Definition of Terms:

agillaceous:
containing clay, or clay particles.

Stigmaria  is the generic name given to the roots of the Sigillaria tree. 

Stigmaria ficoides are the roots of the Sigillaria tree; they are recognized by (and known for) the round
pit marks (or dots) that are all over them.  These dot/spots (areole) are remnants of rootlets, which were
attached to to these roots--before the Sigillaria trees (to which they belonged) were uprooted.

Stigmaria leaves  are the rootlets which were once attached to larger Stigmaria (ficoides) roots. This
term was abandoned around 1850 for "Stigmaria rootlets," or "Rootlets of Stigmaria."

Underclay is a generic term that is used to denote (what is thought to be) a fossil soil.  Sometimes they
are referred to as "seat-earths".

Leaves* : These refer primarily to the leaves of  Poacites.

Poacites: This term refers to the leaves of  Poacites.  This term was used prior to 1868.  Such leaves are
now called  "Cordaites borassifolia."

Sigillaria

in situ: a term used by geologists and paleontologists to indicate that something was buried where is grew, or that it was only buried once, and not moved or re-deposted in another location.

Calamites

Cythere: an old term for what are today known as Ostracods or Ostracodes.

Naiadites

Ctenoptychius

Rhizodus

Spirorbis

Lepidodendron

Alethopteris lonchitica

Cordaites

roof: the rock found  immediately above a coal seam, ore body, or other tabular deposit.  It often consists of  carbonaceous shale.
 

Trigoncarpa

Uniformitarianism: This is a viewpoint which says "the present is the key to the past," and its reasoning is as follows:  Since presently observed sedimentation rates on lake bottoms  (or in the ocean) is under "normal" conditions quite slow, then it is assumed that the rate of sedimentation in the past  must also have been slow.   This view began to be promoted vigorously by Sir Charles Lyell around 1840.  It was also promoted by many other geologists in Europe and the United States -- especially in the later half of  the 19th Century -- with the result  that it is now the only view that is allowed to be published in the geological literature.  This has led to the prevailing belief among scientists that the sedimentary deposits which cover large portions of every continent were laid down slowly over many millions of years. 

 Sir William J. Dawson, (sometimes referred to as John W. Dawson) is the author of  Acadian Geology.     Dawson's book provides us with what is perhaps the most detailed description of the Joggins strata in print.  It was first published in 1855.  Later editions followed.