Double pump.

The hub n has a double set of teeth, which joined together make a toothing that occupies the whole circle forming the face of that hub. And when one semicircle has raised its hammer m, the other toothed semicircle releases its own hammer, and by this the shaft is always loaded by one and the same weight.

The hub m is fixed between the male part of the pump and the little step below, and everything is joined together; their motion is made at the same time in one and the same direction, that is, in descending it presses the water and in rising it takes up as much again.

The water that is poured from the pump weighs less than the water that is in the sheath of the hub, because as the hub descends it pours out the water that lies in the space between the sheath and the hub, down which it descends. That space is made as narrow as possible.

9th. Whatever proportion the thickness of the water pressed downward has to the thickness of the water that rises upward, such has the weight of the water that rises to the weight of the power that makes it rise.

A thing placed in water is less heavy than in air by as much as air is less heavy than water. The rubbing of the heavy body resists the motion of the thing rubbed.

Whether it is better that the water go up all at once in a single lift, or indeed in two. It is answered that in a single lift the wheel could not sustain all the water it raises in two, because in the half-turn of the wheel it would raise 100 pounds and no more; and if it had to raise the 200 pounds in the whole turn, it would not raise them unless that wheel doubled its diameter, and in doubling that diameter it would double the time. Therefore it is better and more economical to make that wheel sub-double rather than double, etc.

The descent of the hub does not lower as far as the skin of the water, because in touching the water it would diminish its weight.

The hub must weigh somewhat more than the water that remains continually in the pump, together with the water standing in the sheath of that hub; for if the water weighed as much as the hub, the hub would not raise it.

And if, for the sake of argument, the driver of the water were made ten times thicker than the pipe of the escaping water, and were given ten times less motion than this, what would its office be? It is answered, by the 9th of this, that the water would rise the tenth part of what it rose before, at the height of that pipe from which it first rose.

On the nature of gravity.

Gravity is an accident joined to bodies removed from their natural place.

On the nature of levity.

Levity joined with gravity, as are unequal weights joined in a balance, or light liquids placed beneath liquids or other dense ones heavier than it, which ...

Of the water that descends through an inverted siphon composed of pipes of various widths: if the water of the larger pipe is of a higher surface than the water of the smaller pipe, only that water of the larger pipe will have gravity in itself which, in its lower part, is joined with the water of the smaller pipe.

1st. Waters joined together do not come to rest unless their surface is in every part equally distant from the centre of the world.

Therefore the inverted siphon a c p d t, being full of water in a c and full of air in t d, if the pipes are of triple proportion of capacity one to the other, the water that rises through the pipe d t will be of triple motion to the motion of the water that descends through the pipe a b; and by the first of this, the two surfaces of the waters will remain of equal heights.

The concavities a b receive within themselves the fingers of the hand in descending the spiral staircase: that is, the channel a receives within itself the four smaller fingers, and b receives the thumb; and the channels c d do the same in climbing, holding the four smaller fingers in the channel c and the thumb in d. The rib n m receives within itself the board f o, which is the front of the step.

The wall of this spiral staircase is square, being made in a corner of the house.