1. That air or some other gas is to be compressed by work done upon it and that upon expanding it will do a greater amount of work than was required for the compression, or
2. That a bag empty, or partially filled with air, or other gas, can be easily immersed, and that if blown full of gas while immersed it will, in its tendency to float, do more work than was required to immerse it, or
3. That the weight of the atmosphere and its consequent pressure upon vacua can be utilized to drive a piston, or compress a bag and by some sort of means at the same time produce another vacua ready for a similar operation, the loss of the driven piston, or the compressed bag being utilized to drive machinery, if desired.
It is now believed by all scientific men that none of these things are possible. In the first place, it is well known that compressed air will do exactly the same work in regaining its former volume that was expended upon it to compress it, and this with absolute exactness. In compressing the gas with a piston the force exerted upon the rod to drive the piston must be sufficient not only to compress the gas but also to overcome the friction of the tight fitting piston, and further, if the pressure on the rod be removed, the expanding gas will deliver against the face of the piston exactly the force and energy required to drive the piston for the compression, but not all of this can be returned to any machinery driven by the piston-rod, for a part will be lost in the friction of the tight-fitting parts. Thus here, as elsewhere, there is an exact equivalent of energy a part of which is consumed in friction, and only a part available for returned motion. The same thing is true in compressing a bag, except that possibly the bending of the fabric is less resistance than the friction of the tight-fitting piston. Still, the bending of the fabric is some resistance, and consequently the bag so expanding cannot return all the energy required for its compression, the difference being the loss, however slight, in the bending of the fabric of which the bag is made.
Again, let us admit that a dilated bag is easily immersed in water, and that if inflated with air there will be considerable tendency to rise, but how much energy is required for the inflation? It is manifest that if it is immersed the weight of the water and its consequent pressure will resist the attempted inflation, and must be overcome before the inflation is complete. The deeper the immersion the more the compression, and consequently the more work required for the inflation. If a bag having a contents of one cubic foot were immersed a mile in fresh water, and if it should be attempted to inflate it, the reader will perhaps be surprised to know that the inflation would have to be done against a pressure of substantially 2,400 pounds to the square inch. It is simple that the deeper the bag is immersed the more work it will do in rising to the surface, but it is equally plain that the deeper it is immersed the more energy is required for its inflation. In each case the work of inflating is exactly equal to the work returned in rising to the surface, and there is not one whit to spare for running machinery of any kind.
The third classes of devices above mentioned assume atmospheric pressure, and a piston driven by atmospheric pressure. This is easily attained, but in order for atmospheric pressure to drive a piston it must only be on one side of the piston, and when the piston has been driven what force and energy will be required to put it in a position again such that there will be atmosphere on only one side, and a vacuum into which it can retire, on the other side? It is easily answered. The same work must be done, and the same work exactly, to put the piston again in the position with the vacuum with equal dimensions into which it can be driven by atmospheric pressure, that first drove it to occupy the vacuum—exactly the same work, and no less and no more, except that the amount lost by friction must be supplied in addition.