BOOK IV. (continued 3)

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 the History (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 his Archetype 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 the History 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 of Special Homology by which the bones of all vertebrates are referred to their corresponding bones in the human skeleton, and of General Homology, by which the bones are referred to the parts of vertebræ which they represent, Mr. Owen treats of Serial 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, the basioccipital, basisphenoid, presphenoid and vomer are homotypes with the centrums of all succeeding vertebræ. The excoccipitals, alisphenoids, orbitosphenoids, and prefrontals, are homotypes with the neurapophyses of all the succeeding vertebræ. The paroccipitals, mactoids and postfrontals, with the transverse processes of 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.

Aphorism XXVI.

In the Terminology of Science it may be necessary to employ letters, numbers, and algebraical symbols.

1. Mineralogy.

I have already said, in Aphorism XV., that symbols have been found requisite as a part of the terminology of Mineralogy. The names proposed by Haüy, borrowed from the crystalline laws, were so inadequate and unsystematic that they could not be retained. He himself proposed a notation for crystalline forms, founded upon his principle of the derivation of such forms from a primitive form, by decrements, on its edges or its angles. To denote this derivation he took the first letters of the three syllables to mark the faces of the PriMiTive form, P, M, T; the vowels A, E, I, O to mark the angles; the consonants B, 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, ¹_B represented the result of a derivation by a decrement of one row on an edge; that is, a rhombic octahedron; and ¹_BP represented 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 by B² ^½_C G² 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 by R, he derived, by a certain process, a series of other rhombohedrons, which he denoted by R + 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.

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)³ we might write 2 R 3. 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 letters O, R, P; and from these are derived, by certain laws, such symbols as

3 O ½, ∞ R 2, ½ P 2,

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 by three numerical 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 not holohedral but hemihedral, 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 under Aphorism 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 numerical relations which it was very important to keep in sight. If N represents Nitrogen and O Oxygen, the compounds of the two elements just mentioned might be denoted by N + 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.

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. If Fe be iron and C be carbon, Fe + O will be the protoxide of iron, and C + 2O will 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 proposed68 that in the first stage of composition the oxygen should be expressed by dots over the letter; and thus the carbonate of iron would be Ḟe + C̈. But Berzelius further introduced into his notation indexes such as in algebra denote involution to the square, cube, &c. Thus Cu being copper, the sulphate of copper is represented by S⃛²C̈u. 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, who 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 + 10H² O.

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.

‘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

K̈ S⃛² + 2A⃛l S⃛³ + 48H² O.

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.

‘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, by KS⁶, KS⁸, KS¹⁰ and 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 is Cu 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) a binary plan of combination, union taking place between pairs of 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 compound Cu O, SO₃ + KO, SO₃.

The most complicated products of inorganic chemistry may be thus shown to be built up by this repeated pairing on the part of their constituents. But with organic bodies the case is remarkably different; no such arrangement can here be traced. In sugar, which is C₁₂ H₁₁ O₁₁, or morphia71, which is C₃₅ H₂₀ NO₆, 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.

It is perhaps a consequence of this peculiarity that organic compounds are unstable in 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.

There is another property of many organic substances which is called the Law of Substitution. The Hydrogen 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 called Dutch liquid has the elements C₄ H₄ Cl₂: 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

C4 H4 Cl2; 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.

Aphorism XXVII.

In using algebraical symbols as a part of scientific language, violations of algebraical analogy are to be avoided, but may be admitted when necessary.

As we 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 use C₂, O₃ rather than C², O³, which signify the square of C and the cube of O. 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.

Aphorism XXVIII.

In a complex science, which is in a state of transition, capricious and detached derivations of terms are common; but are not satisfactory.

In this 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 word Ellagic (acid), made by inverting the word Galle. 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 name Ethal, from the first syllables of the words ether and alcohol, because of its analogy to those liquids in point of composition73. So Liebig has the word chloral74.

Liebig, examining the product of distillation of alcohol, sulphuric acid and amber, found a substance which he termed Aldehyd, from the words Alcohol dehydrogenated75. This mode of making Words has been strongly objected to by Mr. Dumas76. Still more has he objected to the word Mercaptan (of Zeise), which he says rests upon a mere play of words; for it means both mercurium captans and mercurio aptum.

Dumas and Peligot, working on pyroligneous acids, found reason to believe the existence of a substance77 which they called methylene, deriving the name from methy, a spirituous fluid, and hyle, wood. Berzelius remarks that the name should rather be methyl, and that ὕλη may be taken in its signification of matter, to imply the Radical of Wine: and he proposes that the older Æther-Radical, C₄ H₁₀ shall be called Æthyl, the newer, C₂ H₆, Methyl.

This notion of marking by the termination yl the hypothetical compound radical of a series of chemical compounds has been generally adopted; and, as we see from the above reference, it must be regarded as representing the Greek word ὕλη: and such hypothetical radicals of bases have been termed in general basyls.

Bunsen obtained from Cadet’s fuming liquid a substance which he called Alkarsin (alkali-arsenic?): and the substance produced from this by oxidation he called Alkargen78. Berzelius was of opinion, that the true view of its composition was that it contained a compound ternary radical = C⁶ H¹² As², after the manner of organic bodies; and he proposed for this the name79 Kakodyl. Alkarsin is Kakodyl-oxyd, K̇d, Alkargen is Kakodyl-acid, K̈̇d.

The discovery of Kakodyl was the first instance of the insulation of an organic metallic basyl80.

The first of the Hydrocarbon Radicals of the Alcohols was the radical of Tetrylic alcohol obtained by Kolbe from Valerate of Potash, and hence called Valyl C₁₆ H₁₈. Chloroform is perchloride of formyl, the hypothetical radical of formic acid81.

The discovery of such bases goes back to 1815. The substance formerly called Prussiate of Mercury, being treated in a particular manner, was resolved into metallic mercury and Cyanogen. This substance, Cyanogen, is, according to the older nomenclature, Bicarburet of Nitrogen; but chemists are agreed that its most convenient name is Cyanogen, proposed by its discoverer, Gay-Lussac, in 181582. The importance of the discovery consists in this; that this substance was the first compound body which was distinctly proved to enter into combination with elementary substances in a manner similar to that in which they combine with each other.

The truth of our Aphorism (XXV.) that in such a science as chemistry, the history of the scientific nomenclature is the history of the science, appears from this; that the controversies with respect to chemical theories and their application take the form of objections to the common systematic names and proposals of new names instead. Thus a certain compound of potassa, sulphur, hydrogen, and oxygen, may be regarded either as Hydrosulphate of Potassa, or as Sulphide of Potassium in solution, according to different views83. In some cases indeed, changes are made merely for the sake of clearness. Instead of Hydrochloric and Hydrocyanic acid, many French writers, following Thenard, transpose the elements of these terms; they speak of Chlorhydric and Cyanhydric acid; by this means they avoid any ambiguity which might arise from the use of the prefix Hydro, which has sometimes been applied to compounds which contain water84.

An incompleteness in chemical nomenclature was further felt, when it appeared, from the properties of various substances, that mere identity in chemical composition is not sufficient to produce identity of chemical character or properties85. The doctrine of the existence of compounds identical in ultimate composition, but different in chemical properties, was termed Isomerism. Thus chemists enumerate the following compounds, all of which contain carbon and hydrogen in the proportion of single equivalents of each86;—Methylene, Olefiant gas, Propylene, Oil gas, Amylene, Caproylene, Naphthene, Eleene, Peramylene, Cetylene, Cerotylene, Melissine.

I will, in the last place, propound an Aphorism which has already offered itself in considering the history of Chemistry87 as having a special bearing upon that Science, but which may be regarded as the supreme and ultimate rule with regard to the language of Science.

Aphorism XXIX.

In learning the meaning of Scientific Terms, the history of science is our Dictionary: the steps of scientific induction are our Definitions.

It is usual for unscientific readers to complain that the technical terms which they meet with in books of science are not accompanied by plain definitions such as they can understand. But such definitions cannot be given. For definitions must consist of words; and, in the case of scientific terms, must consist of words which require again to be defined: and so on, without limit. Elementary substances in chemistry, for instance, what are they? The substances into which bodies can be analysed, and by the junction of which they are composed. But what is analysis? what is composition? We have seen that it required long and laborious courses of experiment to answer these questions; and that finally the balance decided among rival answers. And so it is in other cases. In entering upon each science, we come upon a new set of words. And how are we to learn the meaning of this collection of words? In what other language shall it be explained? In what terms shall we define these new expressions? To this we are compelled to reply, that we cannot translate these terms into any ordinary or familiar language. Here, as in all other branches of knowledge, the meaning of words is to be sought in the progress of thought. It is only by going back through the successful researches of men respecting the composition and elements of bodies, that we can learn in what sense such terms can be understood, so as to convey real knowledge. In order that they may have a meaning for us, we must inquire what meaning they had in the minds of the authors of our discoveries. And the same is the case in other subjects. To take the instance of Morphology. When the beginner is told that every group of animals may be reduced to an Archetype, he will seek for a definition of Archetype. Such a definition has been offered, to this effect: the Archetype of a group of animals is a diagram embodying all the organs and parts which are found in the group in such a relative position as they would have had if none had attained an excessive development. But, then, we are led further to ask, How are we in each case to become acquainted with the diagram; to know of what parts it consists, and how they are related; and further; What is the standard of excess? It is by a wide examination of particular species, and by several successive generalizations of observed facts, that we are led to a diagram of an animal form of a certain kind, (for example, a vertebrate;) and of the various ways, excessive and defective, in which the parts may be developed.

This craving for definitions, as we have already said, arises in a great degree from the acquaintance with geometry which most persons acquire at an early age. The definitions of geometry are easily intelligible by a beginner, because the idea of space, of which they are modifications, is clearly possessed without any special culture. But this is not and cannot be the case in other sciences founded upon a wide and exact observation of facts.

It was formerly said that there was no Royal Road to Geometry: in modern times we have occasion often to repeat that there is no Popular Road—no road easy, pleasant, offering no difficulty and demanding no toil,—to Comparative Anatomy, Chemistry or any other of the Inductive Sciences.

THE END.

CAMBRIDGE: PRINTED BY C. J. CLAY, M.A. AT THE UNIVERSITY PRESS.

Transcriber’s Notes

Adaptations in this text

In the present text footnotes are numbered by Book and are placed after the paragraph to which they attach; in the original, notes were numbered by chapter. Page numbers appear in colour; where a word was hyphenated across pages the number has been placed before the word. Fractions have been transcribed as numerator ⁄ denominator; the original usually has numerator over a line with denominator below.

Some unusual symbols occur. On pages 357 and 358, there are italic letters with a number written above them. On two occasions B has a 1 above it, and once C has ½ above it. On page 364 a formula is written with two entries containing H on a line above Cl. These superpositions have all been transcribed by superscripting the first and subscripting the second item (with the result that the letters are printed smaller than in the original). The other oddities have been captured in Unicode.

On pages 152 and 197 Whewell uses a raised dot as a decimal point and in footnote 26 of Book III. a comma. These have been replaced by a mid dot.

Inductive Charts

Corrections

Corrections are comparatively few. Apart from the silent ones, they have been marked by dotted red underline, on mouse-over revealing the nature of the change. Given the various editions, some of the internal cross-references turn out to be obsolete or erroneous: note 11 in Book III. The text reads B. viii. c. iii. but it refers actually to Book viii. c. ii. article 3 in earlier editions and in the History of Scientific Ideas, cf. Aphorism 88 in Book I. of the present volume. Compare also Aphorism 19 in this volume’s Book IV. notes 58 and 59 in Book III. refer to Book v. c. i. For the present third edition they should have been aimed at that chapter of the History of Scientific Ideas. On page 252 we are told that the Work is about to conclude, as the first edition did in a way (all the aphorisms were gathered after Book XIII. [= our Book III.], followed by various appendices). But we have Book IV. yet to come, plus some extra illustrations regarding language and symbols in science.

(I might add that I have not checked the many references to Whewell’s other related works. The errors here suggest one might need to take them with a pinch of salt, and help from the browser’s search function.)

There are some inconsistencies, notably in spelling, which have in general not been adjusted; nor have Whewell’s unbalanced quotation marks and positioning of footnote anchors been modernized.