A NEW PATTERN IN SCIENCE' P. LE CORBEILLER Haward University, Cambridge, Massachusetts
C m m s m are justly proud of their long tradition of scientific empiricism. I believe they should also he proud of having presented mankind with a new type of scientific knowledge. First let us illustrate the chemical tradition of empiricism. Here is how Lavoisier defines a chemical element :% If, by the term elements, we mean t o express those simple and indivisible atoms of which matter is composed, i t is extremely probable we know nothing a t all ahout them; but, if we apply the term elements, or principles of bodies, to express our idea of the last point which analysis is capable of reaching, we must admit as elements all the substances into which we are capable, by any means, to reduce bodies by decomposition. Not that we are entitled t o affirm that these substances we consider as simple may not be compounded of two, or even of a greater number of principles; but, since these principles cannot be separated, or rather since we have not hitherto discovered the means of separating them, they act with regard to us as simple substances, and we ought never to suppose them compounded until experiment and observation have proved them to be so.
your belief is justified. To simplify I shall use only two lines of argument: those of Mendeleev and Rutherford. Mendeleev first published his periodic table in 1869. He did not begin with arranging the elements in the order of increasing atomic weights, as is sometimes believed. He took a much broader view of the matter, for this is what he said? Among [the] measura.ble properties of the elements, or of their corresponding compounds, are: (a) isomorphism, or the analogy of erystdline forms; and, oonnected with it, the power to form crystdine mixtures which are isamorphous; (b) the relation of the volumes of analogous compounds of the elements; ( e ) the composition of their saline compounds; and (d) the relation of the atomic weiehts of the elements.. . We shall briefly consider tllese four wpertr of thr nlxtter, wl.ieh are ewecdingly important for a natural ~ n r lIruit/ul group in^^ of the & n e n t r , iarilitating, nor only a gencr~lacquaint.iuet. with rhcm, but also thrir d r t d r d study.
He then built up his table on the basis of these four properties. The table is made up of those famous This is the orthodox doctrine of scientific empiricism. eight columns and a t the bottom of these columns What we assert today fits the experiments which we are the formulas for the corresponding "higher saline have made so far; if tomorrow a new experimental oxides": %O for column I (alkali metals and Cu, Ag, fact contradicts today's theory, that theory will have Au), Ra02or RO for column I1 (alkaline earths and to go overboard. ' Zn, Cd, Hg), and so forth up to RO, for column VIIl For example, today we say that calcium follows (Fe, Co, Ni, etc.). On another line below we find potassium in the periodic table. According to the RH, in column IV (C, etc.), RH3, RE2, RH in columns empirical doctrine, if tomorrow we discovered a new V, VI, and VII. (These lines have disappeared from element among cyclotron products, having an atomic most periodic tables hanging in our classrooms.) Mendeweight greater than 39.096,but less than 40.08, we should leev's argument was this: Magnesium is in column give it its place between potassium and calcium. This I1 because it forms MgO. Aluminum is in column I11 is what a good empiricist would say. Is that what you because it forms AlzOs. A mathematician would have believe yourselves? no difficulty inserting many elements R, R', . . . Of course not. Your mind rebels a t the idea of between these two, forming the oxides RzoOn, R120022, something coming in between alkali metals and alkaline . . .let us say. But that is forbidden by property (b)! earths. You believe that the periodic table, although Mendeleev sums up the whole thing in these words: recent. is solid as granite. Let us examine whether "The absence of intermediate 'elements-for instance Bhscd upon an address presented a t the Thirteenth Summer between magnesium and aluminum. .is essentially Conference of the NEACT, University of Rhode Island, King- the most important part ,,fthe matter" (italics his).
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ston, Rhode Island, August 20,1951. 2 L~vorsrea,A., "Elements of Chemistry," Henry Regnery Co., Inc., Chicago, 1949, Part I, p. 12.
KNEDLER, 3. W., JR., Editor, "Masterworkn of Science," Doubleday and Co., Inc., New York, 1947, p. 539. 553
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Mendeleev's chemical instinct is apparently what prevented him from saying: between fluorine and sodium, because column 0, that of the inert gases, was not foreseen by Mendeleev. However, note that Mendeleev did not begin by ranging all the elements in one row of increasing atomic weights, and then claiming that such a row was complete. He built up columns of elements of similar chemical behavior, and then said that no new column could be inserted between these, because of Gay-Lussac, or Avogadro, or Cannizzaro, as you prefer.4 Because Mendeleev's views had thus a firm experimental basis, further experiment did not disprove what he actually said, (although it disproved what we sometimes make him say); and column 0 placed itself a t the left of column I, the line of the oxide formulas nolr reading: R (inert gases), R 2 0 (alkalies) . . . etc. Now let us turn to Rutherford's scattering experiments (1911). They do not merely support Mendeleev's table; they complete it by bringing in a concept which was entirely new in science, and this is the main point of the present paper. Rutherford bombarded a thin gold foil with alpha particles, found that these were scattered according to some empirical law, and from this law derived the positive electric charge of the gold nucleus which, he assumed, was responsible for the scattering. Next, repeating the experiment with thin foils of other metals, such as silver and platinum, he found the nuclear charges proportional to t,he atomic numbers of the elements. The atomic number Z is that entirely new type of scientific concept to which I wish to draw- your attention. At this stage of the argument it does not mean the number of electrons in the gold or silver atom. The hypothesis of Z electrons was on the contrary introduced shortly afterwards by Rutherford in order to make the atom neutral, while its nucleus carried a charge +Ze. Yo: the atomic number of an element was the rank of this element in the linear list of elements of increasing atomic weight, known at the time; thus, for calcium it was 20. No scient,ific, numerical law among the thousands of those discovered earlier than 1911 (with the notable exception of certain spectroscopic series) ever mentioned the rank of something considered as an element in a sequence. Xote that if such an empirical law were verified with an experimental error less than * 1 / 2 n it would mean that no new element differing from the already known first n elements could ever find place in the sequence. Rutherford's early measurements of the nuclear charge did not have the precision of bet,ter than 1 in 200 necessary to specify the rank of any chemical element in the periodic table. But many investigations during thenext 40 years, those with X-ray spectra in particular, have raised the precision much higher. For instance, Moseley's data (1913) placed themselves
* For an interesting discussion of this point, nee LEONARD K. NASH, "The Atomic-Molecular Theory," Harvard University Press, Cambridge, Mass., 1950.
JOURNAL OF CHEMICAL EDUCATION
on two straight lines, but he could make the kink disappear by assuming an element of rank Z = 43 (technetium, then unknown), thus raising by one unit the ranks of all elements from ruthenium onward^.^ Nothing could show more clearly that in the present list (not table) of chemical elements we now have an experimentally ordered and complete sequence (complete up to the latest known element, that is). The discovery of any new element, assigned a rank less than 98, would modify the atomic numbers of all the elements to the right of it, and thereby contradict numerical measurements undisputably recorded. Thus what we may call Lavoisier's "extreme" empirical attitude, according to which any chemical element A, today so called, could tomorrow be decomposed into two new elements B and C, an attitude entirely correct in its time and for 120 years later, has now become untenable--not because of any theory or a prion' argument, but as the outcome of numerical experiments of increasing precision. I t is the experimental method itself which after three and a half centuries of progress is presenting us with a statement of a type fundamentally new in science: a statement that tells us that we know for sure all the things of a certain kind that can exist; others, me say, cannot occur. There are other statements of the same type in the physical sciences. Consider crystals. From the different kinds of symmetry empirically observed in crystals, one can deduce that any specimen must belong to one of 32 crystal classes. This does not tell us why we observe these symmetries and no others, nor how many types of crystals belong to a given class. But in the 18901s,owing to the progress of the mathematical theory of groups, a completely satisfying result was obtained. Working from the single hypothesis that a crystal consists of a certain pattern periodically repeated in all possible directions, three mathematicians, using different methods, obtained the same result. There exist 230 types of periodic space patterns. They of course distribute themselves among the 32 previously known classes. Two things are particularly remarkable about this result. One is its completeness, the assurance we have that we know all the posszble types of crystalswhereas v e do not know yet how many chemical elements there may be. The other is the vast amount of information thus mathematically derived from the single, simple assumption: Crystals are periodic structures. This, which was once a hypothesis, is of course now experimentally established, since otherwise we could have no X-ray diffraction patterns. Two more examples of a similar character will show what I am getting at. First there is the case of isotopes Our assumption is that nuclei are made up exclusively of protons (mass 1, charge 1) and neutrons (mass 1, charge 0); this implies that the possible isotopes of a particular element constitute a sequence of equal steps, their nuclei being ~ a d up e of Z protons and a certain See 0. OLDENBERG, "Introduction to Atomic Physics," McGraw-Hill Rook Co., Inc., New York, 1949. p. 198
OCTOBER, 1951
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"action," was not popular wit,h physicists: although it. figured in analytical dynamics since the eighteenth century, and so had to be rediscovered by Planck and Einstein. A universe built of atoms, and one made of continuous matter, call for different ways of thinking. Essentially this is heeause the result of an enumeration must always be a whole number. For instance, Planck has remarked that if there are five apples lying on a table, the ratio of the sides of the table will depend upon the velocity of the observer with regard to the table. but the ohserver will always see 5 apples, never 4.90. even if he is trareling very fast. Similarly when wr determine the molecular weight of an element or of a previously analyzed compound by means of one of Raoult's laws me pay no attention to decimals. We decide for instance that the molecule of iodine is I?. because it could not be I,.#or I2.,,as the experiment may have indicated. This is quite in opposition to our respect for decimals in the measurement of a continuous physical quantity. A fundamental difference between an atomic universe and a continuous one is then that exact and complet,e knowledge of a certain limited field may be obtained in the atomic case, but not in the continuous one. This however should not be interpreted in the sense of s final or ahsolute knowledge. The distinction I mean is the following. We know for sure all of the first 9R chemical elements; this is based on a knowledge of the atom's electrons only; the knowledge of the nucleus. and hence of the isotopes, is a further problem whose solution cannot upset the previous enumeration of the electrons. The 32 rrystal clasees, forming a complete We InWt recognize an invisible hand which hold8 the balanro in the formation of compounds. A compound is a substance to set, xere known long before the 230 space groups which which Xature assigns fixed ratios, it is, in short, a heing which they contain were enumerated. Again, the sequence of Xature never create? other than balance in hand, pondere el spectroscopic lines defined by Balmer's formula correWIP77RIW0. sponds both to observation a t a low level of separation We find here what is typical of every atomic theory, and to an analysis which likens the single electron to a in xhatever field: a principle of exclusion. Proust's small revolving planet; more complicated formulas contention was by no means easy to prove, and his correspond to fine-structui.e lines, to the splitting of controversy with Berthollet. is clearly and entertainingly energy levels, and to the analysis of more complicated presented by both J. R. Partington and L. K. Xash. atomic models. Thus to the complete knowledge of Of course if 11-ebelieve in Dalton's atomic theory (1808), the properties of a simple model consisting of atoms 01. the Ian- of const,ant proportions, and that of multiple particles may later be added the study of another model of the same physical system, having a greater proportions as well, follow as simple corollaries. In the study of crystals, Abbe R. J. Haiiy discovered numher of parameters or degrees of freedom. But the in 1784 a law of simple ratios connecting the inter- fact that in an atomic world, our knowledge of a certain sect,ionsof a crystal face with the edges of an imagined subject, say crystal shapes or chemical properties of primitive crystal form. This is of course analogous to elements, can he complete on a certain level, is the new the chemical law of multiple proportions. Thus were scientific pattern to which I have wished to draw the integers: 1, 2: 3, etc., introduced in chemistry and attention. I t may well he that as a chemist the reader may not, crystallography. When integers appeared in Balmer's empirical law for the hydrogen spectrum, and then think this remark so novel. After all chemists have again in the Lyman and Paschen series, it was a settled been dealing with at,oms for more than 150 years. Yet conclusion that an atom of something or other would I don't remember the point being made in t,he many have to be brought in to account for this circumstance. presentations of the philosophy of science which have The quantity which turned out to be made of atoms, come out in recent years. I believe this is because physical science has dealt with continuous variables &PARTINGTON, J. R., "A Short History of Chemistry,'' Mac- from 1600 to 1900, and that many scientists are not yet lnillan and Co., London, 1948, p. 153. thoroughly at home in an atomic universe.
number of neutrons. Our knowledge of atomic nuclei is still very incomplete, but we are beginning to learn something of what combinations of numbers of protons and neutrons best fit together. A second example is that of the spectroscopic series. The confusion of lines in the spectrum of an element seemed for decades to defy rational description, and it was a great thrill to spectroscopists when Balmerin 1885 first gave his formula for the emission spectrum of hydrogen. I t is well known how Balmer's formula was added to by many other workers, such as Rydherg, Lyman, Paschen, and how we now interpret radiation laws of this type as being due to electrons falling from one energy level down to a lower one, the energies of the different possible levels forming one or several sequences. It should now be clear what the various laws me have considered have in common. The electronic shells of the chemical elements are built of discrete, identical electrons. A crystal consists of a definite structure repeated a t regular intervals. Atomic nuclei are built of identical protons and identical neutrons. The energy levels in Bohr's elementary theory are such that the angular momentum of the revolving electron increases by equal steps. Summing up, experience has led us to the conclusion that these four phenomena -and several others which could be mentioned-are atomic. The relevant physical variable does not vary continuously: it can only vary in jumps. The field of natural science where atomicity was first demonstrated is of course chemist,ry. The French chemist Proust recognized the law of constant proportions in 1707, and expressed himself as f o l l o ~ s : ~
