Of The Attraction Of Gravitation

Firstly, I would like to say I'm really sorry that it's taken me so long to put up a new post. Unfortunately for the blog, lots of other interesting things got in the way.

This conversation is the start of a fairly long section on gravity. I'm not expecting much drastically wrong science here; Sir Isaac Newton's description of gravity was comprehensive and is still accurate in most day-to-day contexts. Newton's Principia, in which he laid out the laws of motion, was published around 100 years before the Scientific Dialogues. Bear in mind that it has been two centuries since the Dialogues was first published. I find it quite amazing that this book is two-thirds as old as a work I have considered to be almost impossibly far away on the time-line of science.

CONVERSATION V.

OF THE ATTRACTION OF GRAVITATION.

  F. We will now proceed to discuss another very important general principle in nature ; the attraction of gravitation, or as it is frequently termed, gravity, which is that power by which distant bodies tend towards each other. Of this we have perpetual instances in the falling of bodies to the earth.
  C. Am I, then, to understand that whether this marble falls from my hand, or a loose brick from the top of the house, or an apple from the tree in the orchard, that all these happen by the attraction of gravity ?
  F. It is by the power which is commonly expressed under the term gravity, that all bodies whatever have a tendency to the earth ; and, unless supported, will fall in lines nearly perpendicular to its surface.
  E. But are not smoke, steam, and other light bodies, which we see ascend, exceptions to the general rule ?
  F. It appears so at first sight, and it was formerly received as general opinion, that smoke, steam, &c. possessed no weight : the discovery of the air-pump has shown the fallacy of this notion, for in an exhausted receiver, that is, in a glass jar from which the air is taken away by means of the air-pump, smoke and steam descend by their own weight as completely as a piece of lead. When we come to converse on the subjects of pneumatics and hydrostatics, you will understand that the reason why smoke and other bodies ascend is simply because they are lighter than the atmosphere which surrounds them, and the moment they reach that part of it which has the same gravity with themselves they cease to rise.
  C. Is it, then, by this power that all terrestrial bodies remain firm on earth ?
  F. By gravity, bodies on all parts of the earth (which you know is of globular form) are kept on its surface, because they all, wherever situated, tend to the centre ; and since all have a tendency to the centre, the inhabitants of New Zealand, although nearly opposite to our feet, stand as firm as we do in Great Britain.
  C. This is difficult to comprehend ; nevertheless, if bodies on all parts of the surface of the earth have a tendency to the centre, there seems no reason why bodies should not stand as firm on one part as well as another. Does this power of gravity act alike on all bodies ?
  F. It does, without any regard to their figure or size ; for attraction or gravity acts upon bodies in proportion to the quantity of matter which they contain ; that it, four times a greater force of gravity is exerted upon the a weight of four pounds that upon one of a single pound. The consequence of this principle is, that all bodies at equal distances from the earth fall with equal velocity.
  E. What do you mean, papa, by velocity ?
  F. I will explain it by an example or two : if you and Charles set out together, and you walk a mile in half an hour, but he walk and run two miles in the same time, how much swifter will he go than you ?
  E. Twice as swift.
  F. He does, because, in the same time, he passes over twice as much space ; therefore, we say his velocity is twice as great as yours. Suppose a ball, fired from a cannon, pass through 800 feet in a second of time, and in the same time your brother's arrow pass through 100 feet only, how much swifter does the cannon-ball fly than the arrow ?
  E. Eight times swifter.
  F. Then it has eight times the velocity of the arrow ; and hence you understand that swiftness and velocity are synonymous terms ; and that the velocity of a body is measured by the space it passes over in a given time, as a second, a minute, an hour, &c.
  E. If I let a piece of metal, as a penny-piece, and a feather, fall from my hand at the same time, the penny will reach the ground much sooner than the feather. Now how do you account for this if all bodies are equally affected by gravitation, and descend with equal velocities, when at the same distance from the earth ?
  F. Though the penny and feather will not, in the open air, fall with equal velocity ; yet if the air be taken away, which is easily done, by a little apparatus connected with the air-pump, they will descend in the same time. Therefore the true reason why light and heavy bodies do not fall with equal velocities, is, that the former, in proportion to its weight, meets with a much greater resistance from the air than the latter.
  C. It is then, I imagine, from the same cause that, if I drop a penny and a piece of light wood into a vessel of water, the penny shall reach the bottom, but the wood, after descending a small way, rises to the surface.
  F. In this case, the resisting medium is water instead of air, and the copper, being about nine times heavier than its bulk of water, falls to the bottom without apparent resistance. But the wood, being much lighter than water, cannot sink in it ; therefore, though by its momentum * it sinks a small distance, yet, as soon as that is overcome by the resisting medium, it rises to the surface, being the lighter substance.


* The explanation of this term will be found in the next Conversation.

There are a couple of bits of terminology which I'm going to have to get into before they irritate me any further. The Reverend frequently refers to velocity and weight. These terms have very specific definitions in modern mechanics; this may seem slightly pedantic, nevertheless I'm going to attempt to explain them.
In these writings (as well as most contemporary non-scientific contexts) velocity may be considered as being synonymous with the words swiftness and speed. Scientifically speaking, this is incorrect: speed is how fast an object is moving; velocity is a combination of how fast an object is moving and its direction of motion; swiftness is not a scientific term at all. Speed is a scalar (i.e. simply a numeric) property of an object while velocity is a vector (i.e. magnitude and direction) property. There will more than likely be other examples of the muddling of scalar and vector quantities in chapters to come, hopefully I can keep my rantings to a minimum when this happens.

There is also a very important distinction between the words mass and weight, which is essential in correctly understanding gravity. All objects have a mass, it is a measure of how much matter the object consists of. There are two separate definitions of mass which are equivalent; these being how hard it is to change the speed of an object and how strongly gravitational forces affect (and are created) by the object. The currently agreed base unit of measuring mass is the kilogram, which is practically identical to the mass of a litre of water. On the other hand, weight is a measure of how much force acts on an object due to the acceleration of gravity acting on its mass. Weight is appropriately measured in Newtons, named simply in honour of the great scientist rather than any sort of comment regarding his weight. At the surface of the earth, the acceleration due to gravity is 9.8 ms^-2 (I'll explore this in more depth in a later post). A 10 kilogram object would have a mass of 10kg wherever you placed it (possibly not in a black hole, but let's not get into that right now). This 10kg object weighs about 98 Newtons at the surface of the earth; but, it would weigh little more than 16 Newtons on the surface of The Moon. Although I haven't seen any of the dialogues use the word mass, one conversation does touch on this difference a bit later.

The text seems to confuse the effects of drag (otherwise known as air or fluid resistance) and buoyancy. The distinction between these seems to be apparent in places, while completely missing elsewhere. Buoyancy is exhibited where things float on or in fluids that are less dense than themselves; as in the cases of the smoke, steam and the piece of light wood in this conversation. Drag is a force resisting movement through a fluid which depends very much on the surface area of the object trying to move through the medium. The feather in the example falls much slower, due to the drag force created being high in comparison to the gravitational force acting upon it.

In the case of the light wood falling into the water, many of these different forces are in action. At all times it is experiencing exactly the same gravitational force, causing an acceleration downwards. While falling through the air, it experiences a small amount of resisting (i.e. upwards) force due to drag. As it meets the water, some of its downwards velocity (and therefore momentum) is lost on impact with the surface causing displacement in the water (otherwise known as ripples). Once below the water, the object experiences a combination of the downwards gravitational force and an upwards force due to the wood being less dense than water (i.e. buoyancy). Whichever way it is travelling, there is an opposite resisting force due to the drag of the water. This drag is much greater than that the object experienced in the air, as water's viscosity is much greater than that of air.

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