Levity

²² If the phenomena of Huygens and Wren are discovered, the cause will be what I have said.

Because in this state of our globe, struck or projected things are carried away more by the air and aether than by their own impetus, just as a moved water carries away things swimming or lying in it.

That is evident by this reason, because from the abstract [theory] of motion, the ratio from [abstract] reasons, nothing restores itself to its prior line even when an impediment is removed, because no endeavor without motion lasts beyond a moment.

But things struck and impelled upon a plane, when they encounter a small mound in their motion, slant their course as if by a certain art, and once the impediment is removed, they resume it.

This is because the impediment was objectified only to the body, not to the air or aether; as one vanishes, another succeeds it.

Just as two lights, on account of their rarity, penetrate each other without being confused, so those two aethers of the concurring bodies carry their own bodies along and are mutually transferred into the other.

From this comes that permutation of motions and regions after a concurrence.

The same is the cause of the Vibration of Pendulums, so many times repeated and gradually vanishing: the impetus of the impelling aether—collected by a particular condensation and dilation and restoring itself—carries the seized object even beyond the endeavor of its own gravity.

Thus, the object, having fallen down, is raised again to the other side, and soon, being dispersed and vanishing, the aether allows it to be cast down again by another aether that is now less elastic.

This matter is reciprocated until rest, so that the same cause applies to pendulums and vibrating strings.

From here also, the ratio of the isochronism of vibrations is rendered: for the higher the fall, the stronger it is; therefore, the greater the compression.

Therefore, as height diminishes, so does compression; but compression is the cause of restoration, and restoration is the cause of the speed of falling back.

Height, therefore, and speed (or force and space) are diminished together.

If the space is as much less as the force (or speed) is less, the motion will be isochronous, or completed in the same time.

Therefore, when the same aether from a moving thing strikes one that is resting or meeting it, it is transferred into the resting or meeting thing and deserts the impinging one.

This results in that divarication or permutation of paths and speeds of Huygens and Wren, of which we have given more examples in the problem of light in Theory of Motion, problem 11.

If the aether is double, it sends each of its rays through the same opening at the same time without confusion.

This is why a violent motion:

• is weak at the beginning and end, but strong in the middle
• increases for some time and then soon decreases

Suppose a stone or a lead bullet is projected by me or by gunpowder; at the beginning, the speed will increase because the motion imparted to the projectile is violent, while the motion of the projector is natural.

For my muscles, like a taut bow, relax and restore themselves to their natural state with great force.

The ratio is the same for gunpowder, whose compressed substance erupts from an open fire.

The natural motion of a thing restoring itself increases continuously; therefore, the same motion, continuously accelerating itself, is impressed upon the projectile, which it exercises as long as it is strong enough to overcome the air.

But when the air has recollected itself and begun to react and restore itself, this motion of restoration in the air is likewise natural and accelerated[cite: 1]. Consequently, the decrement of the projectile’s impetus is accelerated by the increment of the reacting agent.

But to proceed, it has..

[24]

…this also presents a difficulty if you look at the abstract reasons of motion: experience teaches that a larger thing outweighs a smaller one, and the impetus from a large thing is far stronger than from a small one;

Yet, in a free state of nature, it matters not at all for motion how great the length is in contiguous things, nor in continuous things according to Theory of Motion 23, 24, nor indeed how great the thickness or width is[cite: 1].

But sensible bodies appear to be continuous and contiguous rather than actually being so.

Hence, when the first part of a larger impetus has broken the impetus of a smaller adversary by its own destruction, the other discontinuous part—being animated even by the arrival of new air and aether—overcomes it easily with supervening recent forces.

But in truly continuous things, the impetus of all parts is consumed at once.

Whence, by the benefit of division, things not to be despised can be achieved in mechanics, which I trust I shall demonstrate at some time through use itself[cite: 1].

²³ From gravity, the levity of less heavy things follows by accident. The entire doctrine of Hydrostatics was first established by Archimedes.

Wood is lighter than water because wood has more aether than earth.

[25]

Wood ascends in water because liquids have imaginary cylinders that are affected by gravitation in innumerable assignable ways. The aether in the wood cancels this gravity, and the liquid is arranged parallel to the horizon.

Therefore, a heterogeneous thing brought into water, since it raises as much water as the space it occupies, will create a cylinder in which it exists, unequal in weight to others.

Consequently, it will sink if it is heavier, or be raised if it is lighter.

Similarly, if something is made lighter than the neighboring air, it will be raised in the air until it reaches a higher and more subtle region of air, and consequently a region lighter than itself, where it will hang.

This is also why:

• clouds hang in the air and
• smoke ascends.

The art of flying could be reached if something could be prepared by human art to be lighter than air.

Lana and Vossius says this would be achieved if a concave vessel were provided so large that the air enclosed within it outweighed the container or vessel itself.

Therefore, with the air exhausted by an already known artifice and the vessel hermetically sealed (suppose it to be glass), the whole vessel will be lighter than an equal space of air.

Whatever is lighter than an equal space of liquid ascends in it.

Therefore, the given vessel will ascend in the air[cite: 1]. And to bring the matter to calculations (for Lana’s [calculations] are minor): let there be a glass bubble so small that the water contained and the glass containing it roughly balance in weight; let us call its semi-diameter, as a measure of magnitude, ( $a$ )

Let the weight, whether of the glass or the water, which by hypothesis is the same, be called ( $b$ ) as a measure of the destined weight[cite: 1]. Finally, from the observations of the most learned Boyle and others…

26]**

…let us suppose air to be a thousand times lighter than water.[cite: 1] Now let there be a glass bubble made of glass of equal thickness, a thousand times larger than the previous one, or whose semi-diameter is $1000a$ .[cite: 1] Its spherical surface, or the glass container, will be greater than the glass of the measuring bubble in the duplicate ratio of the radius, and consequently will weigh $1,000,000b$ .

The water of this bubble will be greater than the water of the measuring bubble in the triplicate ratio of the radius, and consequently will weigh $1,000,000,000b$ .

Therefore, if this bubble is not filled with water, but with air, since air is a thousand times lighter than water by hypothesis, it will weigh only $1,000,000b$ .[cite: 1] And consequently, it will equipoise with the glass of the bubble.

If the air is exhausted from the bubble as much as possible, it will weigh approximately as much as an equal space of air.[cite: 1] And if a bubble of radius $1500a$ is taken and exhausted, it will be notably lighter than an equal space of air, and consequently, it will ascend in it.[cite: 1] If the proportion of air to water were greater, the bubble should be made correspondingly larger.

But whether bubbles of such great magnitude can be conveniently made, and exhausted within, and remain without rupture and endure, I do not take it upon myself to say.