Everyone Should Read What Galileo Wrote Part 2

Written by Dr Jerry L Krause on December 12, 2017. Posted in Current News

Why should everyone read what Galileo wrote?  To see what Galileo pondered.

Part 2 is the result of James McGinn’s comments to the previous posting—Everyone Should Read What Galileo Wrote!!!  (https://principia-scientific.org/everyone-should-read-what-galileo-wrote/)  If one first reads McGinn’s comments, one might see how what Galileo pondered so long ago might apply to them.

 In the midst of what I consider a mathematical dialogue Galileo wrote (which character does not matter for Galileo wrote all the dialogues):

Having broken a solid into many parts, having reduced it to the finest of powder and having resolved it into its infinitely small indivisible atoms why may we not say that this solid has been reduced to a single continuum [un solo continuo] perhaps a fluid like water or mercury of even a liquefied metal?  And do we not see stones melt into glass and the glass itself under strong heat more fluid than water?  Are we then to believe that substances become fluid in virtue of being resolved into their infinitely small indivisible components? 

I am not able to find any better means of accounting for certain phenomena of which the following is one.  When I take a hard substance such as stone or metal and when I reduce it by means of a hammer or fine file to the most minute and impalpable powder, it is clear that its finest particles, although when taken one by one are, on account of their smallness, imperceptible to our sight and touch, are nevertheless finite in size, possess shape, and capability of being counted. 

It is also true that when once heaped up they remain in a heap; and if an excavation be made within limits the cavity will remain and the surrounding particles will not rush in to fill it; if shaken the particles come to rest immediately after the external disturbing agent is removed; the same effects are observed in all piles of larger and larger particles, of any shape, even if spherical, as is the case with piles of millet, wheat, lead shot, and every other material.  But if we attempt to discover such properties in water we do not find them; for when once heaped up it immediately flattens out unless held up by some vessel or other external retaining body; when hollowed out it quickly rushes to fill the cavity; and when disturbed it fluctuates for a long time and sends out it waves through great distances. 

Seeing that water has less firmness [consistenza] than the finest of powder, in fact no consistence whatever, we may, it seems to me, very reasonably conclude that the smallest particles into which it can be resolved are quite different from finite and divisible particles; indeed the only difference I am able to discover is that the former are indivisible.  The exquisite transparency of water also favors this view; for the most transparent crystal when broken and ground and reduced to powder loses its transparency; the finer the grinding the greater the loss; but in the case of water where the attrition is of the highest degree we have extreme transparency. 

Gold and silver when pulverized with acids [acque forti] more finely than is possible with any file still remain powders,* and do not become fluids until the finest particles [gl’ indivisibili] of fire or of the rays the sun dissolve them, as I think, into their ultimate, indivisible, and infinitely small components.  *It is not clear what Galileo here means by saying that gold and silver when treated with acids still remain powders. [Trans.]

This phenomenon of light which you mention is one which I have many times remarked with astonishment.  I have, for instance, seen lead melted instantly by means of a concave mirror only three hands [palmi] in diameter.  Hence I think that if the mirror were very large, well-polished and of a parabolic figure, it would just as readily and quickly melt any other metal, seeing that the small mirror, which was not well polished and had only a spherical shape, was able so energentically to melt lead and burn every combustible substance.  Such effects as these render credible to me the marvels accomplished by the mirrors of Archimedes.

I stop quoting Crew and de Salvio’s translation because Galileo continued for three more pages where he wrote:

What a sea we are gradually slipping into without knowing it!  With vacua and infinites and indivisibles and instantaneous motions, shall we ever be able, even by means of a thousand discussions, to reach dry land.

Given this ‘knowledge’ of Sutcliffe that the earth’s natural atmosphere is always composed of oxygen and nitrogen molecules, water molecules, and condensation nuclei, which allow water molecules (vapor) to condense on their surface to form (grow into) larger droplets or ice particles so that water vapor supersaturation never occurs, it seems a puzzle that McGinn does not recognize his ‘collected groups’ of water molecules are actually condensation nuclei which have long been accepted as a necessary component of the natural atmosphere.

However, despite what Sutcliffe wrote in 1966, condensation nuclei do not receive much attention in the meteorology textbook I have read.  Maybe the problem is that he and I have not read the ‘right’ textbooks.   Nor do I know if he has read what R. C. Sutcliffe, a meteorologist wrote in his book—Weather and Climate­­—page 46-49.  Which I quote since this 1966 book might also not be conveniently available to a reader.

Fundamentally, the problem is that of the changes of state of water substance, H₂O, between its vapour, liquid, and solid states, a field of classical physics in which some very firm answers can be given.  The production of visible cloud is the condensation from vapour to liquid or solid and we may as well begin at this stage.  We generally say that air can hold no more than a definite maximum amount of invisible gaseous water, more or less according as the temperature is high or low, but the statement is acceptable only with reservations.  In the first place, the presence of air—that is the unpolluted mixture of pure permanent gases—has little to do with the process.  It is the amount of vapour in the available space that matters, the number of molecules of H₂O per cubic centimetre, and the presence of the other gases is not directly relevant.  In this respect, it might be more correct to say that the space and not the air is more or less saturated with vapour, but in meteorology insistence on this distinction would be quite unnatural and confusing.  The air is always present, the vapour contributing rarely more the 1 per cent by weight and usually very much less than this; the vapour moves with the air, has the same temperature as the air and expands or contracts with the air.  For most purposes it is helpful to think of the vapour as being in the air and quite unambiguous to say the air is dry or moist, has a low relative humidity or is saturated.  However, in considering the physics of phase change the presence of air is not always relevant.

When liquid water and gaseous vapour are present side by side one needs only to think of the exchange of molecules across the interface to have a clear mental image of evaporation and condensation going on continuously.  The molecules in the liquid are in incessant motion and a small proportion, moving more rapidly than the average, escape from the liquid surface by overcoming the inter-molecular attractive force which binds the liquid together; in much the same way a rocket, given sufficient speed, will escape from the earth’s gravitation force.  The warmer the liquid the greater the speed of the molecules and the greater the number which have the necessary escape velocity—the warmer the water the more rapid the evaporation.  At the same time, any molecules from the vapour which penetrate the liquid surface are captured and condensation takes place, at a rate which depends upon the vapour temperature and density—or the vapour pressure.  The net effect of the two processes going on continuously is either condensation or evaporation and there is a state of balance when escape and capture are at the same rate:  in this case, the air is just saturated with respect to the liquid surface.

It has been necessary to labour over this image of the processes in terms of molecular movements in order to appreciate the difficulties which arise when the vapour exists in the atmosphere far removed from any liquid surface.  The air might be supersaturated, in the sense that if there were liquid present the vapour would quickly be captured by it, but in the absence of any liquid there is no obvious reason why condensation should ever begin and experiment proves that the argument is a valid one.  If air is carefully purified by filtering, it will not produce cloud droplets even if cooled by expansion far beyond its normal saturation point or dew point.  C. T. R. Wilson, working with his famous expansion cloud chamber, was able to show this quite conclusively late in the last century.  His method of purifying the air was to allow the droplets produced during cloud formation to settle out of the chamber and to repeat the process several times with the same sampler of air.  Ultimately four-fold supersaturations, that is humidities of 400 per cent, were necessary to produce condensation in the purified air.

These results, obtained first by Wilson and broadly confirmed by many later experimenters, have a very important bearing on natural meteorology, not because supersaturation occurs in the atmosphere but because it does not occur:  why is it that in the atmosphere condensation to clouds invariably happens as soon as normal saturation is reached?  The answer is that the natural atmosphere, however clean it may appear to be, is always supplied with a sufficient number of minute particles of salts, acids, or other substances which serve just as well as liquid water in capturing water molecules from the vapour.  These are the ‘nuclei of condensation’, and are effective as soon as the air becomes even slightly supersaturated.  As a matter of fact, there are many observations of clouds in air whose relative humidity is considerably below 100 per cent, evidence of nuclei which are hygroscopic, but methods of measurement within natural cloud are not sufficiently refined to prove that even slight supersaturation ever occurs.  If for practical purposes we assume that cloud will always form in the atmosphere when ordinary saturation is attained (that is relative to a flat surface of pure water), we shall not go far wrong.  Microscopic counting shows that the droplets forming in an ordinary cloud are measured in hundreds or even thousands to the cubic centimetre, millions to the litre, numbers which may strike one as incredibly large until we become familiar with the minuteness of the particles with which cloud physics has to deal.  We shall need to return to these problems of nuclei and droplets when the process of raindrop formation is considered, but mean while we may note that although the nuclei are extremely numerous they are generally quite invisible and utterly negligible as a contribution to the weight of the air, which can still be treated as a ‘perfect gas’ in most meteorological calculations.

When the air contains exceptionally large amounts of dust or smoke products it is noticeably hazy but the cleanest of air on days of excellent visibility is yet well laden with the finer nuclei of condensation.  Cloud droplets measuring on average say 10µ* (*µ=micron, 0.01 millimetre) in diameter and occurring in numbers of 1000 per cubic centimetre are spaced at about I millimeter apart and less than 1-millionth of the whole volume consists of water.  But such an aggregate is quite different from the aggregate of nuclei and is very much a visible cloud.  A thickness of about 100 metres will suffice for almost every ray of light entering the cloud to strike a droplet many times and be absorbed, reflected, or refracted, so casting a strong shadow in sunlight and destroying the definition of any object looked at through the cloud, that is producing bad visibility—indeed a technical ‘fog’ to an observer within the cloud.

Given this ‘knowledge’ of Sutcliffe that the earth’s natural atmosphere is always composed of oxygen and nitrogen molecules, water molecules, and condensation nuclei, which allow water molecules (vapor) to condense on their surface to form (grow into) larger droplets or ice particles so that water vapor supersaturation never occurs, it seems a puzzle that McGinn does not recognize his ‘collected groups’ of water molecules are actually condensation nuclei which have long be accepted as a necessary component of the natural atmosphere.  However, despite what Sutcliffe wrote in 1966, condensation nuclei do not receive much attention in the meteorology textbook I have read.  Maybe the problem is that he and I have not read the ‘right’ textbooks.

Michell Sienko and Robert Plane in their textbook, Chemistry: Principles and Properties (1966), included five pages (192-196) about colloids and their properties.

There are systems which are neither obviously homogeneous nor obviously heterogeneous.  …   Between coarse suspensions and true solutions there is a region of change from heterogeneity to homogeneity.  In this region dispersed particles are so small that they do not form an obviously separate phase, but they are not so small that they can be said to be in true solution.  This state of subdivision is called the colloidal state.  On standing, the particles of a colloid do not separate out at any appreciable rate; they cannot be seen under a microscope; nor can they be separated by filtration.  The dividing lines between colloids and solutions and between colloids are not rigorously fixed, since a continuous gradation of particle size is possible.  Usually, however, colloids are defined as a separate class on the basis of size.  When the particle size lies between about 10^-7 and 10^-4 cm, the dispersion is called a colloid, a colloidal suspension, or a colloidal solution.

Colloids are frequently classified on the basis of the states of aggregation of the component phases … The more important classifications are sols, emulsions, gels, and aerosols. …  An aerosol is a colloid made by dispersing either a solid or a liquid in a gas.  The former is called a smoke and the latter a fog.

When a beam of light is passed through a solution or a pure liquid, the path of the beam is not visible from the side.  The dissolved particles are too small to scatter much light.  In a colloid the particles are big enough to scatter the light.  Therefore, when a beam of light is turned on a colloid, an observer to one side can see the path of the beam.  This effect, called the Tyndall effect, can be produced readily by turning a column of light on an aqueous solution of sodium thiosulfate, Na₂S₂O₃, and adding a few drops of dilute acid.  The ensuing chemical reaction produces elemental sulfur.  The light beam is invisible until the sulfur particles aggregate to colloidal dimensions. 

For years, if not a decade or two, I have been aware of a scattering theory, by which clouds scattered light, which Richard Feynman explained to his physics class at Caltech. (The Feynman Lectures on Physics (1963), Vol I, pp 32-8,32-9)  I have found no one who has directly referred to what he taught.  Which does not imply that no one has.

Feynman, in explaining the phenomenon of light (radiation) scattering by cloud droplets, never identifies what observed scattering he is explaining.  However, after explaining his theory, Feynman began to summarize:

That is to say, the scattering of water in lumps of N molecules each is N times more intense than the scattering of the single atoms.  So as the water agglomerates the scattering increases.  Does it increase as infinitum?  No!  When does this analysis being to fail?  How many atoms can we put together before we cannot drive this argument any further?  Answer:  If the water drop gets so big that from one end to the other is a wavelength or so, then the atoms are no longer in phase because they are too far apart.  So as we keep increasing the size of the droplets we get more and more scattering, until such a time that a drop get about the size of a wavelength, and then the scattering does not increase anywhere nearly as rapidly as the drop gets bigger.  Furthermore, the blue disappears, because for long wavelengths the drops can be bigger, before this limit is reached, than they can be for short wavelengths.  Although the short waves scatter more per atom than the long waves, there is a bigger enhancement for the red end of the spectrum than for the blue end when all the drops are bigger than the wavelength, so the color is shifted from the blue toward the red.

Now we can make an experiment that demonstrates this.  We can make particles that are very small at first, and then gradually grow in size.  We use a solution of sodium thiosulfate (hypo) with sulfuric acids, which precipitates very fine grains of sulphur.  As the sulphur precipitates, the grains first start very small, and the scattering is a little bluish.  As it precipitates more it gets more intense, and then it will get whitish as the particles get bigger.

Hence, there can be no doubt that Feynman, during the academic year 1961-62, had explained to his students the long observed Tyndall Effect, or Tyndall Scattering, reviewed by Sienko and Plane.

A greater puzzle than why McGinn, and others, seem not to recognize that he, in his commonly rejected understanding, is referring to condensation nuclei, is:  Why is not Feynman’s explanation of Tyndall scattering more commonly recognized, understood, and applied to better understand the interaction of radiation (all) with condensation nuclei and cloud droplets (particles)?  We must ponder as Galileo pondered.  But maybe first we need to read as Galileo read.

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