The law that a given shape when enlarged increases much more rapidly in volume than in surface has, in our brief survey, bound together a wide diversity of facts in astronomy, geology, geography, navigation, engineering, mechanics, physics, and chemistry. A good many times I have brought it before young folks as a means of linking together everyday observations and principles of sweeping comprehensiveness. Boys and girls are apt to think that there is a formidable barrier between science and common knowledge. No such barrier exists. The sun, his planets and their moons; the forces which carve mountains and valleys; the arts of shipbuilders, of designers of bridges, office-buildings, and lighthouses; the plans of the inventors of machinery; the rules discovered by investigators who pass from appearances to the underlying reality of molecule and atom, are all within the sway of the elementary law we have been studying. There is a gain in thus pursuing a connecting thread of classification, conferring order as it does on what might else be an assemblage of things collected at random. A law such as that of size links into unity, and fastens in the memory a vast array of observations and experiments which otherwise would have no associating tie, no common illumination. CHAPTER XI PROPERTIES Food nourishes . . . Weapons and tools are strong and lasting . . . Clothing adorns and protects . . . Shelter must be durable . . . Properties modified by art . . . High utility of the bamboo . . . Basketry finds much to use . . . Aluminium, how produced and utilized . . . Unwelcome qualities turned to profit . . . Properties long worthless are now gainful . . . Properties may be created at need. Materials are valued for their properties as well as their forms. We now pass to a rapid survey of properties as observed in gifts of nature, as modified by art, as turned to account in many ingenious ways, as studied by the investigators who would fain know in what particulars of ultimate form, size and motion, properties may really consist.