Then, with a simplicity of exposition in which one recognised the teacher who had always endeavoured to place his ideas within the range of his hearers, he said—
'If you picture to yourself all the bodies in nature—mineral, animal, or vegetable, and consider even the objects formed by the hands of man, you will see that they divide themselves into two great categories. The one has a plane of symmetry and the other has not. Take, for instance, a table, a chair, a playing die, or the human body; we can imagine a plane passing through these objects which divides each of them into two absolutely similar halves. Thus, a plane passing through the middle of the seat and of the back of an arm-chair would have, on its right and left, identical parts; in like manner a vertical plane passing through the middle of the forehead, nose, mouth, and chin of an individual, would have similar parts to the right and to the left. All these objects, and a multitude of similar ones, constitute our first category. They have, as mathematicians express it, one or several planes of symmetry.
'But, as regards the repetition of similar parts, it is far from being the case that all bodies are constituted in the manner here described. Consider, for example, your right hand: it is impossible to find for it a plane of symmetry. Whatever be the position of a plane which you imagine cutting the hand, you will never find on the right of this plane exactly the same as you find on its left. The same remark applies to your left hand, to your right ear and to your left ear, to your right eye and to your left eye; to your two arms, your two legs, and your two feet. The human body, taken as a whole, has a plane of symmetry, but none of the parts composing one or the other of its halves has such a plane. The stalk of a plant whose leaves are distributed spirally round its stem has not a plane of symmetry, nor has a spiral staircase such a plane; but a straight one has. You see this?
'It would have been truly extraordinary, would it not, if the various kinds of minerals, such as sea salt, alum, the diamond, rock crystal, and so many others which illustrate the great law of crystallisation, and which clothe themselves in geometric forms, should not present to us examples of the two categories of which we have just been speaking? They do so in fact. Thus a cube, which has the form of a player's die, has a plane of symmetry; it has indeed several planes. The form of the diamond, which is a regular octahedron, has also several planes of symmetry. It is thus also with the great majority of the mineral forms met with in nature or in the laboratory. They have generally one or several planes of symmetry. There are, however, exceptions. Rock crystal, which is found in prisms, often of large volume, in the fissures of certain primitive rocks, has no plane of symmetry. This crystal exhibits certain small facets, distributed in such a manner that in their totality they might be compared to a helix, or spiral, or screw, which are all objects not possessing a plane of symmetry.
'Every object which has a plane of symmetry, when placed before a looking-glass, has an image which is rigorously identical with the object itself. The image can be superposed upon the reality. Place a chair before a mirror; the image faithfully reproduces the chair. The mirror also reproduces the human body considered as a whole. But place before the mirror your right hand and you will see a left hand. The right hand is not superposable on the left, just as the glove of your right hand cannot be fitted to your left, and inversely.'
Then reverting to the beginnings of his studies in crystallography, Pasteur recounted to me briefly that, after having gone through the work of M. de la Provostaye, he perceived that a very interesting fact had escaped the notice of this skilful physicist. M. de la Provostaye had failed to observe that the crystalline forms of tartaric acid and of its compounds all belong to the group of objects which have not a plane of symmetry. Certain minute facets had escaped him. In other words, Pasteur discerned that the crystalline form of tartaric acid, placed before a mirror, produced an image which was not superposable upon the crystal itself. The same was found to be true of the forms of all the chemical compounds of this acid. On the other hand, he imagined that the crystalline form of paratartaric acid, and of all the compounds of this acid, would be found to form part of the group of natural objects which have a plane of symmetry.
Pasteur was transported with joy by this double result. He saw in it the possibility of reaching by experiment the explanation of the difficulty which the note of Mitscherlich had thrown down as a kind of challenge to science, when it signalised an optical difference between two chemical compounds affirmed to be otherwise rigorously identical. Pasteur reasoned thus:—Since I find tartaric acid and all its tartrates without a plane of symmetry, while its isomer, paratartaric acid, and its compounds have such a plane, I will hasten to prepare the tartrate and the paratartrate of the note of Mitscherlich. I will compare their forms, and in all probability the tartrate will be found dissymmetrical—that is to say, without a plane of symmetry—while the paratartrate will continue to have such a plane. Henceforward the absolute identity stated by Mitscherlich to exist between the forms of these two compounds will have no existence. It will be proved that he has erred, and his note will no longer have in it anything mysterious. As the optic action proper to the tartrates spoken of in his note manifests itself by a deviation of the plane of polarisation to the right, we have here a kind of dissymmetry which has nothing incompatible with the dissymmetry of form. On the contrary, these two dissymmetries can be referred to one and the same cause. In like manner, the absence of dissymmetry in the form of the paratartrate will be connected with the optical neutrality of that compound.
The fulfilment of Pasteur's hopes was only partial. The tartrates of soda and ammonia presented, as did all the other tartrates, the dissymmetry manifested by the absence of any plane of symmetry; that is to say, the crystals of this salt placed before a mirror produced an image which was not superposable upon the crystal. It was like a right hand having its left for an image. With regard to the paratartrates of soda and ammonia, one circumstance struck Pasteur in a quite unexpected manner. Far from establishing in the crystals of this salt the absence of all dissymmetry, he found that they all manifestly possessed it. But, strange to say, certain crystals possessed it in one sense and other crystals in a sense opposite. Some of these crystals, when placed before a mirror, produced the image of the others, and one of the two kinds of crystals corresponded rigorously in form with the tartrate prepared by means of the tartaric acid of the grape. Pasteur continued his reasoning thus:—Since there is no difference between the form of the tartrate derived from the tartaric acid of the grape and one of the two kinds of crystals deposited at the moment of crystallisation of the paratartrate, the simple observation of the dissymmetry proper to each will enable me to separate, by hand, all the crystals of the paratartrate which are identical with those of the tartrate. By ordinary chemical processes I ought to be able to extract a tartaric acid identical with that of the grape, possessing all its physical, mineralogical, and chemical properties—that is to say, a tartaric acid possessing, like the natural tartaric acid of the grape, dissymmetry of form, and exerting an action on polarised light. Per contra, I ought to be able to extract from the second sort of crystals, associated with the former in the paratartaric group, an acid which will reproduce ordinary tartaric acid, but possessing a dissymmetry of an inverse kind and exerting an action equally inverse on polarised light.
With a feverish ardour Pasteur hastened to make this double experiment. Imagine his joy when he saw his anticipations not only realised but realised with an exactitude truly mathematical. His delight was so great that he quitted the laboratory abruptly. Hardly had he gone out when he met the assistant of the physical professor. He embraced him, exclaiming, 'My dear Monsieur Bertrand, I have just made a great discovery! I have separated the double paratartrate of soda and ammonia into two salts of inverse dissymmetry, and exerting an inverse action on the plane of polarisation of light. I am so happy that a nervous tremulousness has taken possession of me, which prevents me from looking again through the polariscope. Let us go to the Luxembourg, and I will explain it all to you.'
These results excited in a high degree the attention of the Academy of Sciences, where sat, at the time now referred to, Arago, Biot, Dumas, De Senarmont, and Balard. It might be said without exaggeration that the Academy was astounded. At the same time there were many members who were slow to believe in this discovery. Charged with drawing up the report, M. Biot began by requiring from Pasteur the verification of each point which he had announced. To this verification M. Biot brought his habitual precision, which was associated with a kind of suspicious scepticism.