This can be demonstrated by the tube shown in Fig. 29. If water is allowed to flow through a tube constricted in some places, and provided with glass gauge-pipes at various points to indicate the pressure in the pipe at those places, it is found that the pressure, as indicated by the height of the water in the gauge-glasses at the narrow parts of the tube, is less than that which it would have at those places if the tube were of uniform section and length, and passed the same quantity of water. We can formulate this fact under a general law which controls fluid motion also in other cases, viz. that _where the velocity of the liquid is greatest, there the pressure is least_. It is evident, since the tube is wider in some places than in others, and as a practically incompressible liquid is being passed through it, that the speed of the liquid must be greater in the narrow portions of the tube than in the wider ones. But experiment shows that after allowing for what may be called the proper hydraulic gradient of the tube, the pressure is least in those places, viz. the constricted portions, where the velocity of the liquid is greatest. This general principle is of wide application in the science of hydraulics, and it serves to enable us to interpret aright many perplexing facts met with in physics. We can, in the next place, gather together the various facts concerning fluid flow which have been explained above, and apply them to elucidate the problems raised by the passage through water of a ship or a fish. Let us consider, in the first place, a body totally submerged, such as a fish, a torpedo or a submarine boat, and discuss the question why a resistance is experienced when an attempt is made to drag or push such a body through water. The old-fashioned notion was that the water has to be pushed out of the way to make room for the fish to move forward, and also has to be sucked in to fill up the cavity left behind. Most persons who have not been instructed in the subject, perhaps even now have the idea that this so-called “head resistance” is the chief cause of the resistance experienced when we make a body of any shape move through water. A common assumption is also that the object of making a ship’s bows sharp is that they may cut into the water like a wedge, and more easily push it out of the way. Scientific investigation has, however, shown that both of these notions are erroneous. The resistance felt in pulling or pushing a boat through the water is not due to resistance offered by the water in virtue of its inertia. No part of this resistance arises from the exertion required to displace the water or push it out of the way.