=Characteristics of the Velocity Curve.=—This velocity curve is both interesting and surprising, if we have not given the subject any previous thought. It might occur to us that the air expands in volume in the tube, and we might reason from this fact that the velocity of the air would increase as it flowed through the tube, but very few of us would be able to see that the rate of increase of velocity also increases. That is to say, it gains in velocity more rapidly as it approaches the open end of the tube. If the velocity were represented on the diagram by a straight horizontal line, we should know that it was constant in all parts of the tube, which would be the case if water were flowing instead of air. If it were represented by a straight inclined line, like the dashed line N V, then we should know that the velocity increased as the air flowed along the tube, but that it increased at a uniform rate. The slope of the line would indicate the rate of increase. Neither of these suppositions represent correctly the velocity of the air at all points in the tube; this can only be done by a curved line such as we have shown. The slope of the curve at any point represents the rate of increase of velocity of the air at that point. If the curve is nearly horizontal, then we know that the velocity does not increase much; but if the curve is steep, then we know that it is increasing rapidly, the actual velocity being indicated by the vertical height of the curve above the horizontal line M U.