The Different States of Matter

In the true aspect of the structure of matter the limits must be drawn in an entirely different way.

The fundamental distinction is between the two lines of the following scheme of ’ equations':

molecule == solid == crystal. gas == liquid == amorphous.

We must explain these statements briefly. The so-called amorphous solids are either not really amorphous or not really solid. In ‘amorphous’ charcoal fibre the rudimentary structure of the graphite crystal has been disclosed by X-rays. So charcoal is a solid, but also crystalline.

Where we find no crystalline structure we have to regard the thing as a liquid with very high ‘viscosity’ (internal friction). Such a substance discloses by the absence of a well-defined melting temperature and of a latent heat of melting that it is not a true solid. When heated it softens gradually and eventually liquefies without discontinuity.

I remember that at the end of the first Great War we were given in Vienna an asphalt-like substance as a substitute for coffee. It was so hard that one had to use a chisel or a hatchet to break the little brick into pieces, when it would show a smooth, shell-like cleavage. Yet, given time, it would behave as a liquid, closely packing the lower part of a vessel in which you were unwise enough to leave it for a couple of days.

The continuity of the gaseous and liquid state is a well-known story. You can liquefy any gas without discontinuity

by taking your way ‘around’ the so-called critical point. But we shall not enter on this here.

The Distinction That Really Matters

We have thus justified everything in the above scheme, except the main point, namely, that we wish a molecule to be regarded as a solid == crystal.

The reason for this is that the atoms forming a molecule, whether there be few or many of them, are united by forces of exactly the same nature as the numerous atoms which build up a true solid, a crystal. The molecule presents the same solidity of structure as a crystal. Remember that it is precisely this solidity on which vve draw to account for the permanence of the gene!

The distinction that is really important in the structure of matter is whether atoms are bound together by those ‘solidify- ing’ Heitler-London forces or whether they are not. In a solid and in a molecule they all are. In a gas of single atoms (as e.g. mercury vapour) they are not. In a gas composed of mole- cules, only the atoms within every molecule are linked in this way.

The Aperiodic Solid

A small molecule might be called ’the germ of a solid’.

Starting from such a small solid germ, there seem to be two different ways of building up larger and larger associations.

One is the comparatively dull way of repeating the same structure in three directions again and again. That is the way followed in a growing crystal.

Once the periodicity is estab- lished, there is no definite limit to the size of the aggregate.

The other way is that of building up a more and more extended aggregate without the dull device of repetition.

That is the case of the more and more complicated organic molecule in which every atom, and every group of atoms, plays an individual role, not entirely equivalent to that of many others (as is the case in a periodic structure).

I call that an aperiodic crystal or solid.

I believe a gene - or the whole chromosome fibre I - is an aperiodic solid.

The Variety Of Contents Compressed In The Miniature Code

How can this tiny speck of material, the nucleus of the fertilized egg, contain an elaborate code-script involving all the future development of the organism?

A well-ordered association of atoms, endowed with sufficient resistivity to keep its order permanently, appears to be the only conceivable material structure that offers a variety of possible (‘isomeric’) arrangements, sufficiently large to embody a complicated system of ‘determinations’ within a small spatial boundary.

The number of atoms in such a structure need not be very large to produce an almost unlimited number of possible arrangements. For illustration, think of the Morse code.

The 2 different signs of dot and dash in well-ordered groups of not more than four allow of thirty different specifications.

If you allowed yourself the use of a third sign, in addition to dot and dash, and used groups of not more than ten, you could form 88,S 72 different ’letters’; with five signs and groups up to 25, the number is 372,529,029,846, 19 1,4°5.

It may be objected that the simile is deficient, because our Morse signs may have different composition (e.g ..- - and .. -) and thus they are a bad analogue for isomerism.

To remedy this defect, let us pick, from the third example, only the combinations of exactly 25 symbols and only those containing exactly S out of each of the supposed S types (S dots, S dashes, etc.).

A rough count gives you the number of combinations as 62,33°,000,000,000, where the zeros on the right stand for figures which I have not taken the trouble to compute.

In the actual case, by no means ’every’ arrange- ment of the group of atoms will represent a possible molecule; moreover, it is not a question of a code to be adopted arbitrarily, for the code-script must itself be the operative factor bringing about the development.

But, on the other hand, the number chosen in the example (25) is still very small, and we have envisaged only the simple arrangements in one line.

What we wish to illustrate is simply that with the molecular picture of the gene it is no longer inconceivable that the miniature code should precisely correspond with a highly complicated and specified plan of development and should somehow contain the means to put it into operation.

Comparison With Facts: Degree Of Stability; Discontinuity Of Mutations

Can my theory really account for the high degree of permanence we observe?

Are threshold values of the required amount - high multiples of the average heat energy kT - reasonable, are they within the range known from ordinary chemistry?

The answer is yes.

The molecules of any substance which the chemist is able to isolate at a given temperature must at that temperature have a lifetime of at least minutes.

(That is putting it mildly; as a rule they have much more.)

Thus the threshold values the chemist encounters are of necessity precisely of the order of magnitude required to account for practically any degree of permanence the biologist may encounter;

Thresholds varying within a range of about 1:2 will account for lifetimes ranging from a fraction of a second to tens of thousands of years.

But let me mention figures, for future reference. The ratios W/kT mentioned by way of example on p. 5 I, viz.

W = 30 , 50, 60, kT

producing lifetimes of

los., 16 months, 30,000 years,

respectively, correspond at room temperature with threshold values of

o·g, I ·5, 1·8 electron-volts.

The ’electron-volt’ unit can be visualized.

For example, the third number (I ·8) means that an electron, accelerated by a voltage of about 2 volts, would have acquired just sufficient energy to effect the transition by impact.

For comparison, the battery of an ordinary pocket flash-light has 3 volts.

Thus, an isomeric change of configuration in some part of our molecule, produced by a chance fluctuation of the vibrational energy, can be a sufficiently rare event to be interpreted as a spontaneous mutation.

Thus we account, by the very principles of quantum mechanics, for the most amazing fact about mutations, the fact by which they first attracted de Vries’s attention, namely, that they are ‘jumping’ variations, no intermediate forms occurring.