Malus gave the name polarisation to the change which the light underwent in the process of reflection. Later, the expression plane of polarisation was used to designate the plane of reflection, that is to say, the plane containing the incident ray and the normal to the reflecting surface.
Malus' discoveries in connection with polarised light were not limited to this. It had long been known that a ray of direct light was always separated into two beams of white light, of equal intensity, in its passage through a rhomboid of calcium carbonate. Thus the flame of a taper viewed through such a rhomboid is always double, and the two images are equally bright.
Huygens and Newton had already noticed that light, after its passage through a crystal of Iceland spar, no longer behaves like direct light. Thus, when we study one or other of the images of the taper, just mentioned, through a second rhomboid, we observe (1) that there is not always bifurcation of the ray; (2) that when bifurcation does take place, the two new images have not the same intensity. So that the light which has traversed a doubly refracting crystal is different from ordinary or direct light. Assuming this, Malus showed that the change produced in light by double refraction was identical with that arising during reflection from the surfaces of opaque or transparent bodies; in other words, that the two rays, ordinary and extraordinary, given by doubly refracting crystals, were polarised rays.
From the first Malus established these fertile discoveries so clearly, using so much care and precision, both as regards fact and expression, that one would think in reading them that his memoirs had been written yesterday. But he was prevented from continuing his work, having been cut off prematurely in 1812, at the age of 37. Happily for science, two celebrated physicists, Biot and Arago, at that time young and full of activity, took up the legacy he had bequeathed, and speedily distinguished themselves by brilliant discoveries in the new path opened to science by Malus.
In 1811, Arago noticed that, when a ray of polarised light is analysed by a rhomboid of Iceland spar, after it has traversed, normally to the surface, a section of rock crystal cut perpendicularly to the axis, it always gives two images in all positions of the rhomboid; and, further, that these are coloured in complementary tints. When the thickness of the spar does not suffice for complete separation of the rays the image is white where they are superposed.
This experiment showed a two-fold anomaly in regard to the ordinary laws of doubly refracting crystals. All other uniaxial crystals, cut normally to the axis, would have given two white, instead of two coloured images, and in two positions of the analysing rhomboid, separated by an angle of 90°, the two images would have been reduced to one.
Arago's conclusion was that the results of the above experiment are precisely those which should follow if it be assumed that the two differently coloured rays from the incident beam of white light are polarised in different planes on leaving the plate of quartz.
Arago did not continue the study of these striking phenomena, and Biot, from 1813 onward, enunciated the physical laws governing them, carefully isolating them from all those with which they seemed to have been confused by Arago.
Biot produced the polarised ray with light from each of the parts of the simple spectrum separately, and found that the original plane of polarisation was deviated through an angle proportional to the thickness of the plate; that this angle was different for each of the primary colours and increased with the refrangibility according to a fixed law. He also made the exceedingly curious observation that of plates obtained from different crystals of quartz, some deviated the plane of polarisation to the right and others to the left, in each case according to the same laws.
But Biot's most remarkable discovery in connection with this kind of phenomena is undoubtedly that of the deviation of the plane of polarisation produced by a number of natural organic products, such as oil of turpentine, solutions of sugar, of camphor, and of tartaric acid. The first mention of this fact occurs in the bulletin of the Société Philomatique for December 1815.
To understand this Lecture it is essential particularly to recollect the existence of this rotative property in tartaric acid, and its absence in paratartaric or racemic acid, an acid isomeric with tartaric acid.
There exist, therefore, organic products which, when themselves liquid, or when dissolved in water, possess the rotative property, and resemble in this respect solid crystallised quartz. But it must be noted here that the analogy with quartz is superficial only. The deviation of the plane of polarisation is common to both, but the character of the phenomenon is quite different.
Thus quartz deviates; but it must be crystallised. Dissolved, or solid and not crystallised, it lacks the property. Not only must it be crystallised, but it must be cut in plates perpendicular to the axis. As soon as the plate is slightly inclined to the direction of the ray, the effect is diminished and finally disappears.
Sugar deviates (and what is said of sugar is true of all the other organic products), but the sugar must be dissolved, or solid and amorphous as in barley-sugar. In the crystallised state it was impossible to discover any effect.
The tube containing the solution of sugar may be inclined. The deviation does not alter for equal thicknesses. And, what is more, active agitation of the liquid by means of clock-work leaves the phenomenon the same.
So that, from the first, Biot quite definitely concluded that the action produced by the organic bodies was a molecular one, peculiar to the ultimate particles and depending on their individual constitution. In quartz the phenomenon is a consequence of the mode of aggregation of the crystalline particles.
These are the physical precedents, if I may so express myself, for the researches which I am about to lay before you. We must next consider their mineralogical precedents.
Let us imagine a right prism with rhombic base. The eight basal edges are identical edges. If one is truncated, the other seven must be truncated, and in the same manner. The four vertical edges are of another kind. In general, they will not be truncated at the same time with the basal ones, and if they are it will be differently.
These examples will suffice to make clear the law of symmetry and its application.
Nothing is simpler than to have a precise conception of hemihedry. It has long been known--in fact Haüy was acquainted with the most noted examples--that in a crystal sometimes only the half of the identical parts are modified simultaneously, and in the same manner. In such cases hemihedry is said to exist. Thus the cube ought to have its eight solid angles all truncated at once. But in certain cases this only occurs to four of them. Boracite furnishes an example of this nature. In these circumstances the modification takes place in such a way that, if the four truncations are produced so as to obliterate the faces of the cube, a regular tetrahedron is obtained. If the modification were applied to the four remaining angles, it would give rise to another regular tetrahedron, identical with and superposable on the first, and differing from it only by its position on the cube.
In the same way let us again consider our right prism truncated on the eight basal edges. In certain species the truncation takes place on one half only of the edges, and here again the result is that, as the truncations occur on the opposite edges of each base, and alternately at the two extremities, these truncations, if produced, give rise to a tetrahedron. As in the case of the cube, two tetrahedra are possible, differently placed with reference to the prism, according as one or other of the sets of four truncations is preserved; but here the two tetrahedra are not absolutely identical. They are symmetrical tetrahedra. They cannot be superposed.
These notions will be sufficient to enable us to understand what hemihedry is, and what is understood by hemihedral faces or forms.
Now quartz, of which we were speaking a short time ago, is one of the few minerals in which Haüy discovered hemihedral faces. Everybody knows the ordinary form of this mineral, a regular hexagonal prism terminated by two six-faced pyramids. It is evident that the trihedral angles situated at the base of the pyramidal faces are identical, and, therefore, if one of these bears a face, all the others should exhibit the same modification. This is the case with the so-called rhomb-face of the mineralogists.
But Haüy was the first to observe, in certain specimens, a face very different from these, which he designated by the letter x, inclined more towards one side than the other, without being double, as the law of symmetry would require in this case. Another strange peculiarity of these crystals did not escape crystallographers, namely, that this face x was inclined sometimes in one sense, sometimes in the other. Haüy, who liked to give suitable names to each variety of a species called the variety of quartz bearing the face x plagihedral. The crystals in which the face x was inclined to the right, when the crystal was oriented in a given manner, were called right plagihedra; those in which x was inclined in the opposite sense, left plagihedra.
Nothing, however, is more variable than this character. Here it exists, there it is absent. On one and the same crystal there are angles bearing the face x, others which ought to bear it are without it. Sometimes both right and left plagihedral faces are found. Nevertheless, all who were conversant with crystals agreed in admitting that there was in a quartz a true hemihedry in two opposite senses.
We should notice here a very ingenious association of ideas, due to Sir John Herschel, which was communicated to the Royal Society of London in 1820.
I have already said that Biot made the remarkable observation, that among different specimens of quartz some deviated the plane of polarized light in one sense, and the others in the opposite sense, to the right and to the left respectively. This being established, Herschel connected Haüy's crystallographic discovery with Biot's physical one. Experiment confirmed the idea of an actual relation between right and left plagihedra and the right and left senses of the optical deviations. Specimens of quartz bearing the face x in the same sense, all deviate the plane of polarized light in one sense.
Such is the statement of the principal facts antecedent to the researches of which I am about to give you a short account.
This peculiarity in the forms of the tartrates was not very obvious. This will be readily conceived, seeing that it had not been observed before. But when, in a species, its presence was doubtful, I always succeeded in making it manifest by repeating the crystallization and slightly modifying the conditions. Sometimes the crystals bore all the faces demanded by the law of symmetry, but the hemihedry was still betrayed by an unequal development of one half of the faces. This is seen, for example, in tartar emetic. It must be admitted that a circumstance which adds greatly to the difficulty in recognising hemihedry is the frequent irregularities of the crystals, which never develop quite freely. From this cause there arise deformations, arrestments of development in one direction or another, faces suppressed by accident, etc. Unless in circumstances of an almost exceptional character, the recognition of hemihedry, particularly in laboratory crystals, demands very attentive study. To this we must add the fact that, although hemihedry may be possible in a given form, and although it is a function of the internal structure of the substance, it may not be indicated externally, any more than one finds on every crystal of a cubic species all the forms compatible with the cube.
But however these things may be, I repeat that I found the tartrates hemihedral.
This observation would probably have remained sterile without the following one.
Let a, b, c, be the parameters of the crystal form of any tartrate, and α, β, γ, the angles of the crystallographic axes. The latter are ordinarily perpendicular, or slightly oblique. In addition, the ratio of two parameters, such as a and b, is almost the same in the various tartrates, whatever may be their composition, their quantity of water of crystallisation, or the nature of the bases; c alone shows sensible variations. There is a kind of semi-isomorphism among all the tartrates. One would imagine that the tartaric group dominated and stamped with similarity the forms of all the various substances in spite of the difference in the other constituent elements.
The results of this are, a resemblance in the forms of all tartrates, and the possibility of parallel orientation, taking, for example, as basis of orientation the position of the axes a and b.
Now if we compare the disposition of the hemihedral faces on all the prisms of the primitive forms of the tartrates, when they are oriented in the same manner, this disposition is found to be the same.
These results, which have been the foundation of all my later work, may be summed up in two words: the tartrates are hemihedral, and that in the same sense.
Guided then on the one hand by the fact of the existence of molecular rotatory polarization, discovered by Biot in tartaric acid and all its compounds, and on the other by Herschel's ingenious correlation, and yet again by the sagacious views of M. Delafosse, with whom hemihedry has always been a law of structure and not an accident of crystallization, I believed that there might be a relation between the hemihedry of the tartrates and their property of deviating the plane of polarized light.
It is important thoroughly to grasp the development of the conceptions: Haüy and Weiss observe that quartz possesses hemihedral faces and that these faces incline to the right on some specimens and to the left on others. Biot on his part finds that quartz crystals likewise separate themselves into two sets, in relation to their optical properties, the one set deviating the plane of polarized light to the right, the other to the left, according to the same laws. Herschel in his turn supplies to these hitherto isolated facts the bond of union, and says--plagihedra of one kind deviate in the same sense; plagihedra of the other kind deviate in the opposite sense.
For my own part I find that all tartrates are plagihedral, if I may so express myself, and that in the same sense; so that I might presume that here, as in the case of quartz, there was a relation between the hemihedry and the circular polarization. At the same time the essential differences to which I have just referred between circular polarization in quartz and in tartaric acid must not be neglected.
Thanks to the above discoveries, and to the relations which I have just enumerated, we are now in possession of a preconceived notion (for it is still nothing more than that) as to the possible inter-relation of the hemihedry and the rotative power of the tartrates.
Being very anxious to find by experiment some support for this still purely speculative view, my first thought was to see whether the very numerous crystallisable organic products which possess the molecular rotative property, have hemihedral crystalline forms, an idea which had not previously occurred to any one in spite of Herschel's correlation. This investigation met with the success which I anticipated.
I also occupied myself with the examination of the crystalline forms of paratartaric acid and its salts. These substances are isomeric with the tartaric compounds, but had all been found by Biot to be inactive towards polarized light. None of them exhibited hemihedry.
Thus the idea of the inter-relation of the hemihedry and the molecular rotatory power of natural organic products gained ground.
I was soon enabled to establish it clearly by a wholly unexpected discovery.
"The double paratartrate and the double tartrate of soda and ammonia have the same chemical composition, the same crystalline form with the same angles, the same specific weight, the same double refraction, and consequently the same inclination in their optical axes. When dissolved in water their refraction is the same. But the dissolved tartrate deviates the plane of polarisation, while the paratartrate is indifferent, as has been found by M. Biot for the whole series of those two kinds of salts. Yet," adds Mitscherlich, "here the nature and number of the atoms, their arrangement and distances, are the same in the two substances compared."
This note of Mitscherlich's attracted my attention forcibly at the time of its publication. I was then a pupil in the École Normale, reflecting in my leisure moments on these elegant investigations of the molecular constitution of substances, and having reached, as I thought at least, a thorough comprehension of the principles generally accepted by physicists and chemists. The above note disturbed all my ideas. What precision in every detail! Did two substances exist which had been more fully studied and more carefully compared as regards their properties? But how, in the existing conditions of the science, could one conceive of two substances so closely alike without being identical? Mitscherlich himself tells us what was, to his mind, the consequence of this similarity:
The nature, the number, the arrangement, and the distance of the atoms are the same. If this is the case what becomes the definition of chemical species, so rigorous, so remarkable for the time at which it appeared, given by Chevreul in 1823? In compound bodies a species is a collection of individuals identical in the nature, the proportion, and the arrangement of their elements.
In short, Mitscherlich's note remained in my mind as a difficulty of the first order in our mode of regarding material substances.
You will now understand why, being preoccupied, for the reasons already given, with a possible relation between the hemihedry of the tartrates and their rotative property, Mitscherlich's note of 1844 should recur to my memory. I thought at once that Mitscherlich was mistaken on one point. He had not observed that his double tartrate was hemihedral while his paratartrate was not. If this is so, the results in his note are no longer extraordinary; and further, I should have, in this, the best test of my preconceived idea as to the inter-relation of hemihedry and the rotatory phenomenon.
I hastened therefore to re-investigate the crystalline form of Mitscherlich's two salts. I found, as a matter of fact, that the tartrate was hemihedral, like all the other tartrates which I had previously studied, but, strange to say, the paratartrate was hemihedral also. Only, the hemihedral faces which in the tartrate were all turned the same way, were, in the paratartrate inclined sometimes to the right and sometimes to the left. In spite of the unexpected character of this result, I continued to follow up my idea. I carefully separated the crystals which were hemihedral to the right from those hemihedral to the left, and examined their solutions separately in the polarising apparatus. I then saw with no less surprise than pleasure that the crystals hemihedral to the right deviated the plane of polarisation to the right, and that those hemihedral to the left deviated it to the left; and when I took an equal weight of each of the two kinds of crystals, the mixed solution was indifferent towards the light in consequence of the neutralisation of the two equal and opposite individual deviations.
Thus, I start with paratartaric acid; I obtain in the usual way the double paratartate of soda and ammonia; and the solution of this deposits, after some days, crystals all possessing exactly the same angles and the same aspect. To such a degree is this the case that Mitscherlich, the celebrated crystallographer, in spite of the most minute and severe study possible, was not able to recognise the smallest difference. And yet the molecular arrangement in one set is entirely different from that in the other. The rotatory power proves this, as does also the mode of asymmetry of the crystals. The two kinds of crystals are isomorphous, and isomorphous with the corresponding tartrate. But the isomorphism presents itself with a hitherto unobserved peculiarity; it is the isomorphism of an asymmetric crystal with its mirror image. This comparison expresses the fact very exactly. Indeed, if, in a crystal of each kind, I imagine the hemihedral facets produced till they meet, I obtain two symmetrical tetrahedra, inverse, and which cannot be superposed, in spite of the perfect identity of all their respective parts. From this I was justified in concluding that, by the crystallisation of the double paratartrate of soda and ammonia, I had separated two symmetrically isomorphous atomic groups, which are intimately united in paratartaric acid. Nothing is easier than to show that these two species of crystals represent two distinct salts from which two different acids can be extracted.
Using the treatment always employed in such cases, the purpose is served by precipitating each salt with a salt of lead or baryta, and then isolating the acids by means of sulphuric acid.
The study of these acids is of immense interest. I do not know any that is more interesting.
But before enlarging on it allow me to introduce here some recollections in connection with their discovery.
"My dear child, I have loved science so much throughout my life that this makes my heart throb."
You will pardon me, gentlemen, these personal recollections which have never been effaced from my mind. In our day, and with our habits, they would offend in a scientific memoir, but they have seemed to me not out of place in an oral account; and perhaps the biographical interest of such recollections will constitute one of the advantages of the kind of instruction which the Société Chimique of Paris inaugurates to-day.
Indeed there is more here than personal reminiscences. In Biot's case the emotion of the scientific man was mingled with the personal pleasure of seeing his conjectures realised. For more than thirty years Biot had striven in vain to induce chemists to share his conviction that the study of rotatory polarisation offered one of the surest means of gaining a knowledge of the molecular constitution of substances.
One of them, that which comes from crystals of the double salt hemihedral to the right, deviates to the right, and is identical with ordinary tartaric acid. The other deviates to the left, like the salt which furnishes it. The deviation of the plane of polarisation produced by these two acids is rigorously the same in absolute value. The right acid follows special laws in its deviation, which no other active substance had exhibited. The left acid exhibits them, in the opposite sense, in the most faithful manner, leaving no suspicion of the slightest difference.
That paratartaric acid is really the combination, equivalent for equivalent, of these two acids, is proved by the fact that, if somewhat concentrated solutions of equal weights of each of them are mixed, as I shall do before you, their combination takes place with disengagement of heat, and the liquid solidifies immediately on account of the abundant crystallisation of paratartaric acid, identical with the natural product.[1]
In accord with their chemical and crystallographic properties, all that can be done with one acid can be repeated with the other under the same conditions, and in each case we get identical, but not superposable products; products which resemble each other like the right and left hands. The same forms, the same faces, the same angles, hemihedry in both cases. The sole dissimilarity is in the inclination to right or left of the hemihedral facets and in the sense of the rotatory power.
Now recall the definition of a chemical species which I gave a few minutes ago:-- the aggregate of individuals identical in the nature, the proportion, and the arrangement of the elements. All the properties of substances are the same. The arrangement alone differs. The great interest of isomerism has been to introduce into the science the principle that substances may be, and are, essentially different solely because the arrangement of the atoms is not the same in their chemical molecules.
But no isomeric bodies existed whose relations in respect to molecular arrangement could be known. This desideratum was supplied for the first time by the discovery of the constitution of paratartaric acid, and of the constitutional relations of the right and left tartaric acids. We know, on the one hand, that the molecular structures of the two tartaric acids are asymmetric, and on the other, that they are rigorously the same, with the sole difference of showing asymmetry in the opposite senses. Are the atoms of the right acid grouped on the spirals of a dextrogyrate helix, or placed at the summits of an irregular tetrahedron, or disposed according to some particular asymmetric grouping or other? We cannot answer these questions. But it cannot be a subject of doubt that there exists an arrangement of the atoms in an asymmetric order, having a non-superposable image. It is not less certain that the atoms of the left acid realise precisely the asymmetric grouping which is the inverse of this. Lastly, we know that paratartaric acid results from the juxtaposition of these two inversely asymmetric atomic groupings.
Henceforth the observation of the chemical and physical resemblances and differences, corresponding to these arrangements whose relations are known to us, offers especial interest, and gives solid foundations to molecular mechanics. It enables us to establish the connection of the physical and chemical properties, with the molecular arrangement which determines their very existence, or conversely it enables us to pass from the properties to their primary cause.
A résumé of these general relations between the properties and corresponding atomic arrangements may be given as follows:--
(1.) When the elementary atoms of organic products are grouped asymmetrically, the crystalline form of the substance manifests the molecular asymmetry in nonsuperposable hemihedry.
The cause of hemihedry is thus recognised.
(2.) The existence of this same molecular asymmetry betrays itself, in addition, by the optical rotative property.
The causes of rotatory polarisation is likewise determined.[2]
(3.) When the non-superposable molecular asymmetry is realised in opposite senses, as happens in the right and left tartaric acids and all their derivatives, the chemical properties of these identical and inverse substances are rigorously the same. From this it follows that this mode of contrast, and of similarity, does not alter the ordinary play of chemical affinities.
I am in error: there is a restriction to make on this last point, an important and eminently instructive restriction. Time does not permit me to develop it deliberately and suitably to-day. It will find a place in the next lecture.[3]
[2]Fresnel, with one of those flashes of genius, of which he had so many, had a sort of presentiment of this cause of rotatory polarisation.
He expresses himself thus, in one of his memoirs, in vol. xxviii. of the Annales de chimie et de physique, 1825:-- "Rock crystal shows optical phenomena which cannot be reconciled with complete parallelism of the molecular lines, and which would seem to indicate a progressive and regular deviation of these lines in the passage from one layer of the medium to the next."
[3]The restriction that Pasteur discusses in the next lecture has to do with the interactions of asymmetric substances with other asymmetric substances. The right and left forms of tartaric acid interact identically with substances which possess no asymmetry (such as potassium), but differences arise when they interact with other asymmetric substances (such as quinine). --CJG
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