FURTHER ILLUSTRATIONS OF THE APHORISMSON SCIENTIFIC LANGUAGE, FROM THERECENT COURSE OF SCIENCES.1.Botany.Thenomenclature of Botany as rescued from confusion by Linnæus, has in modern times been in some danger of relapsing into disorder or becoming intolerably extensive, in consequence of the multiplication of genera by the separation of one old genus into several new ones, and the like subdivisions of the higher groups, as subclasses and classes. This inconvenience, and the origin of it, have been so well pointed out by Mr. G. Bentham65, that I shall venture to adopt his judgment as an Aphorism, and give his reasons for it.65Linnæan Society’s Proceedings, vol. ii. p. 30 (June, 1857).AphorismXXIII.It is of the greatest importance that the Groups which give their substantive names to every included species should remain large.Itwill be recollected that according to the Linnæan nomenclature, the genus is marked by a substantive, (asRosa), and the species designated by an adjective added to this substantive, (asRosa Alpina); while the natural orders are described by adjectives taken substantively, (asRosaceæ), But this rule, though it has been universally assented to in theory, has often been deviated from in practice. The number of known species having much increased, and the language of Linnæus and the principles of Jussieu having much augmented the facilities for the study of affinities, botanists have become aware that the species of a genus and the genera of an order can be collected into intermediate groups347as natural and as well defined as the genera and orders themselves, and names are required for these subordinate groups as much as for the genera and orders.Now two courses have been followed in providing names for these subordinate groups.1. The original genera (considering the case of genera in the first place) have been preserved, (if well founded); and the lower groups have been calledsubgenera,sections,subsections,divisions, &c.: and the original names of the genera have been maintained for the purpose of nomenclature, in order to retain a convenient and stable language. But when these subordinate groups are so well defined and so natural, that except for the convenience of language, they might be made good genera, there are given also to these subordinate groups, substantive or substantively-taken adjective names. When these subordinate groups are less defined or less natural, either no names at all are given, and they are distinguished by figures or signs such as *, **, or § 1, § 2, &c. or there are given them mere adjective names.Or, 2, To regard these intermediate groups between species and the original genera, as so many independent genera; and to give them substantive names, to be used in ordinary botanical nomenclature.Now the second course is that which has produced the intolerable multiplication of genera in modern times; and the first course is the only one which can save botanical nomenclature from replunging into the chaos in which Linnæus found it. It was strongly advocated by the elder De Candolle; although in the latter years of his life, seeing how general was the disposition to convert his subgenera and sections into genera, he himself more or less gave in to the general practice. The same principle was adopted by Endlichen, but he again was disposed to go far in giving substantive names to purely technical or ill-defined subsections of genera.The multiplication of genera has been much too common. Botanists have a natural pride in establishing new genera (or orders); and besides this, it is felt how useful it is, in the study of affinities, to define and348name all natural groups in every grade, however numerous they may be: and in the immense variety of language it is found easy to coin names indefinitely.But the arguments on the other side much preponderate. In attempting to introduce all these new names into ordinary botanical language, the memory is taxed beyond the capabilities of any mind, and the original and legitimate object of the Linnæan nomenclature is wholly lost sight of. In a purely scientific view it matters little if the Orders are converted into Classes or Alliances, the Genera into Orders, and the Sections or Subsections into Genera: their relative importance does not depend on the names given to them, but on their height in the scale of comprehensiveness. But for language, the great implement without which science cannot work, it is of the greatest importance, as our Aphorism declares, That the groups which give their substantive names to every species which they include, should remain large. If, independently of the inevitable increase of Genera by new discoveries, such old ones asFicus,Begonia,Arum,Erica, &c. are divided into 10, 20, 30, or 40 independent Genera, with names and characters which are to be recollected before any one species can be spoken of;—if Genera are to be reckoned by tens of thousands instead of by thousands;—the range of any individual botanist will be limited to a small portion of the whole field of the sciences.And in like manner with regard to Orders, so long as the number of Orders can be kept within, or not much beyond a couple of hundred, it may reasonably be expected that a botanist of ordinary capacity shall obtain a sufficient general idea of their nature and characters to call them at any time individually to his mind for the purpose of comparison: but if we double the number of Orders, all is confusion.The inevitable confusion and the necessity of maintaining in some way the larger groups, have been perceived by those even who have gone the furthest in lowering the scale of Orders and Genera. As a remedy for this confusion, they propose to erect the old genera into independent orders, and the old orders into classes349or divisions. But this is but an incomplete resumption of the old principles, without the advantage of the old nomenclature.And it will not be asserted, with regard to these new genera, formed by cutting up the old ones, that the new group is better defined than the group above it: on the contrary, it is frequently less so. It is not pretended thatUrostigmaorPhannacosyce, new genera formed out of the old genusFicus, are better defined than the genusFicus: or that the new genera which have lately been cut out of the old genusBegonia, form more natural groups thanBegoniaitself does. The principle which seems to be adopted in such subdivisions of old genera is this: that the lowest definable group above a species is a genus. If we were to go a step further, every species becomes a genus with a substantive name.It ought always to be recollected that though the analytical process carried to the uttermost, and separating groups by observation of differences, is necessary for the purpose of ascertaining the facts upon which botany or any other classificatory science is based, it is a judicious synthesis alone, associating individuals by the ties of language, which can enable the human mind to take a comprehensive view of these facts, to deduce from them the principles of the science, or to communicate to others either facts or principles.2.Comparative Anatomy.The Language of Botany, as framed by Linnæus, and regulated by his Canons, is still the most notable and successful example of scientific terminology which has obtained general reception among naturalists. But the Language of Anatomy, and especially of the Comparative Anatomy of the skeleton, has of late been an object of great attention to physiologists; and especially to Mr. Owen; and the collection of terms which he has proposed are selected with so much thought and care, that they may minister valuable lessons to us in this part of our subject.There is, at first sight, this broad difference between the descriptive language of Botany and of Comparative350Anatomy; that in the former science, we have comparatively few parts to describe, (calyx,corolla,stamen,pistil,pericarp,seed, &c.): while each of these parts is susceptible of many forms, for describing which with precision many terms must be provided: in Comparative Anatomy, on the other hand, the skeletons of many animals are to be regarded as modifications of a common type, and the terms by which their parts are described are to mark this community of type. The terminology of Botany has for its objectdescription; the language of Comparative Anatomy must have for its basismorphology. Accordingly, Mr. Owen’s terms are selected so as to express the analogies, or, as he calls them, thehomologiesof the skeleton; those parts of the skeleton being termedhomologues, which have the same place in the general type, and therefore ought to have the same name.Yet this distinction of the basis of botanical and anatomical terminology is not to be pushed too far. The primary definitions in botany, as given by Linnæus, are founded on morphological views; and imply a general type of the structure of plants. These are his definitions (Phil. Bot.Art. 86).Calyx,Cortexplantæ in Fructificatione præsens.Corolla,Liberplantæ in Flora præsens.Stamen, Viscus pro Pollinis præparatione.Pistillum, Viscus fructui adherens pro Pollinis receptione.Pericarpium, Viscus gravidum seminibus, quæ matura dimittit.But in what follows these leading definitions, the terms are descriptive merely. Now in Comparative Anatomy, an important object of terms is, to express what part of the type each bone represents—to answer the question,whatis it? before we proceed, assuming that we know what it is, to describe its shape. The difficulty of this previous question is very great when we come to the bones of the head; and when we assume, as morphology leads us to do, that the heads of all vertebrated animals, including even fishes, are composed of homologous bones. And, as I have already351said in the History (b. xvii. c. 7), speaking of Animal Morphology, the best physiologists are now agreed that the heads of vertebrates may be resolved into a series of vertebræ, homologically repeated and modified in different animals. This doctrine has been gradually making its way among anatomists, through a great variety of views respecting details; and hence, with great discrepancies in the language by which it has been expressed. Mr. Owen has proposed a complete series of terms for the bones of the head of all vertebrates; and these names are supported by reasons which are full of interest and instruction to the physiologist, on account of the comprehensive and precise knowledge of comparative osteology which they involve; but they are also, as I have said, interesting and instructive to us, as exemplifying the reasons which may be given for the adoption of words in scientific language. The reasons thus given agree with several of the aphorisms which I have laid down, and may perhaps suggest a few others. Mr. Owen has done me the great honour to quote with approval some of these aphorisms. The terms which he has proposed belong, as I have already said, to theTerminology, not to theNomenclatureof Zoology. In the latter subject, the Nomenclature (the names of species) the binary nomenclature established by Linnæus remains, in its principle, unshaken, simple and sufficient.I shall best derive from Mr. Owen’s labours and reflexions some of the instruction which they supply with reference to the Language of Science, by making remarks on his terminology with reference to such aphorisms as I have propounded on the subject, and others of a like kind.Mr. Owen, in hisHomologies of the Vertebrate Skeleton, has given in a Tabular Form his views of the homology of the bones of the head of vertebrates, and the names which he consequently proposes for each bone, with the synonyms as they occur in the writings of some of the most celebrated anatomical philosophers, Cuvier, Geoffroy, Hallmann, Meckel and Wagner, Agassiz and Soemmering. And he has added to this Table his reasons for dissenting from his predecessors352to the extent to which he has done so. He has done this, he says, only where nature seemed clearly to refuse her sanction to them; acting upon the maxim (ourAphorism X.) that new terms and changes of terms which are not needed in order to express truth, are to be avoided. The illustrations which I have there given, however, of this maxim, apply rather to the changes in nomenclature than in terminology; and though many considerations apply equally to these two subjects, there are some points in which the reasons differ in the two cases: especially in this point:—the names, both of genera and of species, in a system of nomenclature, may be derived from casual or arbitrary circumstances, as I have said inAphorism XIII. But the terms of a scientific terminology ought to cohere as a system, and therefore should not commonly be derived from anything casual or arbitrary, but from some analogy or connexion. Hence it seems unadvisable to apply to bones terms derived from the names of persons, asossa wormiana; or even from an accident in anatomical history, asos innominatum.It is further desirable that in establishing such a terminology, each bone should be designated by a single word, and not by a descriptive phrase, consisting of substantive and adjective. On this ground Mr. Owen proposespresphenoidforsphenöide anterieur. So alsoprefrontalis preferred toanterior frontal, andpostfrontaltoposterior frontal. And the reason which he gives for this is worthy of being stated as an Aphorism, among those which should regulate this subject. I shall therefore state it thus:AphorismXXIV.It is advisable to substitute definite single names for descriptive phrases as better instruments of thought.Itwill be recollected by the reader that in the case of the Linnæan reform of the botanical nomenclature of species, this was one of the great improvements which was introduced.Again: some of the first of the terms which Mr. Owen proposes illustrate, and confirm by their manifest claim353to acceptance, a maxim which we stated asAphorism XXII.: namely, When alterations in technical terms become necessary, it is desirable that the new term should contain in its form some memorial of the old one.Thus for ‘basilaire,’ which Cuvier exclusively applies to the ‘pars basilaris’ of the occiput, and which Geoffroy as exclusively applies (in birds) to the ‘pars basilaris’ of the sphenoid, Mr. Owen substitutes the termbasioccipital.Again: for the term ‘suroccipital’ of Geoffroy, Mr. Owen proposesparoccipital, to avoid confusion and false suggestion: and with reference to this word, he makes a remark in agreement with what we have said in the discussion ofAphorism XXI.: namely, that the combination of different languages in the derivation of words, though to be avoided in general, is in some cases admissible. He says, ‘If the purists who are distressed by such harmless hybrids as “mineralogy,” “terminology,” and “mammalogy,” should protest against the combination of the Greek prefix to the Latin noun, I can only plead that servility to a particular source of the fluctuating sounds of vocal language is a matter of taste: and that it seems no unreasonable privilege to use such elements as the servants of thought; and in the interests of science to combine them, even though they come from different countries, when the required duty is best and most expeditiously performed by their combination.’So again we have illustrations of ourAphorism XII., that if terms are systematically good they are not to be rejected because they are etymologically inaccurate. In reference to that bone of the skull which has commonly been calledvomer, the ploughshare: a term which Geoffroy rejected, but which Mr. Owen retains, he says, ‘When Geoffrey was induced to reject the termvomeras being applicable only to the peculiar form of the bone in a small portion of the vertebrata, he appears not to have considered that the old term, in its wider application, would be used without reference to its primary allusion to the ploughshare, and that becoming, as it354has, a purely arbitrary term, it is superior and preferable to any partially descriptive one.’Another condition which I have mentioned inAphorism XX., as valuable in technical terms is, that they should be susceptible of such grammatical relations as their scientific use requires.This is, in fact, one of the grounds of the Aphorism which we have already borrowed from Mr. Owen, that we are to prefer single substantives to descriptive phrases. For from such substantives we can derive adjectives, and other forms; and thus the term becomes, as Mr. Owen says,a better instrument of thought. Hence, he most consistently mentions it as a recommendation of his system of names, that by them the results of a long series of investigations into the special homologies of the bones of the head are expressed in simple and definite terms,capable of every requisite inflectionto express the proportion of the parts.I may also, in reference to this same passage in Mr. Owen’s appeal in behalf of his terminology, repeat what I have said underAphorism X.: that the persons who may most properly propose new scientific terms, are those who have much new knowledge to communicate: so that the vehicle is commended to general reception by the value of what it contains. It is only to eminent discoverers and profound philosophers that the authority is conceded of introducing a new system of terms; just as it is only the highest authority in the state which has the power of putting a new coinage into circulation. The long series of investigations of which the results are contained in Mr. Owen’s table of synonyms, and the philosophical spirit of his generalizations, entitles him to a most respectful hearing when he appeals to the Professors and Demonstrators of Human Anatomy for an unbiassed consideration of the advantages of the terms proposed by him, as likely to remedy the conflicting and unsettled synonymy which has hitherto pervaded the subject.There is another remark which is suggested by the works on Comparative Anatomy, which I am now considering. I have said in various places that Technical355Terms are a necessary condition of the progress of a science. But we may say much more than this: and the remark is so important, that it deserves to be stated as one of our Aphorisms, as follows:AphorismXXV.In an advanced Science, the history of the Language of the Science is the history of the Science itself.I havealready stated in previous Aphorisms (VIII.andXI.) that Terms must be constructed so as to be fitted to enunciate general propositions, and that Terms which imply theoretical views are admissible for this purpose. And hence it happens that the history of Terms in any science which has gone through several speculative stages, is really the history of the generalizations and theories which have had currency among the cultivators of the science.This appears in Comparative Anatomy from what we have been saying. The recent progress of that science is involved in the rise and currency of the Terms which have been used by the anatomists whose synonyms Mr. Owen has to discuss; and the reasons for selecting among these, or inventing others, include those truths and generalizations which are the important recent steps of the science. The terms which are given by Mr. Owen in his table to denote the bones of the head are good terms,iftheyaregood terms, because their adoption and use is the only complete way of expressing the truths of homology: namely, of that Special Homology, according to which all vertebrate skeletons are referred to the human skeleton as their type, and have their parts designated accordingly.But further: there is another kind of homology which Mr. Owen callsGeneralHomology, according to which the primary type of a vertebrate animal is merely a series of vertebræ; and all limbs and other appendages are only developements of the parts of one or another of the vertebræ. And in order to express this view, and in proportion as the doctrine has become current amongst356anatomists, the parts of vertebræ have been described by terms of a degree of generality which admit of such an interpretation. And here, also, Mr. Owen has proposed a terminology for the parts of the vertebræ, which seems to convey more systematically and comprehensively than those of preceding writers the truths to which they have been tending. Each vertebra is composed of acentrum,neurapophysis,parapophysis,pleurapophysis,hæmaphysis,neural spineandhæmal spine, with certain exogenous parts.The opinion that the head, as well as the other parts of the frame of vertebrates, is composed of vertebræ, is now generally accepted among philosophical anatomists. In theHistory(Hist. I. S.b. xvii. c. 7, sect. 1), I have mentioned this opinion as proposed by some writers; and I have stated that Oken, in 1807 published a ‘Program’On the signification of the bones of the Skull, in which he maintained, that these bones are equivalent to four vertebræ: while Meckel, Spix, and Geoffroy took views somewhat different. Cuvier and Agassiz opposed this doctrine, but Mr. Owen has in hisArchetype and Homologies of the Vertebrate Skeleton(1848), accepted the views of Oken, and argued at length against the objections of Cuvier, and also those of Mr. Agassiz. As I have noted in the last edition of theHistory of the Inductive Sciences(b. xvii. c. 7), he gives a Table in which the Bones of the Head are resolved into four vertebræ, which he terms the Occipital, Parietal, Frontal and Nasal Vertebræ respectively: the neural arches of which agree with what Oken called the Ear-vertebra, the Jaw-vertebra, the Eye-vertebra, and the Nose-vertebra.Besides these doctrines ofSpecial Homologyby which the bones of all vertebrates are referred to their corresponding bones in the human skeleton, and ofGeneral Homology, by which the bones are referred to the parts of vertebræ which they represent, Mr. Owen treats ofSerial Homology, the recognition of the same elements throughout the series of segments of the same skeleton; as when we shew in what manner the arms correspond to the legs. And thus, he says, in the head also, thebasioccipital,basisphenoid,presphenoidandvomerare357homotypes with thecentrumsof all succeeding vertebræ. Theexcoccipitals,alisphenoids,orbitosphenoids, andprefrontals, are homotypes with theneurapophysesof all the succeeding vertebræ. Theparoccipitals,mactoidsandpostfrontals, with thetransverse processesof all the succeeding vertebræ: and so on. Perhaps these examples may exemplify sufficiently for the general reader both Mr. Owen’s terminology, and the intimate manner in which it is connected with the widest generalizations to which anatomical philosophy has yet been led.The same doctrine, that the history of the Language of a Science is the history of the Science, appears also in the recent progress of Chemistry; but we shall be better able to illustrate our Aphorism in this case by putting forward previously one or two other Aphorisms bearing upon the history of that Science.AphorismXXVI.In the Terminology of Science it may be necessary to employ letters, numbers, and algebraical symbols.1.Mineralogy.I havealready said, inAphorism XV., that symbols have been found requisite as a part of the terminology of Mineralogy. Thenamesproposed by Haüy, borrowed from the crystalline laws, were so inadequate and unsystematic that they could not be retained. He himself proposed anotationfor crystalline forms, founded upon his principle of the derivation of such forms from aprimitiveform, bydecrements, on itsedgesor itsangles. To denote this derivation he took the first letters of the three syllables to mark the faces of thePriMiTiveform,P,M,T; the vowelsA,E,I,Oto mark the angles; the consonantsB,C,D, &c. to mark the edges; and numerical exponents, annexed in various positions to these letters, represented the law and manner of derivation. Thus when the primitive form was a cube,1Brepresented the result of a derivation by a decrement of one row358on an edge; that is, a rhombic octahedron; and1BPrepresented the combination of this octahedron with the primitive cube. In this way the pentagonal dodecahedron, produced by decrements of 2 to 1 on half the edges of the cube, was represented byB²½CG² ²GNot only, however, was the hypothesis of primitive forms and decrements untenable, but this notation was too unsystematic to stand long. And when Weiss and Mohs established the distinction of Systems of Crystallography66, they naturally founded upon that distinction a notation for crystalline forms. Mohs had several followers; but his algebraical notation so barbarously violated all algebraical meaning, that it was not likely to last. Thus, from a primitive rhombohedron which he designated byR, he derived, by a certain process, a series of other rhombohedrons, which he denoted byR+ 1,R+ 2,R− 1,&c.; and then, by another mode of derivation from them, he obtained forms which he marked as(R+ 2)²,(R+ 2)³,&c. In doing this he used the algebraical marks of addition and involution without the smallest ground; besides many other proposals no less transgressing mathematical analogy and simplicity.66Hist. Ind. Sc.b. xv. c. 4.But this notation might easily suggest a better. If we take a primitive form, we can generally, by two steps of derivation, each capable of numerical measure, obtain any possible face; and therefore any crystalline form bounded by such faces. Hence all that we need indicate in our crystalline laws is the primitive form, and two numerical exponents; and rejecting all superfluity in our symbols, instead of(R+ 2)³we might write 2R3. Nearly of this kind is the notation of Naumann. The systems of crystallization, the octahedral or tessular, the rhombic, and the prismatic, are marked by the lettersO,R,P; and from these are derived, by certain laws, such symbols as3O½, ∞R2, ½P2,359which have their definite signification flowing from the rules of the notation.But Professor Miller, who has treated the subject of Crystallography in the most general and symmetrical manner, adopts the plan of marking each crystalline plane bythreenumerical indices. Thus in the Octahedral System, the cube is {100}; the octahedron is {111}; the rhombic dodecahedron is {011}; the pentagonal dodecahedron is π {012}; where π indicates that the form is notholohedralbuthemihedral, only half the number of faces being taken which the law of derivation would give. This system is the most mathematically consistent, and affords the best means of calculation, as Professor Miller has shown; but there appears to be in it this defect, that though an essential part of the scheme is the division of crystalline forms into Systems,—the Octahedral, Pyramidal, Rhombohedral and Prismatic,—this division does not at all appear in the notation.But whatever be the notation which the crystallographer adopts, it is evident that he must employ some notation; and that, without it, he will be unable to express the forms and relations of forms with which he has to deal.2.Chemistry.The same has long been the case in Chemistry. As I have stated elsewhere67, the chemical nomenclature of the oxygen theory was for a time very useful and effective. But yet it had defects which could not be overlooked, as I have already stated underAphorism II.The relations of elements were too numerous, and their numerical properties too important, to be expressed by terminations and other modifications of words. Thus the compounds of Nitrogen and Oxygen are the Protoxide, the Deutoxide, Nitrous Acid, Peroxide of Nitrogen, Nitric Acid. The systematic nomenclature here, even thus loosely extended, does not express our knowledge. And the Atomic Theory, when established, brought to view numerical360relations which it was very important to keep in sight. IfNrepresents Nitrogen andOOxygen, the compounds of the two elements just mentioned might be denoted byN+O,N+ 2O,N+ 3O,N+ 4O,N+ 5O. And by adopting a letter for each of the elementary substances, all the combinations of them might be expressed in this manner.67Hist. Ind. Sc.b. xiv. c. 6.But in chemistry there are different orders of combination. A salt, for instance, is a compound of a base and an acid, each of which is already compound. IfFebe iron andCbe carbon,Fe+Owill be the protoxide of iron, andC+ 2Owill be carbonic acid; and the carbonate of iron (more properly carbonate of protoxide of iron), may be represented by(Fe+O) + (C+ 2O)where the brackets indicate the first stage of composition.But these brackets and signs of addition, in complex cases, would cumber the page in an inconvenient degree; and oxygen is of such very wide occurrence, that it seems desirable to abridge the notation so far as it is concerned. Hence Berzelius proposed68that in the first stage of composition the oxygen should be expressed by dots over the letter; and thus the carbonate of iron would beḞe+C̈. But Berzelius further introduced into his notation indexes such as in algebra denote involution to the square, cube, &c. ThusCubeing copper, the sulphate of copper is represented byS⃛²C̈u. This notation, when first proposed, was strongly condemned by English chemists, and Berzelius’s reply to them may be taken as stating the reasons in favour of such notation. He says69, ‘We answer to the opponents, that undoubtedly the matter may be looked at in various lights. The use of Formulæ has always, for a person who has not accustomed himself to them, something repulsive; but this is easy to overcome. I agree with my opponent,361who says that nothing can be understood in a Formula which cannot be expressed in words; and that if the words express it as easily as the Formula, the use of the latter would be a folly. But there are cases in which this is not so; in which the Formula says in a glance what it would take many lines to express in words; and in which the expression of the Formula is clearer and more easily apprehended by the reader than the longer description in words. Let us examine such a Formula, and compare it with the equivalent description in words. Take, for example, crystallized sulphate of copper, of which the Formula isC̈uS⃛² + 10H²O.Now this Formula expresses the following propositions:‘That the salt consists of one atom of copper-oxide combined with 2 atoms of sulphuric acid and with 10 atoms of water; that the copper-oxide contains two atoms of oxygen; and that the sulphuric acid contains 3 atoms of oxygen for one atom of sulphur; that its oxygen is three times as much as that of the oxide; and that the number of atoms of oxygen in the acid is 6; and that the number of atoms of oxygen in the water is 10; that is, 5 times the number in the oxide; and that finally the salt contains, of simple atoms, 1 copper, 2 sulphur, 20 hydrogen, and 18 oxygen.68System of Mineralogy, 1816.69Jahresbericht, 1824, p. 119.‘Since so much is expressed in this brief Formula, how very long would the explanation be for a more composite body, for example, Alum; for which the Formula isK̈S⃛² + 2A⃛l S⃛³ + 48H²O.It would take half a page to express all which this Formula contains.‘Perhaps it may be objected that it is seldom that any one wants to know all this at once. But it might reasonably be said in reply, that the peculiar value of the Formula consists in this, that it contains answers to all the questions which can be asked with regard to the composition of the body.362‘But these Formulæ have also another application, of which I have sometimes had occasion to make use. Experiments sometimes bring before us combinations which cannot be foreseen from the nomenclature, and for which it is not always easy to find a consistent and appropriate name. In writing, the Formula may be applied instead of a Name: and the reader understands it better than if one made a new name. In my treatise upon the sulphuretted alkalies I found Degrees of Sulphur-combination, for which Nomenclature has no name. I expressed them, for example, byKS6,KS8,KS10and I believed that every one understood what was thereby meant. Moreover, I found another class of bodies in which an electro-negative sulphuretted metal played the part of an Acid with respect to an electro-positive sulphuretted metal, for which a whole new nomenclature was needed; while yet it were not prudent to construct such a nomenclature, till more is known on the subject. Instead of new names I used formulas; for example,KS² + 2As S³,instead of saying the combination of 2 atoms of Sulphuret of Arsenic containing 3 atoms of Sulphur, with one atom of Sulphuret of Potassium (Kali) with the least dose of sulphur.’Berzelius goes on to say that the English chemists had found themselves unable to find any substitutes for his formulæ when they translated his papers.Our English chemists have not generally adopted the notation of oxygen by dots; but have employed commas or full stops and symbols (, or . and +), to denote various degrees of union, and numerical indices. Thus the double sulphate of copper and potash isCu O,SO3+KO,SO3.What has been said is applicable mainly to inorganic bodies (as salts and minerals)70. In these bodies there is (at least according to the views of many intelligent chemists) abinaryplan of combination, union taking363place betweenpairsof elements, and the compounds so produced again uniting themselves to other compound bodies in the same manner. Thus, in the above example, copper and oxygen combine into oxide of copper, potassium and oxygen into potash, sulphur and oxygen into sulphuric acid; sulphuric acid in its turn combines both with oxide of copper and oxide of potassium, generating a pair of salts which are capable of uniting to form the double compoundCu O,SO3+KO,SO3.70Fownes’sChemistry. Part iii.The most complicated products of inorganic chemistry may be thus shown to be built up by this repeatedpairingon the part of their constituents. But with organic bodies the case is remarkably different; no such arrangement can here be traced. In sugar, which isC12H11O11,or morphia71, which isC35H20NO6,the elements are as it were bound together into a single whole, which can enter into combination with other substances, and be thence discharged with properties unaltered; the elements not being obviously arranged in any subordinate groups. Hence the symbols for those substances are such as I have given above, no marks of combination being used.71Fownes’sChemistry, p. 354.It is perhaps a consequence of this peculiarity that organic compounds areunstablein comparison with inorganic. In unorganic substances generally the elements are combined in such a way that the most powerful affinities are satisfied72, and hence arises a state of very considerable permanence and durability. But in an organic substance containing three or four elements, there are often opposing affinities nearly balanced, and when one of these tendencies by some accident obtains a preponderance and the equilibrium is destroyed, then the organic body breaks up into two or more new bodies of simpler and more permanent constitution.72SeeHist. Ind. Sc.b. xiv. c. 3.There is another property of many organic substances which is called theLaw of Substitution. The364Hydrogen of the organic substance may often be replaced by Chlorine, Bromine, Iodine, or some other elements, without the destruction of the primitive type or constitution of the compound so modified. And this substitution may take place by several successive steps, giving rise to a series of substitution-compounds, which depart more and more in properties from the original substance. This Law also gives rise to a special notation. Thus a certain compound calledDutch liquidhas the elementsC4H4Cl2:but this substance is affected by chlorine (Cl) in obedience to the law of substitution; one and two equivalents of hydrogen being successively removed by the prolonged action of chlorine gas aided by sunshine. The successive products may be thus writtenC4H4Cl2;C4{H3Cl}Cl2;C4{H2Cl2}Cl2.Perhaps at a future period, chemical symbols, and especially those of organic bodies, may be made more systematic and more significant than they at present are.AphorismXXVII.In using algebraical symbols as a part of scientific language, violations of algebraical analogy are to be avoided, but may be admitted when necessary.Aswe must in scientific language conform to etymology, so must we to algebra; and as we are not to make ourselves the slaves of the former, so also, not to the latter. Hence we reject such crystallographical notation as that of Mohs; and in chemistry we useC2,O3rather thanC2,O3, which signify the square ofCand the cube ofO. But we may use, as we have said, both the comma and the sign of addition, for chemical combination, for the sake of brevity, though both steps of combination are really addition.365AphorismXXVIII.In a complex science, which is in a state of transition, capricious and detached derivations of terms are common; but are not satisfactory.Inthis remark I have especial reference to Chemistry; in which the discoveries made, especially in organic chemistry, and the difficulty of reducing them to a system, have broken up in several instances the old nomenclature, without its being possible at present to construct a new set of terms systematically connected. Hence it has come to pass that chemists have constructed words in a capricious and detached way: as by taking fragments of words, and the like. I shall give some examples of such derivations, and also of some attempts which have more of a systematic character.I have mentioned (Aph.XX.sect. 7) the wordEllagic(acid), made by inverting the wordGalle. Several words have recently been formed by chemists by taking syllables from two or more different words. Thus Chevreul discovered a substance to which he gave the nameEthal, from the first syllables of the wordsetherandalcohol, because of its analogy to those liquids in point of composition73. So Liebig has the wordchloral74.
FURTHER ILLUSTRATIONS OF THE APHORISMSON SCIENTIFIC LANGUAGE, FROM THERECENT COURSE OF SCIENCES.
1.Botany.
Thenomenclature of Botany as rescued from confusion by Linnæus, has in modern times been in some danger of relapsing into disorder or becoming intolerably extensive, in consequence of the multiplication of genera by the separation of one old genus into several new ones, and the like subdivisions of the higher groups, as subclasses and classes. This inconvenience, and the origin of it, have been so well pointed out by Mr. G. Bentham65, that I shall venture to adopt his judgment as an Aphorism, and give his reasons for it.
65Linnæan Society’s Proceedings, vol. ii. p. 30 (June, 1857).
AphorismXXIII.
It is of the greatest importance that the Groups which give their substantive names to every included species should remain large.
Itwill be recollected that according to the Linnæan nomenclature, the genus is marked by a substantive, (asRosa), and the species designated by an adjective added to this substantive, (asRosa Alpina); while the natural orders are described by adjectives taken substantively, (asRosaceæ), But this rule, though it has been universally assented to in theory, has often been deviated from in practice. The number of known species having much increased, and the language of Linnæus and the principles of Jussieu having much augmented the facilities for the study of affinities, botanists have become aware that the species of a genus and the genera of an order can be collected into intermediate groups347as natural and as well defined as the genera and orders themselves, and names are required for these subordinate groups as much as for the genera and orders.
Now two courses have been followed in providing names for these subordinate groups.
1. The original genera (considering the case of genera in the first place) have been preserved, (if well founded); and the lower groups have been calledsubgenera,sections,subsections,divisions, &c.: and the original names of the genera have been maintained for the purpose of nomenclature, in order to retain a convenient and stable language. But when these subordinate groups are so well defined and so natural, that except for the convenience of language, they might be made good genera, there are given also to these subordinate groups, substantive or substantively-taken adjective names. When these subordinate groups are less defined or less natural, either no names at all are given, and they are distinguished by figures or signs such as *, **, or § 1, § 2, &c. or there are given them mere adjective names.
Or, 2, To regard these intermediate groups between species and the original genera, as so many independent genera; and to give them substantive names, to be used in ordinary botanical nomenclature.
Now the second course is that which has produced the intolerable multiplication of genera in modern times; and the first course is the only one which can save botanical nomenclature from replunging into the chaos in which Linnæus found it. It was strongly advocated by the elder De Candolle; although in the latter years of his life, seeing how general was the disposition to convert his subgenera and sections into genera, he himself more or less gave in to the general practice. The same principle was adopted by Endlichen, but he again was disposed to go far in giving substantive names to purely technical or ill-defined subsections of genera.
The multiplication of genera has been much too common. Botanists have a natural pride in establishing new genera (or orders); and besides this, it is felt how useful it is, in the study of affinities, to define and348name all natural groups in every grade, however numerous they may be: and in the immense variety of language it is found easy to coin names indefinitely.
But the arguments on the other side much preponderate. In attempting to introduce all these new names into ordinary botanical language, the memory is taxed beyond the capabilities of any mind, and the original and legitimate object of the Linnæan nomenclature is wholly lost sight of. In a purely scientific view it matters little if the Orders are converted into Classes or Alliances, the Genera into Orders, and the Sections or Subsections into Genera: their relative importance does not depend on the names given to them, but on their height in the scale of comprehensiveness. But for language, the great implement without which science cannot work, it is of the greatest importance, as our Aphorism declares, That the groups which give their substantive names to every species which they include, should remain large. If, independently of the inevitable increase of Genera by new discoveries, such old ones asFicus,Begonia,Arum,Erica, &c. are divided into 10, 20, 30, or 40 independent Genera, with names and characters which are to be recollected before any one species can be spoken of;—if Genera are to be reckoned by tens of thousands instead of by thousands;—the range of any individual botanist will be limited to a small portion of the whole field of the sciences.
And in like manner with regard to Orders, so long as the number of Orders can be kept within, or not much beyond a couple of hundred, it may reasonably be expected that a botanist of ordinary capacity shall obtain a sufficient general idea of their nature and characters to call them at any time individually to his mind for the purpose of comparison: but if we double the number of Orders, all is confusion.
The inevitable confusion and the necessity of maintaining in some way the larger groups, have been perceived by those even who have gone the furthest in lowering the scale of Orders and Genera. As a remedy for this confusion, they propose to erect the old genera into independent orders, and the old orders into classes349or divisions. But this is but an incomplete resumption of the old principles, without the advantage of the old nomenclature.
And it will not be asserted, with regard to these new genera, formed by cutting up the old ones, that the new group is better defined than the group above it: on the contrary, it is frequently less so. It is not pretended thatUrostigmaorPhannacosyce, new genera formed out of the old genusFicus, are better defined than the genusFicus: or that the new genera which have lately been cut out of the old genusBegonia, form more natural groups thanBegoniaitself does. The principle which seems to be adopted in such subdivisions of old genera is this: that the lowest definable group above a species is a genus. If we were to go a step further, every species becomes a genus with a substantive name.
It ought always to be recollected that though the analytical process carried to the uttermost, and separating groups by observation of differences, is necessary for the purpose of ascertaining the facts upon which botany or any other classificatory science is based, it is a judicious synthesis alone, associating individuals by the ties of language, which can enable the human mind to take a comprehensive view of these facts, to deduce from them the principles of the science, or to communicate to others either facts or principles.
2.Comparative Anatomy.
The Language of Botany, as framed by Linnæus, and regulated by his Canons, is still the most notable and successful example of scientific terminology which has obtained general reception among naturalists. But the Language of Anatomy, and especially of the Comparative Anatomy of the skeleton, has of late been an object of great attention to physiologists; and especially to Mr. Owen; and the collection of terms which he has proposed are selected with so much thought and care, that they may minister valuable lessons to us in this part of our subject.
There is, at first sight, this broad difference between the descriptive language of Botany and of Comparative350Anatomy; that in the former science, we have comparatively few parts to describe, (calyx,corolla,stamen,pistil,pericarp,seed, &c.): while each of these parts is susceptible of many forms, for describing which with precision many terms must be provided: in Comparative Anatomy, on the other hand, the skeletons of many animals are to be regarded as modifications of a common type, and the terms by which their parts are described are to mark this community of type. The terminology of Botany has for its objectdescription; the language of Comparative Anatomy must have for its basismorphology. Accordingly, Mr. Owen’s terms are selected so as to express the analogies, or, as he calls them, thehomologiesof the skeleton; those parts of the skeleton being termedhomologues, which have the same place in the general type, and therefore ought to have the same name.
Yet this distinction of the basis of botanical and anatomical terminology is not to be pushed too far. The primary definitions in botany, as given by Linnæus, are founded on morphological views; and imply a general type of the structure of plants. These are his definitions (Phil. Bot.Art. 86).Calyx,Cortexplantæ in Fructificatione præsens.Corolla,Liberplantæ in Flora præsens.Stamen, Viscus pro Pollinis præparatione.Pistillum, Viscus fructui adherens pro Pollinis receptione.Pericarpium, Viscus gravidum seminibus, quæ matura dimittit.
But in what follows these leading definitions, the terms are descriptive merely. Now in Comparative Anatomy, an important object of terms is, to express what part of the type each bone represents—to answer the question,whatis it? before we proceed, assuming that we know what it is, to describe its shape. The difficulty of this previous question is very great when we come to the bones of the head; and when we assume, as morphology leads us to do, that the heads of all vertebrated animals, including even fishes, are composed of homologous bones. And, as I have already351said in the History (b. xvii. c. 7), speaking of Animal Morphology, the best physiologists are now agreed that the heads of vertebrates may be resolved into a series of vertebræ, homologically repeated and modified in different animals. This doctrine has been gradually making its way among anatomists, through a great variety of views respecting details; and hence, with great discrepancies in the language by which it has been expressed. Mr. Owen has proposed a complete series of terms for the bones of the head of all vertebrates; and these names are supported by reasons which are full of interest and instruction to the physiologist, on account of the comprehensive and precise knowledge of comparative osteology which they involve; but they are also, as I have said, interesting and instructive to us, as exemplifying the reasons which may be given for the adoption of words in scientific language. The reasons thus given agree with several of the aphorisms which I have laid down, and may perhaps suggest a few others. Mr. Owen has done me the great honour to quote with approval some of these aphorisms. The terms which he has proposed belong, as I have already said, to theTerminology, not to theNomenclatureof Zoology. In the latter subject, the Nomenclature (the names of species) the binary nomenclature established by Linnæus remains, in its principle, unshaken, simple and sufficient.
I shall best derive from Mr. Owen’s labours and reflexions some of the instruction which they supply with reference to the Language of Science, by making remarks on his terminology with reference to such aphorisms as I have propounded on the subject, and others of a like kind.
Mr. Owen, in hisHomologies of the Vertebrate Skeleton, has given in a Tabular Form his views of the homology of the bones of the head of vertebrates, and the names which he consequently proposes for each bone, with the synonyms as they occur in the writings of some of the most celebrated anatomical philosophers, Cuvier, Geoffroy, Hallmann, Meckel and Wagner, Agassiz and Soemmering. And he has added to this Table his reasons for dissenting from his predecessors352to the extent to which he has done so. He has done this, he says, only where nature seemed clearly to refuse her sanction to them; acting upon the maxim (ourAphorism X.) that new terms and changes of terms which are not needed in order to express truth, are to be avoided. The illustrations which I have there given, however, of this maxim, apply rather to the changes in nomenclature than in terminology; and though many considerations apply equally to these two subjects, there are some points in which the reasons differ in the two cases: especially in this point:—the names, both of genera and of species, in a system of nomenclature, may be derived from casual or arbitrary circumstances, as I have said inAphorism XIII. But the terms of a scientific terminology ought to cohere as a system, and therefore should not commonly be derived from anything casual or arbitrary, but from some analogy or connexion. Hence it seems unadvisable to apply to bones terms derived from the names of persons, asossa wormiana; or even from an accident in anatomical history, asos innominatum.
It is further desirable that in establishing such a terminology, each bone should be designated by a single word, and not by a descriptive phrase, consisting of substantive and adjective. On this ground Mr. Owen proposespresphenoidforsphenöide anterieur. So alsoprefrontalis preferred toanterior frontal, andpostfrontaltoposterior frontal. And the reason which he gives for this is worthy of being stated as an Aphorism, among those which should regulate this subject. I shall therefore state it thus:
AphorismXXIV.
It is advisable to substitute definite single names for descriptive phrases as better instruments of thought.
Itwill be recollected by the reader that in the case of the Linnæan reform of the botanical nomenclature of species, this was one of the great improvements which was introduced.
Again: some of the first of the terms which Mr. Owen proposes illustrate, and confirm by their manifest claim353to acceptance, a maxim which we stated asAphorism XXII.: namely, When alterations in technical terms become necessary, it is desirable that the new term should contain in its form some memorial of the old one.
Thus for ‘basilaire,’ which Cuvier exclusively applies to the ‘pars basilaris’ of the occiput, and which Geoffroy as exclusively applies (in birds) to the ‘pars basilaris’ of the sphenoid, Mr. Owen substitutes the termbasioccipital.
Again: for the term ‘suroccipital’ of Geoffroy, Mr. Owen proposesparoccipital, to avoid confusion and false suggestion: and with reference to this word, he makes a remark in agreement with what we have said in the discussion ofAphorism XXI.: namely, that the combination of different languages in the derivation of words, though to be avoided in general, is in some cases admissible. He says, ‘If the purists who are distressed by such harmless hybrids as “mineralogy,” “terminology,” and “mammalogy,” should protest against the combination of the Greek prefix to the Latin noun, I can only plead that servility to a particular source of the fluctuating sounds of vocal language is a matter of taste: and that it seems no unreasonable privilege to use such elements as the servants of thought; and in the interests of science to combine them, even though they come from different countries, when the required duty is best and most expeditiously performed by their combination.’
So again we have illustrations of ourAphorism XII., that if terms are systematically good they are not to be rejected because they are etymologically inaccurate. In reference to that bone of the skull which has commonly been calledvomer, the ploughshare: a term which Geoffroy rejected, but which Mr. Owen retains, he says, ‘When Geoffrey was induced to reject the termvomeras being applicable only to the peculiar form of the bone in a small portion of the vertebrata, he appears not to have considered that the old term, in its wider application, would be used without reference to its primary allusion to the ploughshare, and that becoming, as it354has, a purely arbitrary term, it is superior and preferable to any partially descriptive one.’
Another condition which I have mentioned inAphorism XX., as valuable in technical terms is, that they should be susceptible of such grammatical relations as their scientific use requires.
This is, in fact, one of the grounds of the Aphorism which we have already borrowed from Mr. Owen, that we are to prefer single substantives to descriptive phrases. For from such substantives we can derive adjectives, and other forms; and thus the term becomes, as Mr. Owen says,a better instrument of thought. Hence, he most consistently mentions it as a recommendation of his system of names, that by them the results of a long series of investigations into the special homologies of the bones of the head are expressed in simple and definite terms,capable of every requisite inflectionto express the proportion of the parts.
I may also, in reference to this same passage in Mr. Owen’s appeal in behalf of his terminology, repeat what I have said underAphorism X.: that the persons who may most properly propose new scientific terms, are those who have much new knowledge to communicate: so that the vehicle is commended to general reception by the value of what it contains. It is only to eminent discoverers and profound philosophers that the authority is conceded of introducing a new system of terms; just as it is only the highest authority in the state which has the power of putting a new coinage into circulation. The long series of investigations of which the results are contained in Mr. Owen’s table of synonyms, and the philosophical spirit of his generalizations, entitles him to a most respectful hearing when he appeals to the Professors and Demonstrators of Human Anatomy for an unbiassed consideration of the advantages of the terms proposed by him, as likely to remedy the conflicting and unsettled synonymy which has hitherto pervaded the subject.
There is another remark which is suggested by the works on Comparative Anatomy, which I am now considering. I have said in various places that Technical355Terms are a necessary condition of the progress of a science. But we may say much more than this: and the remark is so important, that it deserves to be stated as one of our Aphorisms, as follows:
AphorismXXV.
In an advanced Science, the history of the Language of the Science is the history of the Science itself.
I havealready stated in previous Aphorisms (VIII.andXI.) that Terms must be constructed so as to be fitted to enunciate general propositions, and that Terms which imply theoretical views are admissible for this purpose. And hence it happens that the history of Terms in any science which has gone through several speculative stages, is really the history of the generalizations and theories which have had currency among the cultivators of the science.
This appears in Comparative Anatomy from what we have been saying. The recent progress of that science is involved in the rise and currency of the Terms which have been used by the anatomists whose synonyms Mr. Owen has to discuss; and the reasons for selecting among these, or inventing others, include those truths and generalizations which are the important recent steps of the science. The terms which are given by Mr. Owen in his table to denote the bones of the head are good terms,iftheyaregood terms, because their adoption and use is the only complete way of expressing the truths of homology: namely, of that Special Homology, according to which all vertebrate skeletons are referred to the human skeleton as their type, and have their parts designated accordingly.
But further: there is another kind of homology which Mr. Owen callsGeneralHomology, according to which the primary type of a vertebrate animal is merely a series of vertebræ; and all limbs and other appendages are only developements of the parts of one or another of the vertebræ. And in order to express this view, and in proportion as the doctrine has become current amongst356anatomists, the parts of vertebræ have been described by terms of a degree of generality which admit of such an interpretation. And here, also, Mr. Owen has proposed a terminology for the parts of the vertebræ, which seems to convey more systematically and comprehensively than those of preceding writers the truths to which they have been tending. Each vertebra is composed of acentrum,neurapophysis,parapophysis,pleurapophysis,hæmaphysis,neural spineandhæmal spine, with certain exogenous parts.
The opinion that the head, as well as the other parts of the frame of vertebrates, is composed of vertebræ, is now generally accepted among philosophical anatomists. In theHistory(Hist. I. S.b. xvii. c. 7, sect. 1), I have mentioned this opinion as proposed by some writers; and I have stated that Oken, in 1807 published a ‘Program’On the signification of the bones of the Skull, in which he maintained, that these bones are equivalent to four vertebræ: while Meckel, Spix, and Geoffroy took views somewhat different. Cuvier and Agassiz opposed this doctrine, but Mr. Owen has in hisArchetype and Homologies of the Vertebrate Skeleton(1848), accepted the views of Oken, and argued at length against the objections of Cuvier, and also those of Mr. Agassiz. As I have noted in the last edition of theHistory of the Inductive Sciences(b. xvii. c. 7), he gives a Table in which the Bones of the Head are resolved into four vertebræ, which he terms the Occipital, Parietal, Frontal and Nasal Vertebræ respectively: the neural arches of which agree with what Oken called the Ear-vertebra, the Jaw-vertebra, the Eye-vertebra, and the Nose-vertebra.
Besides these doctrines ofSpecial Homologyby which the bones of all vertebrates are referred to their corresponding bones in the human skeleton, and ofGeneral Homology, by which the bones are referred to the parts of vertebræ which they represent, Mr. Owen treats ofSerial Homology, the recognition of the same elements throughout the series of segments of the same skeleton; as when we shew in what manner the arms correspond to the legs. And thus, he says, in the head also, thebasioccipital,basisphenoid,presphenoidandvomerare357homotypes with thecentrumsof all succeeding vertebræ. Theexcoccipitals,alisphenoids,orbitosphenoids, andprefrontals, are homotypes with theneurapophysesof all the succeeding vertebræ. Theparoccipitals,mactoidsandpostfrontals, with thetransverse processesof all the succeeding vertebræ: and so on. Perhaps these examples may exemplify sufficiently for the general reader both Mr. Owen’s terminology, and the intimate manner in which it is connected with the widest generalizations to which anatomical philosophy has yet been led.
The same doctrine, that the history of the Language of a Science is the history of the Science, appears also in the recent progress of Chemistry; but we shall be better able to illustrate our Aphorism in this case by putting forward previously one or two other Aphorisms bearing upon the history of that Science.
AphorismXXVI.
In the Terminology of Science it may be necessary to employ letters, numbers, and algebraical symbols.
1.Mineralogy.
I havealready said, inAphorism XV., that symbols have been found requisite as a part of the terminology of Mineralogy. Thenamesproposed by Haüy, borrowed from the crystalline laws, were so inadequate and unsystematic that they could not be retained. He himself proposed anotationfor crystalline forms, founded upon his principle of the derivation of such forms from aprimitiveform, bydecrements, on itsedgesor itsangles. To denote this derivation he took the first letters of the three syllables to mark the faces of thePriMiTiveform,P,M,T; the vowelsA,E,I,Oto mark the angles; the consonantsB,C,D, &c. to mark the edges; and numerical exponents, annexed in various positions to these letters, represented the law and manner of derivation. Thus when the primitive form was a cube,1Brepresented the result of a derivation by a decrement of one row358on an edge; that is, a rhombic octahedron; and1BPrepresented the combination of this octahedron with the primitive cube. In this way the pentagonal dodecahedron, produced by decrements of 2 to 1 on half the edges of the cube, was represented byB²½CG² ²G
Not only, however, was the hypothesis of primitive forms and decrements untenable, but this notation was too unsystematic to stand long. And when Weiss and Mohs established the distinction of Systems of Crystallography66, they naturally founded upon that distinction a notation for crystalline forms. Mohs had several followers; but his algebraical notation so barbarously violated all algebraical meaning, that it was not likely to last. Thus, from a primitive rhombohedron which he designated byR, he derived, by a certain process, a series of other rhombohedrons, which he denoted byR+ 1,R+ 2,R− 1,&c.; and then, by another mode of derivation from them, he obtained forms which he marked as(R+ 2)²,(R+ 2)³,&c. In doing this he used the algebraical marks of addition and involution without the smallest ground; besides many other proposals no less transgressing mathematical analogy and simplicity.
66Hist. Ind. Sc.b. xv. c. 4.
But this notation might easily suggest a better. If we take a primitive form, we can generally, by two steps of derivation, each capable of numerical measure, obtain any possible face; and therefore any crystalline form bounded by such faces. Hence all that we need indicate in our crystalline laws is the primitive form, and two numerical exponents; and rejecting all superfluity in our symbols, instead of(R+ 2)³we might write 2R3. Nearly of this kind is the notation of Naumann. The systems of crystallization, the octahedral or tessular, the rhombic, and the prismatic, are marked by the lettersO,R,P; and from these are derived, by certain laws, such symbols as
3O½, ∞R2, ½P2,359
which have their definite signification flowing from the rules of the notation.
But Professor Miller, who has treated the subject of Crystallography in the most general and symmetrical manner, adopts the plan of marking each crystalline plane bythreenumerical indices. Thus in the Octahedral System, the cube is {100}; the octahedron is {111}; the rhombic dodecahedron is {011}; the pentagonal dodecahedron is π {012}; where π indicates that the form is notholohedralbuthemihedral, only half the number of faces being taken which the law of derivation would give. This system is the most mathematically consistent, and affords the best means of calculation, as Professor Miller has shown; but there appears to be in it this defect, that though an essential part of the scheme is the division of crystalline forms into Systems,—the Octahedral, Pyramidal, Rhombohedral and Prismatic,—this division does not at all appear in the notation.
But whatever be the notation which the crystallographer adopts, it is evident that he must employ some notation; and that, without it, he will be unable to express the forms and relations of forms with which he has to deal.
2.Chemistry.
The same has long been the case in Chemistry. As I have stated elsewhere67, the chemical nomenclature of the oxygen theory was for a time very useful and effective. But yet it had defects which could not be overlooked, as I have already stated underAphorism II.The relations of elements were too numerous, and their numerical properties too important, to be expressed by terminations and other modifications of words. Thus the compounds of Nitrogen and Oxygen are the Protoxide, the Deutoxide, Nitrous Acid, Peroxide of Nitrogen, Nitric Acid. The systematic nomenclature here, even thus loosely extended, does not express our knowledge. And the Atomic Theory, when established, brought to view numerical360relations which it was very important to keep in sight. IfNrepresents Nitrogen andOOxygen, the compounds of the two elements just mentioned might be denoted byN+O,N+ 2O,N+ 3O,N+ 4O,N+ 5O. And by adopting a letter for each of the elementary substances, all the combinations of them might be expressed in this manner.
67Hist. Ind. Sc.b. xiv. c. 6.
But in chemistry there are different orders of combination. A salt, for instance, is a compound of a base and an acid, each of which is already compound. IfFebe iron andCbe carbon,Fe+Owill be the protoxide of iron, andC+ 2Owill be carbonic acid; and the carbonate of iron (more properly carbonate of protoxide of iron), may be represented by
(Fe+O) + (C+ 2O)
where the brackets indicate the first stage of composition.
But these brackets and signs of addition, in complex cases, would cumber the page in an inconvenient degree; and oxygen is of such very wide occurrence, that it seems desirable to abridge the notation so far as it is concerned. Hence Berzelius proposed68that in the first stage of composition the oxygen should be expressed by dots over the letter; and thus the carbonate of iron would beḞe+C̈. But Berzelius further introduced into his notation indexes such as in algebra denote involution to the square, cube, &c. ThusCubeing copper, the sulphate of copper is represented byS⃛²C̈u. This notation, when first proposed, was strongly condemned by English chemists, and Berzelius’s reply to them may be taken as stating the reasons in favour of such notation. He says69, ‘We answer to the opponents, that undoubtedly the matter may be looked at in various lights. The use of Formulæ has always, for a person who has not accustomed himself to them, something repulsive; but this is easy to overcome. I agree with my opponent,361who says that nothing can be understood in a Formula which cannot be expressed in words; and that if the words express it as easily as the Formula, the use of the latter would be a folly. But there are cases in which this is not so; in which the Formula says in a glance what it would take many lines to express in words; and in which the expression of the Formula is clearer and more easily apprehended by the reader than the longer description in words. Let us examine such a Formula, and compare it with the equivalent description in words. Take, for example, crystallized sulphate of copper, of which the Formula is
C̈uS⃛² + 10H²O.
Now this Formula expresses the following propositions:‘That the salt consists of one atom of copper-oxide combined with 2 atoms of sulphuric acid and with 10 atoms of water; that the copper-oxide contains two atoms of oxygen; and that the sulphuric acid contains 3 atoms of oxygen for one atom of sulphur; that its oxygen is three times as much as that of the oxide; and that the number of atoms of oxygen in the acid is 6; and that the number of atoms of oxygen in the water is 10; that is, 5 times the number in the oxide; and that finally the salt contains, of simple atoms, 1 copper, 2 sulphur, 20 hydrogen, and 18 oxygen.
68System of Mineralogy, 1816.
69Jahresbericht, 1824, p. 119.
‘Since so much is expressed in this brief Formula, how very long would the explanation be for a more composite body, for example, Alum; for which the Formula is
K̈S⃛² + 2A⃛l S⃛³ + 48H²O.
It would take half a page to express all which this Formula contains.
‘Perhaps it may be objected that it is seldom that any one wants to know all this at once. But it might reasonably be said in reply, that the peculiar value of the Formula consists in this, that it contains answers to all the questions which can be asked with regard to the composition of the body.362
‘But these Formulæ have also another application, of which I have sometimes had occasion to make use. Experiments sometimes bring before us combinations which cannot be foreseen from the nomenclature, and for which it is not always easy to find a consistent and appropriate name. In writing, the Formula may be applied instead of a Name: and the reader understands it better than if one made a new name. In my treatise upon the sulphuretted alkalies I found Degrees of Sulphur-combination, for which Nomenclature has no name. I expressed them, for example, byKS6,KS8,KS10and I believed that every one understood what was thereby meant. Moreover, I found another class of bodies in which an electro-negative sulphuretted metal played the part of an Acid with respect to an electro-positive sulphuretted metal, for which a whole new nomenclature was needed; while yet it were not prudent to construct such a nomenclature, till more is known on the subject. Instead of new names I used formulas; for example,
KS² + 2As S³,
instead of saying the combination of 2 atoms of Sulphuret of Arsenic containing 3 atoms of Sulphur, with one atom of Sulphuret of Potassium (Kali) with the least dose of sulphur.’
Berzelius goes on to say that the English chemists had found themselves unable to find any substitutes for his formulæ when they translated his papers.
Our English chemists have not generally adopted the notation of oxygen by dots; but have employed commas or full stops and symbols (, or . and +), to denote various degrees of union, and numerical indices. Thus the double sulphate of copper and potash isCu O,SO3+KO,SO3.
What has been said is applicable mainly to inorganic bodies (as salts and minerals)70. In these bodies there is (at least according to the views of many intelligent chemists) abinaryplan of combination, union taking363place betweenpairsof elements, and the compounds so produced again uniting themselves to other compound bodies in the same manner. Thus, in the above example, copper and oxygen combine into oxide of copper, potassium and oxygen into potash, sulphur and oxygen into sulphuric acid; sulphuric acid in its turn combines both with oxide of copper and oxide of potassium, generating a pair of salts which are capable of uniting to form the double compoundCu O,SO3+KO,SO3.
70Fownes’sChemistry. Part iii.
The most complicated products of inorganic chemistry may be thus shown to be built up by this repeatedpairingon the part of their constituents. But with organic bodies the case is remarkably different; no such arrangement can here be traced. In sugar, which isC12H11O11,or morphia71, which isC35H20NO6,the elements are as it were bound together into a single whole, which can enter into combination with other substances, and be thence discharged with properties unaltered; the elements not being obviously arranged in any subordinate groups. Hence the symbols for those substances are such as I have given above, no marks of combination being used.
71Fownes’sChemistry, p. 354.
It is perhaps a consequence of this peculiarity that organic compounds areunstablein comparison with inorganic. In unorganic substances generally the elements are combined in such a way that the most powerful affinities are satisfied72, and hence arises a state of very considerable permanence and durability. But in an organic substance containing three or four elements, there are often opposing affinities nearly balanced, and when one of these tendencies by some accident obtains a preponderance and the equilibrium is destroyed, then the organic body breaks up into two or more new bodies of simpler and more permanent constitution.
72SeeHist. Ind. Sc.b. xiv. c. 3.
There is another property of many organic substances which is called theLaw of Substitution. The364Hydrogen of the organic substance may often be replaced by Chlorine, Bromine, Iodine, or some other elements, without the destruction of the primitive type or constitution of the compound so modified. And this substitution may take place by several successive steps, giving rise to a series of substitution-compounds, which depart more and more in properties from the original substance. This Law also gives rise to a special notation. Thus a certain compound calledDutch liquidhas the elementsC4H4Cl2:but this substance is affected by chlorine (Cl) in obedience to the law of substitution; one and two equivalents of hydrogen being successively removed by the prolonged action of chlorine gas aided by sunshine. The successive products may be thus written
C4H4Cl2;C4{H3Cl}Cl2;C4{H2Cl2}Cl2.
Perhaps at a future period, chemical symbols, and especially those of organic bodies, may be made more systematic and more significant than they at present are.
AphorismXXVII.
In using algebraical symbols as a part of scientific language, violations of algebraical analogy are to be avoided, but may be admitted when necessary.
Aswe must in scientific language conform to etymology, so must we to algebra; and as we are not to make ourselves the slaves of the former, so also, not to the latter. Hence we reject such crystallographical notation as that of Mohs; and in chemistry we useC2,O3rather thanC2,O3, which signify the square ofCand the cube ofO. But we may use, as we have said, both the comma and the sign of addition, for chemical combination, for the sake of brevity, though both steps of combination are really addition.365
AphorismXXVIII.
In a complex science, which is in a state of transition, capricious and detached derivations of terms are common; but are not satisfactory.
Inthis remark I have especial reference to Chemistry; in which the discoveries made, especially in organic chemistry, and the difficulty of reducing them to a system, have broken up in several instances the old nomenclature, without its being possible at present to construct a new set of terms systematically connected. Hence it has come to pass that chemists have constructed words in a capricious and detached way: as by taking fragments of words, and the like. I shall give some examples of such derivations, and also of some attempts which have more of a systematic character.
I have mentioned (Aph.XX.sect. 7) the wordEllagic(acid), made by inverting the wordGalle. Several words have recently been formed by chemists by taking syllables from two or more different words. Thus Chevreul discovered a substance to which he gave the nameEthal, from the first syllables of the wordsetherandalcohol, because of its analogy to those liquids in point of composition73. So Liebig has the wordchloral74.