Cube-root extractor.
The cone displaces water as the cube of its depth of immersion, in this case within 1 and 3 as limits.
Square-root extractor.
Wedge displaces water as the square of its depth of immersion.
From Effect to Cause.
A mechanic, no less than a geometer, may show sagacity in taking up a question in reverse, and reasoning from effect to cause. An expert printer examines a spoiled sheet as it leaves the press, observing that it is smeared and crumpled with a decided skew. At once he stops the machinery and puts his finger on a lever that has become crooked, or on the wheel that has been strained out of true. Mr. Joseph V. Woodworth says of milling cutters:—“When a cutter is broken by being wrongly run backwards on to the work, the breakage is characteristic. Although the man who broke it will be absolutely sure that it ran in the right direction, the cracks down the face of the teeth tell a different story.”
In his manual on steel, Mr. William Metcalf reads a record equally legible to a trained eye:—“If an axe, after tempering, is found cracked near the corners of its edge, these corners have been hotter than the middle of the blade. If a crack appears at the middle of the edge, there the heat was greater than at the corners; snipping and comparing the grains will tell the story. If a somewhat straight crack is noticed, near the edge and parallel thereto, the chances are that the crack indicates a seam.”
At this point let us for a few moments leave the field of mechanics, and notice how inferring cause from effect may aid students of rocks, of the heavens, of the human frame. A geologist, observing a dense limestone, learns how severe the pressure which brought loose sediment to this compactness. In the glass-like texture of quartz he finds an equally plain record of intense heat. The scorings on rock-surfaces, in lines from northward to southward, disclose to him the paths in which ages ago the glaciers moved from their birth-places in the polar zones. In astronomy a feat of inference incomparably more difficult was accomplished by John Couch Adams and Urbain Leverrier, each independently of the other. The orbit of Uranus displayed certain minute irregularities which they referred to a planet, at that time not as yet observed, whose place they indicated. Their remarkable inference was verified by the discovery of Neptune on September 23, 1846.
In a path remote indeed from that of the observer of planet and star, the surgeon in much the same way reasons from result to cause. In 1870 Fritsch and Bitzig, two German investigators, observed that in applying an electric shock to a well defined area of the brain of a chloroformed dog, its limbs moved. One part of the brain thus excited would cause the fore-leg to twitch, another part would lead the hind-leg to move. When a specific area of the animal’s brain was taken away, a corresponding part of its body—the eyes, ears, or limbs, were permanently paralyzed. From studies thus begun it has been clearly proved that in the brain of animals there is a division of labor, each activity being as much localized within the skull as it is externally in the nose, ears, or feet. The examination of human victims of disease and injury has confirmed all this. A patient may have suffered loss of power to write, to speak, to stand firmly on his feet, for weeks or months before the end. The cause in many cases is found to be a tumor, sometimes no larger than a pea, which has pressed down upon a particular area of the brain and so given rise to the trouble. A depressed fragment of bone in fracture of the skull has a similar effect. With these facts in mind, when a surgeon is called in to treat a patient who is suffering from loss of power to write, speak or stand, he lifts the sufferer’s skull for a small space over the specially indicated area, relieving the depressed fracture, or exposing the small tumor, which he removes, usually with restoration to health.