Of Matter: Of the Divisibility of Matter

In this instalment Father suffers from a major episode of the expositions. I think he may have some anecdotes which he has a great urge to share with the children. This is precisely the sort of conversation during which I imagine Charles and Emma getting extremely bored and tickling each other.

You should probably prepare yourself for mathematics and some apparently bad science.

CONVERSATION II.

OF MATTER. - OF THE DIVISIBILITY OF MATTER

  F. Do you understand what philosophers mean when they make use of the word matter ?
  E. Are not all things which we see and feel composed of matter?
  F. Every thing which is the object of our senses is composed of matter differently modified or arranged. But in a philosophical sense matter is defined to be an extended, solid, inactive and moveable substance.
  C. If by extension is meant length, breadth, and thickness, matter, undoubtedly, is an extended substance. Its solidity is manifest by the resistance it makes to the touch.
  E. And the other properties nobody will deny, for all material objects are of themselves without motion ; and yet it may be readily conceived, that, by application of a proper force, there is no body which cannot be moved. But I remember, papa, that you told us something strange about the divisibility of matter, which you said might be continued without end.
  F. I did, some time back, mention this curious and interesting subject, and this is a very fit time for me to explain it.
  C. Can matter indeed be infinitely divided; for I suppose that this is what is meant by a division without end ?
  F. Difficult as this may first appear, yet I think it very capable of proof. Can you conceive of a particle of matter so small as not to have an upper and under surface ?
  C. Certainly every portion of matter, however minute, must have two surfaces at least, and then I see that it follows of course that it it divisible ; that is, the upper and lover surfaces may be separated.
  F. Your conclusion is just ; and though there may be particles of matter too small for us actually to divide, yet this arises from the imperfection of our instruments ; they must nevertheless, in their nature, be divisible.
  E. But you were to give us some remarkable instances of the minute division of matter.
  F. A few years ago a lady spun a single pound of wool into a thread 168,000 yards long. And Mr. Boyle mentions that two grains and a half of silk were spun into a thread 300 yards in length. If a pound of silver, which, you know, contains 5,760 grains, and a single grain of gold, be melted together, the gold will be equally diffused through the whole silver ; insomuch, that if one grain of mass be dissolved in a liquid called aqua fortis, the gold will fall to the bottom. By this experiment, it is evident that a grain may be divided into 5,761 visible parts ; for only the 5,761st part of the gold is contained in a single grain of the mass.
  The goldbeaters, whom you have seen at work in the shops in Long-acre, can spread a grain of gold into a leaf containing 50 square inches, and this leaf may be readily divided into 500,000 parts, each of which is visible to the naked eye: and by the help of a microscope, which magnifies the area of surface of a body 100 times, the 100th part of each of these becomes visible ; that is, the 50-millionth part of a grain of gold will be visible, or a single grain of that metal may be divided into 50 millions of visible parts. But the gold which covers the silver wire used in making what is called gold lace, is spread of a much larger surface, yet it preserves, even if examined by microscope, a uniform appearance. It has been calculated that one grain of gold, under these circumstances, would cover a surface of nearly thirty square yards.
  The natural divisions of matter are still more surprising. In odoriferous bodies, such as camphor, musk and assafœtida, a wonderful subtilty of parts is perceived ; for, though they are perpetually filling a considerable space with odoriferous particles, yet these bodies lose but a very small part of their weight in a great length of time.
  Again, it is said by those who have examined the subject with the best glasses, and whose accuracy may be relied on, that there are more animals in the milt of a single cod-fish, than there are men on the whole earth, and that a single grain of sand is larger than four millions of these animals. Now if it be admitted that these little animals are possessed of organized parts (such as a heart, stomach, muscles, veins, arteries, &c.) and that they are possessed of a complete system of circulating fluids, similar to what is found in larger animals, we seem to approach to an idea of the infinite divisibility of matter. It has indeed been calculated, that a particle of blood of one of these animalcula is as much smaller than a globe one-tenth of an inch in diameter, as that globe is smaller than the whole earth. Nevertheless, if these particles be compared with the particles of light, it is probable that they would be found to exceed them in bulk as mountains do single grains of sand.
  I might enumerate many other instances of the same kind, but these, I doubt not, will be sufficient to convince you into what very minute parts matter is capable of being divided.
  Captain Scoresby, in his Account of the Greenland Seas, state, that, in July, 1818, his vessel sailed for several leagues in water of a very uncommon appearance. The surface was variegated by large patches of a yellowish-green colour. It was found to be produced by animalcula, and microscopes were applies to their examination. In a single drop of the water, examined by a power of 28,224 (magnified superficies) there were 50 in number, on average, in each square of the micrometer glass of 1-340th of an inch in diameter ; and, as the drop occupied a circle on a plate of glass containing 529 of these squares, there must have been in this single drop of water, taken at random out of the sea, and in a place not the most discoloured, about 26,450 animalcula. How inconceivably minute must the vessels, organs, and fluids of these animals be ! A whale requires a sea to sport in : a hundred and fifty millions of these would have ample scope for their evolutions in a tumbler of water !

Where to start? I'll begin with a glossary of some unusual terms that appear in this dialogue:

• Grain - a measure of weight based on a grain of wheat; is still in use in the US. In modern terms it is a mass of exactly 64.79891 milligrams. Father mentions a pound consisting of 5,760 grains; this indicates that he is referring to Troy pounds. This is entirely understandable considering that Troy weights were part of the accepted weights system prior to the introduction of the British Imperial measures in 1824.
• Aqua Fortis - a fantastically alchemical sounding archaic name for Nitric acid.
• Gold lace - according to the Shorter Oxford English Dictionary this is "a braid formerly made of gold or silver wire, now of silk or thread with a thin wrapping of gold".
• Milt - has two meanings, the one I think that is being used here is fish semen/testicle. The other meaning is spleen, although I don't think there should be that many things moving about in one of them.
• Animalcula - microscopic animals, including what we now call protozoa.
• Magnified superficies - seems to mean an increase of the surface area, I found a reference from the Royal Society which equates "magnified 15 times in diameter" to "225 times in superficies"

The assertion of matter being infinitely divisible is quite preposterous from our current level of knowledge. Yet, from the facts available at the beginning of the 19th century, it makes a reasonable amount of sense. Experiments had been done and the results showed that matter appeared structurally identical at every level of division possible. There was no evidence that a limit to this division could be reached; the Rev. Joyce does admit that there was a practical limit to splitting materials due to the lack of precise enough tools to reach smaller parts. This is certainly a case of a theory based on the available evidence which is supported by general consensus. This is not bad science at all, this is how science should work.

The idea of matter being made of discrete indivisible bits had been around for a long time before this book was written. However there was no experimental evidence; this was later found and the theories were developed over the 19th century. From this work Dmitri Mendeleev developed the first periodic table. It wasn't until the very end of that century and into the 20th that scientists discovered that even atoms were divisible (into protons, neutrons and electrons). Later still, some of those subatomic particles were discovered to be divisible yet again (protons and neutrons into quarks). This is where our current understanding still sits; we have The Standard Model, which thousands of scientists around the world are still working to completely prove or disprove and refine. We should have some news regarding this during 2012 from the work being done by the LHC experiments at CERN.

I think it would be an interesting exercise to see how near to the atomic level they reached, so I shall do it in rough approximation. I suspect they were a very long way from it. There is a reasonable chance I shall mess the maths up or approximate too wildly; feel free to help me out in the comments if I do.

Mixing gold and silver together and then seeing if gold is present in a small portion of that mixture is an elegant way of testing the hypothesis. Unfortunately, the quantity of silver required to dilute the gold down to a single atom is mind-bogglingly huge. It turns out there are getting on for 200 million million million atoms of gold in a grain (1.98E18). Repeat the experiment with that many grains of silver instead of 5760 and you'll still end up with a single atom of gold; if you stir it thoroughly enough. It's safe to say that this is not possible to attempt as you would need almost 13 million million metric tons of silver!

In the example of the goldbeaters, 1 grain of gold was spread over an area of 50 square inches. I need to go metric to make sense of this, so that's 0.064798 grams spread to 322.58 square centimetres; that looks a lot simpler doesn't it? The density of gold is 19.30 grams per centimetre cubed, so a grain of gold has the volume of a cube with an edge of just under 1.5 millimetres (approximately 0.00336 centimetres cubed). If the leaf has been uniformly beaten, we can calculate that it's thickness is pretty close to 0.01 millimetres. That's exceptionally thin for any practical purpose. However, the size of an atom is around of 100 picometres (a picometre is truly tiny at 0.000000000001 metres). That means that the gold leaf is still around 100000 atoms thick. The gold lace makers did a great deal better; their leaf would have been around 130 atoms thick. To get an indivisibly thin leaf (i.e. with a thickness of just a single atom), you would have to spread it out over an area a hundred thousand times bigger; a single square sheet with sides 57 metres long should do it. Still, they were exceptionally close to the limit compared to my initial instincts.

I don't really want to think about fish semen but I have for the sake of this post. I have looked into the subject just enough to try to get an idea of whether there is any truth in the statement "there are more animals in the milt of a single cod-fish, than there are men on the whole earth". The population of the world sat somewhere around 1 billion at the time that the book was authored. Even though I couldn't find any hard figures for cod sperm counts, I did discover that male fish have enormous gonads when they're ready to spawn (10-20 percent of their body weight). Considering the figures that I found regarding sperm density in mammalian semen and that fish let all of it out in one go, I think I can say that the statement may well be true; it's definitely in the right ball park.

It's an interesting assumption though that all "animals" have the same level of internal complexity, no matter how small. I guess this is another case of the contemporary tools not allowing them to examine closely enough to see the very real differences that arise in nature at these minute scales.

The account of Captain Scoresby's encounter with a discoloured sea sounds very much like a plankton bloom; a massive collection of tiny ocean plants (phytoplankton) that thrive under certain conditions. Seeing as zooplankton (equally tiny ocean animals) feed on phytoplankton, I can imagine that a bloom would be full of wriggling animalcula. I think that probably, the good Captain was seeing a mixture of both microscopic animals and plants; observing that some of them were moving, he may well have assumed that they were all animals. It looks like the numbers they give are very high; modern studies have recorded blooms with 100 million phytoplankton per litre of sea water.

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