, petrography, sampling theory,
sylviculture—all contribute, to say nothing of sundry classified subjects
which we were not free to mention.
We hope, therefore, that this book, in bringing together the theory
of the subject, in describing some of the applications, and in raising
some of the unsolved problems, will serve a useful purpose to scientists
of all kinds. We also hope that it will bring to the attention of
mathematicians a subject of great intellectual charm with many challenging fields
for further research.