Page:Elementary Text-book of Physics (Anthony, 1897).djvu/126

112 of $$B$$ lying on the other side of that surface. Similarly, the forces which act on $$B$$ are in equilibrium with the forces which act across the surface between the molecules of $$B$$ and $$A$$. Let us consider any area $$s$$ taken in the surface separating $$A$$ and $$B$$. Represent by $$F$$ the sum of the molecular forces which act across that area. If the forces which act across different equal elements of the area be equal, the ratio $$\frac{F}{s}$$ is called generally the pressure per unit area on the surface $$s$$, or, simply, the pressure on the surface. This pressure is positive if the force $$F$$ be directed away from the portion of the whole body which is held in equilibrium, negative if directed toward that portion. It is plain, from the equality of action and reaction, that if this force be directed toward the portion $$A$$ of the body, an equal force is directed toward the portion $$B$$ at every point of the surface which separates $$A$$ and $$B$$.

The name pressure is frequently reserved for a negative pressure in the sense just defined; when the pressure is positive, it is frequently called a tension. In case the force which acts across the surface between $$A$$ and $$B$$ vary from element to element of that surface, the pressure at a point of the surface is the limit of the ratio $$\frac{F}{s}$$, when the area $$s$$ is so drawn that its centre of inertia is always kept at that point, and is diminished indefinitely.

The forces acting across the surface separating $$A$$ and $$B$$ will, in general, make different angles with the surface at the different points of it. Similarly, the pressure which is substituted for the forces makes different angles with the surface at different points. The pressure, being a vector quantity, like the force from which it is derived, may be resolved into components perpendicular to the surface and in the plane tangent to it. It is best, for the sake of greater generality in our statements, to consider the tangential component of pressure as resolved into two components, at right angles to each other in the tangent plane. These components are called respectively, the normal pressure and the tangential pressures.