Apart from this development of the "streptocone" as an important feature in decorative work, it is not without interest in connection with the probable importance and significance of the Japanese double streptocone, as we may call the Tomoye, to note some of its geometrical features. Referring to the Fig. 60, it is obvious that each of the paired streptocones is equal in area to half the enclosing circle, also that each of the two inscribed circles (_a_, _b_) has an area of one-fourth of that of the enclosing circle–and that each arbelus (_c_, _d_) has also an area one-fourth that of the enclosing circle and is equal in area to each of the inscribed circles (_a_, _b_). Each of the two constituent "streptocones" is made up of a _complete_ circle capped by an "arbelus" equal in area to it (namely, one-quarter of that of the big circle). It is obvious that the area of the arbelus formed in a semicircle by two enclosed semicircles which are contiguous and of equal base as in Fig. 60, is equal to that of a circle the diameter of which is the vertical line drawn from the apex of the arbelus to the arc of the semicircle (Fig 60). This is true whether the enclosed contiguous semicircles have chords of equal or unequal length (Fig. 60). This fact was known to the Greek geometricians, as I am informed by Sir Thos. Heath. FOOTNOTE: [8] I am indebted for the figures (not the diagrams) illustrating Chapters XVII., XVIII., XIX. to the report by Mr. Thomas Wilson on the Swastika–in the Smithsonian Reports, 1894. Those interested in this subject will find a vast store of information in that report. CHAPTER XX COAL Coal is so much "a matter of course" in our daily life that most people are only now, when its supply is becoming precarious, anxious to know something of its nature and history. By the word "coal," or "coles," our ancestors understood what we now distinguish as "charcoal," prepared from wood by the "charcoal-burner," or "charbonnier," as the French call him. What we now call "coal" was known to them as "sea-coal," and, later, as "black" or "stone cole," to distinguish it from "brown coal," known nowadays as "lignite," though the name "stone coal" is locally applied in England to that very hard kind of black coal also called "anthracite," of which jet is only an extremely hard and dense variety found in small quantities in the oolitic strata of Whitby, Spain, and other localities.