=Use of Velocity Curves.=—Besides being interesting, a knowledge of the velocity of the air at all points in a tube is of much practical value. It gives us the time a carrier will take in going from one station to another. Usually the first questions asked, when it is proposed to lay a pneumatic tube from station A to station B, are, How quickly can you send a carrier between these points? How much time can be saved? These questions are answered by constructing a velocity curve. Since the velocity changes at every point along a tube, to get the time of transit between two points we must know the average velocity of the air between those points. We can find this approximately from our curve by measuring the height of the curve above the horizontal line M U at a large number of points, and then taking the average of all these heights; but there is a more exact and easier method by means of a mathematical formula. As such formula would be out of place here, we will not give it; suffice it to say, that the average velocity of the air between the tank and the end of the tube, in the case we have assumed, is about seventy-three feet per second (49.7 miles per hour), a little less than one-half the sum of the velocities at the two ends, and a little more than the velocity at the half-mile point. Knowing the average velocity, we can tell how long it takes for a particle of air, and it will be nearly the same for a carrier, to travel from the tank to the end of the tube, by dividing the distance in feet by the average velocity in feet per second. This we find to be one minute 12.3 seconds. Since the air moves more rapidly as it approaches the open end of the tube, a carrier will consume a greater period of time in going from the tank to the quarter mile point than in going from the three-quarter mile point to the open end. The last quarter of a mile will be covered in a little more than fourteen seconds, while the first quarter will require a little more than twenty-one seconds. This difference is surprising, and it becomes even more marked in very long tubes with high initial pressures. This explains why the service between stations located near the end of the tube is more rapid than between stations on other parts of the line. This velocity curve shows us the velocity of the carriers at each station along the line and enables us to regulate our time-locks and to locate the man-holes and circuit-closers connected with each intermediate station. It gives us the length of the “blocks” in our “block system.” When we know the velocity and weight of our carriers, we can compute the energy stored up in them, and from this the length we need to make our air-cushions so as not to have the air too highly compressed. It would be impossible to design our apparatus properly if we did not know the laws that govern the flow of air in the tubes.