Waves, impetus and the centre of gravity of a wedge
Water-waves and their reflection beside wedge-and-cube volume and balance studies
This large sheet joins studies of moving water to studies of the wedge. In the water notes the impetus keeps its line within a still wave, motion rebounds only against an impenetrable object, and every circular wave reflects back toward its origin; a lettered diagram shows waves h a and c a meeting at point a. In the mechanics, a wedge (conio) is analysed as a quarter of its cube and a pyramid as a sixth, its off-cuts a third of the body, and its centre of gravity placed first at a third and then at a quarter of its length. Apparatus sketches and, on the facing half, an array of geared machines and mills accompany the reasoning.
On this page
The centre of gravity of a wedge
The wedge is divided into two equal parts a and b, equal in weight but not in equilibrium. Its centre of gravity lies at a third of its length toward the base, at the intersection of its diameters.
A wedge is a quarter of its cube
The whole wedge is 1/4 of the cube; removing the off-cuts leaves 1/6, a difference of 1/12. Balancing 2 against 1 and dividing the pyramidal wedge in three places its balance at a third of its length, and its centre of gravity at a quarter of the length.
Impetus keeps its line within a still wave
The impetus holds to its line within the motionless wave of a great current, like a sunbeam in the course of the winds. The wave of impetus is sometimes still in a strong current and sometimes swiftest in still water, as on the surface of marshes; and why does one blow raise several waves?
Circular waves reflect toward their origin
Motion does not rebound unless stopped by an object impenetrable to it. The striking of every circular wave made in still water rebounds toward its beginning, by the same portion that is lacking to complete the greater circle.
Volume ratios of wedge, pyramid and cube
The wedge a b c d e f is exactly a quarter of its whole cube, and the pyramid o m q p n is a sixth of the same cube. From the sixth to the quarter there is a difference.
An experimental copper vessel
One apparatus is to be made of prepared copper, solely for the experiment, with a rim soldered on. Alternatively it may be fixed in a ring, after the fashion of the bottom of a box.