This elementary law I traced that year in a variety of illustrations presented in “A Class in Geometry,” published by A. S. Barnes & Co., New York. Our excursions, since extended, are here given as an example of the knitting value of a pervasive rule kept constantly in mind. Earth Sculpture. Our planet in diverse ways illustrates the law, just stated, of surfaces and volumes. Forces of unresting activity quietly transform the hills and plains, the sea coasts and lake shores of the world, and so gradually that in many cases detection proceeds only by noting the changes wrought in a century. For the most part these forces break up large masses into fragments, or slowly wear away the surfaces of rocks into dust. A lichen takes root on a granite ledge, and in a few years reduces the rock to powder. Rain always contains a little acid, so that in time flint itself is consumed, for all its hardness. Water soaking through soils to form underground streams has hollowed out vast caves, as notably in Virginia and Kentucky. Limestones and sandstones are of open texture, and take up much moisture into their pores; in cold weather this freezes, and in expansion wedges off thin flakes of stone. In the North one sees the ground strewn with such splinters when the warm April sun has melted the snow from beside a limestone fence. Watch the rills as they descend a hillside during a rainstorm and just afterward. They are dark with mud, and on steep declivities they carry down pebbles and bits of broken stone, building up valleys at the expense of high ground. Fed on a huge scale by such mud, the Mississippi River bears in suspension to the Gulf of Mexico a little more than a pound of solid matter in every cubic yard, a prime example of how the waters of the globe gain upon the land. The Falls of Niagara have retreated several miles from their original plunge; the carving of their channel has been wrought much less by the rushing waters than by their burden of abrading earth and sand. The ceaseless churning of water at the foot of the Falls cuts back into the rock, undermining its upper layers, so that ever and anon they break off from the brink of the cataract, with the effect that the stream steadily retires. Throughout the ocean are strong currents to be constantly surveyed and charted on the mariner’s behalf. These currents transport fine mud, and organisms living and dead. Corals flourish best where such currents fetch an abundant supply of food, just as plants thrive best in rich, loose soil. Life in the sea just like life on land is thus dependent on forces which divide large masses into small, and distribute these small masses over wide areas, chiefly by water carriage. Breaking Earth for Removal or Tilth.