The _David_ represented the best type of under-water vessel in the sixties; that she is infinitely inferior to the newest _Holland_ type or some of the French vessels of to-day goes without saying, and it will not be surprising if the submarine of thirty years hence bears the same resemblance to the _Holland_, as the _Holland_ does to the _David_. The ideal submarine boat has a speed as great as that of the fastest torpedo-boat, a very wide radius of action, excellent sea-keeping powers, unlimited quantities of air for power and for respiration by the crew; a means of directing its course by vision upon a moving object whilst itself remaining invisible beneath the surface, and is very habitable and comfortable for long periods of time. The submarine of to-day lacks most of these attributes. It has a slow rate of speed, whether on the surface or submerged, a narrow radius of action, poor sea-keeping powers, a strictly limited quantity of compressed air, and is absolutely blind when beneath the waves. Thus it differs greatly from the ideal boat as sketched above, but its gradual improvement may be safely predicted. We propose in this chapter to describe, in simple language, the working of a vessel intended for under-water navigation, and to consider what improvements are likely to take place. Every submarine boat worked by a crew must of necessity be capable of floating on the surface of the water. This is a self-evident proposition, for the crew must have means of ingress and egress, and the only practical way of entering and leaving the boat is by an opening in the hull when she is on the surface. We have no doubt that the files of the Patent Office would show that many inventors had designed boats which would sink to a certain depth directly they were placed in the water. While in such a system no time is lost in submersion, there would undeniably be difficulties in the way of coming to the surface, &c. The first problem, then, which confronts the designer of a submarine boat is to find the most suitable method of sinking it to the depth at which it is intended to navigate. The most fundamental law of hydrostatics, which applies to all floating bodies, and is equally true of wholly submerged vessels floating at any depth, as of ships of ordinary form, floating on the surface, having only a portion of their volume immersed, is that a ship floating freely and at rest in still water must displace a volume of water having a weight equal to her own weight. The “displacement” of a vessel is defined as the weight of water displaced, which is equal to the weight of the vessel and that of her lading. A ship floating on the surface “displaces” a certain weight of water; in order to force her beneath the surface two methods are open. In the first place, her weight is increased by the introduction of water ballast; thus her “displacement” is altered and she sinks until her weight is again equal to the volume of water displaced.