THE MONIST

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Ernst Mach

A QUARTERLY MAGAZINE OF

PHILOSOPHY AND SCIENCE.

THE MONIST discusses the fundamental problems of Philosophy in their practical relations to the religious, ethical, and sociological questions of the day. The following have contributed to its columns:

  • Prof. Joseph Le Conte,
  • Dr. W. T. Harris,
  • M. D. Conway,
  • Charles S. Peirce,
  • Prof. F. Max MÜller,
  • Prof. E. D. Cope,
  • Carus Sterne,
  • Mrs. C. Ladd Franklin,
  • Prof. Max Verworn,
  • Prof. Felix Klein,
  • Prof. G. J. Romanes,
  • Prof. C. Lloyd Morgan,
  • James Sully,
  • B. Bosanquet,
  • Dr. A. Binet,
  • Prof. Ernst Mach,
  • Rabbi Emil Hirsch,
  • Lester F. Ward,
  • Prof. H. Schubert,
  • Dr. Edm. Montgomery,
  • Prof. C. Lombroso,
  • Prof. E. Haeckel,
  • Prof. H. HÖffding,
  • Dr. F. Oswald,
  • Prof. J. Delboeuf,
  • Prof. F. Jodl,
  • Prof. H. M. Stanley,
  • G. Ferrero,
  • J. Venn,
  • Prof. H. von Holst.

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FOOTNOTES:

[1] Statique expÉrimentale et thÉorique des liquids, 1873. See also The Science of Mechanics, p. 384 et seqq., The Open Court Publishing Co., Chicago, 1893.

[2] Compare Mach, Ueber die Molecularwirkung der FlÜssigkeiten, Reports of the Vienna Academy, 1862.

[3] In almost all branches of physics that are well worked out such maximal and minimal problems play an important part.

[4] Compare Mach, VortrÄge Über Psychophysik, Vienna, 1863, page 41; Compendium der Physik fÜr Mediciner, Vienna, 1863, page 234; and also The Science of Mechanics, Chicago, 1893, pp. 84 and 464.

[5] Like reflexions are found in QuÉtelet, Du systÈme sociale.

[6] For the full development of this idea see the essay "On the Economical Nature of Physical Inquiry," p. 186, and the chapter on "The Economy of Science," in my Mechanics (Chicago: The Open Court Publishing Company, 1893), p. 481.

[7] Science may be regarded as a maximum or minimum problem, exactly as the business of the merchant. In fact, the intellectual activity of natural inquiry is not so greatly different from that exercised in ordinary life as is usually supposed.

[8] This experiment, with its associated reflexions, is due to Galileo.

[9] A development of the theory of musical audition differing in many points from the theory of Helmholtz here expounded, will be found in my Contributions to the Analysis of the Sensations (English translation by C. M. Williams), Chicago, The Open Court Publishing Company, 1897.

[10] Sauveur also set out from Leibnitz's idea, but arrived by independent researches at a different theory, which was very near to that of Helmholtz. Compare on this point Sauveur, MÉmoires de l'AcadÉmie des Sciences, Paris, 1700-1705, and R. Smith, Harmonics, Cambridge, 1749. (See Appendix, p. 346.)

[11] According to Mr. Jules Andrieu, the idea that nature must be tortured to reveal her secrets is preserved in the name crucible—from the Latin crux, a cross. But, more probably, crucible is derived from some Old French or Teutonic form, as cruche, kroes, krus, etc., a pot or jug (cf. Modern English crock, cruse, and German Krug).—Trans.

[12] Xenophon, Memorabilia iv, 7, puts into the mouth of Socrates these words: ??te ??? e??et? ?????p??? a?t? ?????e? e??a?, ??te ?a???es?a? ?e??? ?? ??e?t? t?? ??t???ta ? ??e???? saf???sa? ??? ???????sa?.

[13] Galilei, Discorsi e dimostrazione matematiche. Leyden, 1638. Dialogo Primo.

[14] In the same way, the pitch of a locomotive-whistle is higher as the locomotive rapidly approaches an observer, and lower when rapidly leaving him than if the locomotive were at rest.—Trans.

[15] A kilometre is 0.621 or nearly five-eighths of a statute mile.

[16] Observe, also, the respect in which the wheel is held in India, Japan and other Buddhistic countries, as the emblem of power, order, and law, and of the superiority of mind over matter. The consciousness of the importance of this invention seems to have lingered long in the minds of these nations.—Tr.

[17] This effect is particularly noticeable in the size of workmen on high chimneys and church-steeples—"steeple Jacks." When the cables were slung from the towers of the Brooklyn bridge (277 feet high), the men sent out in baskets to paint them, appeared, against the broad background of heaven and water, like flies.—Trans.

[18] See Joh. MÜller, Vergleichende Physiologie des Gesichtssinnes, Leipsic, 1826.

[19] Delivered before the German Casino of Prague, in the winter of 1871.

A fuller treatment of the problems of this lecture will be found in my Contributions to the Analysis of the Sensations (Jena, 1886), English Translation, Chicago, 1895. J. P. Soret, Sur la perception du beau (Geneva, 1892), also regards repetition as a principle of Æsthetics. His discussions of the Æsthetical side of the subject are much more detailed than mine. But with respect to the psychological and physiological foundation of the principle, I am convinced that the Contributions to the Analysis of the Sensations go deeper.—Mach (1894).

[20] Kant, in his Prolegomena zu jeder kÜnftigen Metaphysik, also refers to this fact, but for a different purpose.

[21] Compare Mach, Fichte's Zeitschrift fÜr Philosophie, 1864, p. 1.

[22] The fact that the first and second differential coefficients of a curve are directly seen, but the higher coefficients not, is very simply explained. The first gives the position of the tangent, the declination of the straight line from the position of symmetry, the second the declination of the curve from the straight line. It is, perhaps, not unprofitable to remark here that the ordinary method of testing rulers and plane surfaces (by reversed applications) ascertains the deviation of the object from symmetry to itself.

[23] See the lecture On the Causes of Harmony.

[24] A. von Oettingen, Harmoniesystem in dualer Entwicklung. Leipsic and Dorpat, 1866.

[25] Compare Mach's Zur Theorie des GehÖrorgans, Vienna Academy, 1863.

[26] A lecture delivered at the International Electrical Exhibition, in Vienna, on September 4, 1883.

[27] If the two bodies were oppositely electrified they would exert attractions upon each other.

[28] The quantity which flows off is in point of fact less than q. It would be equal to the quantity q only if the inner coating of the jar were wholly encompassed by the outer coating.

[29] Rigorously, of course, this is not correct. First, it is to be noted that the jar L is discharged simultaneously with the electrode of the machine. The jar F, on the other hand, is always discharged simultaneously with the outer coating of the jar L. Hence, if we call the capacity of the electrode of the machine E, that of the unit jar L, that of the outer coating of L, A, and that of the principal jar F, then this equation would exist for the example in the text: (F + A)/(L + E) = 5. A cause of further departure from absolute exactness is the residual charge.

[30] Making allowance for the corrections indicated in the preceding footnote, I have obtained for the dielectric constant of sulphur the number 3.2, which agrees practically with the results obtained by more delicate methods. For the highest attainable precision one should by rights immerse the two plates of the condenser first wholly in air and then wholly in sulphur, if the ratio of the capacities is to correspond to the dielectric constant. In point of fact, however, the error which arises from inserting simply a plate of sulphur that exactly fills the space between the two plates, is of no consequence.

[31] As this definition in its simple form is apt to give rise to misunderstandings, elucidations are usually added to it. It is clear that we cannot lift a quantity of electricity to K, without changing the distribution on K and the potential on K. Hence, the charges on K must be conceived as fixed, and so small a quantity raised that no appreciable change is produced by it. Taking the work thus expended as many times as the small quantity in question is contained in the unit of quantity, we shall obtain the potential. The potential of a body K may be briefly and precisely defined as follows: If we expend the element of work dW to raise the element of positive quantity dQ from the earth to the conductor, the potential of a conductor K will be given by V = dW/dQ.

[32] In this article the solidus or slant stroke is used for the usual fractional sign of division. Where plus or minus signs occur in the numerator or denominator, brackets or a vinculum is used.—Tr.

[33] A sort of agreement exists between the notions of thermal and electrical capacity, but the difference between the two ideas also should be carefully borne in mind. The thermal capacity of a body depends solely upon that body itself. The electrical capacity of a body K is influenced by all bodies in its vicinity, inasmuch as the charge of these bodies is able to alter the potential of K. To give, therefore, an unequivocal significance to the notion of the capacity (C) of a body K, C is defined as the relation Q/V for the body K in a certain given position of all neighboring bodies, and during connexion of all neighboring conductors with the earth. In practice the situation is much simpler. The capacity, for example, of a jar, the inner coating of which is almost enveloped by its outer coating, communicating with the ground, is not sensibly affected by charged or uncharged adjacent conductors.

[34] These formulÆ easily follow from Newton's theorem that a homogeneous spherical shell, whose elements obey the law of the inverse squares, exerts no force whatever on points within it but acts on points without as if the whole mass were concentrated at its centre. The formulÆ next adduced also flow from this proposition.

[35] The energy of a sphere of radius r charged with the quantity q is 1/2(q2/r). If the radius increase by the space dr a loss of energy occurs, and the work done is 1/2(q2/r2)dr. Letting p denote the uniform electrical pressure on unit of surface of the sphere, the work done is also 4r2ppdr. Hence p = (1/8r2p)(q2/r2). Subjected to the same superficial pressure on all sides, say in a fluid, our half sphere would be an equilibrium. Hence we must make the pressure p act on the surface of the great circle to obtain the effect on the balance, which is r2pp = 1/8(q2/r2) = 1/8V2.

[36] The arrangement described is for several reasons not fitted for the actual measurement of potential. Thomson's absolute electrometer is based upon an ingenious modification of the electrical balance of Harris and Volta. Of two large plane parallel plates, one communicates with the earth, while the other is brought to the potential to be measured. A small movable superficial portion f of this last hangs from the balance for the determination of the attraction P. The distance of the plates from each other being D we get V = Dv(8pP/f).

[37] This moment of torsion needs a supplementary correction, on account of the vertical electric attraction of the excited disks. This is done by changing the weight of the disk by means of additional weights and by making a second reading of the angles of deflexion.

[38] The jar in our experiment acts like an accumulator, being charged by a dynamo machine. The relation which obtains between the expended and the available work may be gathered from the following simple exposition. A Holtz machine H (Fig. 40) is charging a unit jar L, which after n discharges of quantity q and potential v, charges the jar F with the quantity Q at the potential V. The energy of the unit-jar discharges is lost and that of the jar F alone is left. Hence the ratio of the available work to the total work expended is

½QV/[½QV + (n/2)qv] and as Q = nq, also V/(V + v).

If, now, we interpose no unit jar, still the parts of the machine and the wires of conduction are themselves virtually such unit jars and the formula still subsists V/(V + Sv), in which Sv represents the sum of all the successively introduced differences of potential in the circuit of connexion.

[39] Published in Vol. 5, No. I, of The Monist, October, 1894, being in part a re-elaboration of the treatise Ueber die Erhaltung der Arbeit, Prague, 1872.

[40] On Matter, Living Force, and Heat, Joule: Scientific Papers, London, 1884, I, p. 265.

[41] "Atqui hoc si sit, globorum series sive corona eundem situm cum priore habebit, eademque de causa octo globi sinistri ponderosiores erunt sex dextris, ideoque rursus octo illi descendent, sex illi ascendent, istique globi ex sese continuum et aeternum motum efficient, quod est falsum."

[42] "A igitur, (si ullo modo per naturam fieri possit) locum sibi tributum non servato, ac delabatur in D; quibus positis aqua quae ipsi A succedit eandem ob causam deffluet in D, eademque ab alia istinc expelletur, atque adeo aqua haec (cum ubique eadem ratio sit) motum instituet perpetuum, quod absurdum fuerit."

[43] "Accipio, gradus velocitatis ejusdem mobilis super diversas planorum inclinationes acquisitos tunc esse aequales, cum eorundum planorum elevationes aequales sint."

[44] "Voi molto probabilmente discorrete, ma oltre al veri simile voglio con una esperienza crescer tanto la probabilitÀ, che poco gli manchi all'agguagliarsi ad una ben necessaria dimostrazione. Figuratevi questo foglio essere una parete eretta all'orizzonte, e da un chiodo fitto in essa pendere una palla di piombo d'un'oncia, o due, sospesa dal sottil filo AB lungo due, o tre braccia perpendicolare all'orizzonte, e nella parete segnate una linea orizontale DC segante a squadra il perpendicolo AB, il quale sia lontano dalla parete due dita in circa, trasferendo poi il filo AB colla palla in AC, lasciata essa palla in libertÀ, la quale primieramente vedrete scendere descrivendo l'arco CBD, e di tanto trapassare il termine B, che scorrendo per l'arco BD sormonterÀ fino quasi alla segnata parallela CD, restando di per vernirvi per piccolissimo intervallo, toltogli il precisamente arrivarvi dall'impedimento dell'aria, e del filo. Dal che possiamo veracemente concludere, che l'impeto acquistato nel punto B dalla palla nello scendere per l'arco CB, fu tanto, che bastÒ a risospingersi per un simile arco BD alla medesima altezza; fatta, e piÙ volte reiterata cotale esperienza, voglio, che fiechiamo nella parete rasente al perpendicolo AB un chiodo come in E, ovvero in F, che sporga in fuori cinque, o sei dita, e questo acciocchÈ il filo AC tornando come prima a riportar la palla C per l'arco CB, giunta che ella sia in B, inoppando il filo nel chiodo E, sia costretta a camminare per la circonferenza BG descritta in torno al centro E, dal che vedremo quello, che potrÀ far quel medesimo impeto, che dianzi concepizo nel medesimo termine B, sospinse l'istesso mobile per l'arco ED all'altezza dell'orizzonale CD. Ora, Signori, voi vedrete con gusto condursi la palla all'orizzontale nel punto G, e l'istesso accadere, l'intoppo si metesse piÙ basso, come in F, dove la palla descriverebbe l'arco BJ, terminando sempre la sua salita precisamente nella linea CD, e quando l'intoppe del chiodo fusse tanto basso, che l'avanzo del filo sotto di lui non arivasse all'altezza di CD (il che accaderebbe, quando fusse piÙ vicino al punto B, che al segamento dell' AB coll'orizzontale CD), allora il filo cavalcherebbe il chiodo, e segli avolgerebbe intorno. Questa esperienza non lascia luogo di dubitare della veritÀ del supposto: imperocchÈ essendo li due archi CB, DB equali e similmento posti, l'acquisto di momento fatto per la scesa nell'arco CB, È il medesimo, che il fatto per la scesa dell'arco DB; ma il momento acquistato in B per l'arco CB È potente a risospingere in su il medesimo mobile per l'arco BD; adunque anco il momento acquistato nella scesa DB È eguale a quello, che sospigne l'istesso mobile pel medesimo arco da B in D, sicche universal-mente ogni memento acquistato per la scesa d'un arco È eguale a quello, che puÒ far risalire l'istesso mobile pel medesimo arco: ma i momenti tutti che fanno resalire per tutti gli archi BD, BG, BJ sono eguali, poichÈ son fatti dal istesso medesimo momento acquistato per la scesa CB, come mostra l'esperienza: adunque tutti i momenti, che si acquistano per le scese negli archi DB, GB, JB sono eguali."

[45] "Constat jam, quod mobile ex quiete in A descendens per AB, gradus acquirit velocitatis juxta temporis ipsius incrementum: gradum vero in B esse maximum acquisitorum, et suapte natura immutabiliter impressum, sublatis scilicet causis accelerationis novae, aut retardationis: accelerationis inquam, si adhuc super extenso plano ulterius progrederetur; retardationis vero, dum super planum acclive BC fit reflexio: in horizontali autem GH aequabilis motus juxta gradum velocitatis ex A in B acquisitae in infinitum extenderetur."

[46] "Si gravitas non esset, neque aËr motui corporum officeret, unumquodque eorum, acceptum semel motum continuaturum velocitate aequabili, secundum lineam rectam."

[47] "Si pondera quotlibet, vi gravitatis suae, moveri incipiant; non posse centrum gravitatis ex ipsis compositae altius, quam ubi incipiente motu reperiebatur, ascendere.

"Ipsa vero hypothesis nostra quominus scrupulum moveat, nihil aliud sibi velle ostendemus, quam, quod nemo unquam negavit, gravia nempe sursum non ferri.—Et sane, si hac eadem uti scirent novorum operum machinatores, qui motum perpetuum irrito conatu moliuntur, facile suos ipsi errores deprehenderent, intelligerentque rem eam mechanica ratione haud quaquam possibilem esse."

[48] "Si pendulum e pluribus ponderibus compositum, atque e quiete dimissum, partem quamcunque oscillationis integrae confecerit, atque inde porro intelligantur pondera ejus singula, relicto communi vinculo, celeritates acquisitas sursum convertere, ac quousque possunt ascendere; hoc facto centrum gravitatis ex omnibus compositae, ad eandem altitudinem reversum erit, quam ante inceptam oscillationem obtinebat."

[49] "Notato autem hic illud staticum axioma etiam locum habere:

"Ut spatium agentis ad spatium patientis
 Sic potentia patientis ad potentiam agentis."

[50] "Cependant, comme dans cet ouvrage on ne fut d'abord attentif qu'À considÉrer ce beau dÉveloppement de la mÉcanique qui semblait sortir tout entiÈre d'une seule et mÊme formule, on crut naturellement que la science etait faite, et qu'il ne restait plus qu'À chercher la dÉmonstration du principe des vitesses virtuelles. Mais cette recherche ramena toutes les difficultÉs qu'on avait franchies par le principe mÊme. Cette loi si gÉnÉrale, oÙ se mÊlent des idÉes vagues et ÉtrangÈres de mouvements infinement petits et de perturbation d'Équilibre, ne fit en quelque sorte que s'obsurcir À l'examen; et le livre de Lagrange n'offrant plus alors rien de clair que la marche des calculs, on vit bien que les nuages n'avaient paru levÉ sur le cours de la mÉcanique que parcequ'ils Étaient, pour ainsi dire, rassemblÉs À l'origine mÊme do cette science.

"Une dÉmonstration gÉnÉrale du principe des vitesses virtuelles devait au fond revenir a Établir le mÉcanique entiÈre sur une autre base: car la demonstration d'une loi qui embrasse toute une science ne peut Être autre chose qua la reduction de cette science À une autre loi aussi gÉnÉrale, mais Évidente, ou du moins plus simple que la premiÈre, et qui partant la rende inutile."

[51] TraitÉ de la lumiÈre, Leyden, 1690, p. 2.

[52] "L'on ne sÇaurait douter que la lumiÈre ne consiste dans le mouvement de certaine matiÈre. Car soit qu'on regarde sa production, on trouve qu'iÇy sur la terre c'est principalement le feu et la flamme qui l'engendrent, lesquels contient sans doute des corps qui sont dans un mouvement rapide, puis qu'ils dissolvent et fondent plusieurs autres corps des plus solides: soit qu'on regarde ses effets, on voit que quand la lumiÈre est ramasseÉ, comme par des miroires concaves, elle a la vertu de brÛler comme le feu. c-est-À-dire qu'elle desunit les parties des corps; ce qui marque assurÉment du mouvement, au moins dans la vraye Philosophie, dans laquelle on conÇoit la cause de tous les effets naturels par des raisons de mechanique. Ce qu'il faut faire À mon avis, ou bien renoncer À tout espÉrance de jamais rien comprendre dans la Physique."

[53] Sur la puissance motrice du feu. (Paris, 1824.)

[54] "On objectra peut-Être ici que le mouvement perpÉtuel, dÉmontrÉ impossible par les seules actions mÉcaniques, ne l'est peut-Être pas lorsqu'on emploie l'influence soit de la chaleur, soit de l'ÉlectricitÉ; mais pent-on concevoir les phÉnomÈnes de la chaleur et de l'ÉlectricitÉ comme dus À autre chose qu'À des mouvements quelconques des corps et comme tels ne doivent-ils pas Être soumis aux lois gÉnÉrales de la mÉcanique?"

[55] By this is meant the temperature of a Celsius scale, the zero of which is 273° below the melting-point of ice.

[56] I first drew attention to this fact in my treatise Ueber die Erhaltung der Arbeit, Prague, 1872. Before this, Zeuner had pointed out the analogy between mechanical and thermal energy. I have given a more extensive development of this idea in a communication to the Sitzungsberichte der Wiener Akademie, December, 1892, entitled Geschichte und Kritik des Carnot'schen WÄrmegesetzes. Compare also the works of Popper (1884), Helm (1887), Wronsky (1888), and Ostwald (1892).

[57] Sir William Thomson first consciously and intentionally introduced (1848, 1851) a mechanical measure of temperature similar to the electric measure of potential.

[58] Compare my Analysis of the Sensations, Jena, 1886: English translation, Chicago, 1897.

[59] A better terminology appears highly desirable in the place of the usual misleading one. Sir William Thomson (1852) appears to have felt this need, and it has been clearly expressed by F. Wald (1889). We should call the work which corresponds to a vanished quantity of heat its mechanical substitution-value; while that work which can be actually performed in the passage of a thermal condition A to a condition B, alone deserves the name of the energy-value of this change of condition. In this way the arbitrary substantial conception of the processes would be preserved and misapprehensions forestalled.

[60] An address delivered before the anniversary meeting of the Imperial Academy of Sciences, at Vienna, May 25, 1882.

[61] Primitive Culture.

[62] Tylor, loc. cit.

[63] Essai philosophique sur les probabilitÉs. 6th Ed. Paris, 1840, p. 4. The necessary consideration of the initial velocities is lacking in this formulation.

[64] Principien der Wirthschaftslehre, Vienna, 1873.

[65] It is clear from this that all so-called elementary (differential) laws involve a relation to the whole.

[66] If it be objected, that in the case of perturbations of the velocity of rotation of the earth, we could be sensible of such perturbations, and being obliged to have some measure of time, we should resort to the period of vibration of the waves of sodium light,—all that this would show is that for practical reasons we should select that event which best served us as the simplest common measure of the others.

[67] Measurement, in fact, is the definition of one phenomenon by another (standard) phenomenon.

[68] I have represented the point of view here taken for more than thirty years and developed it in various writings (Erhaltung der Arbeit, 1872, parts of which are published in the article on The Conservation of Energy in this collection; The Forms of Liquids, 1872, also published in this collection; and the Bewegungsempfindungen, 1875). The idea, though known to philosophers, is unfamiliar to the majority of physicists. It is a matter of deep regret to me, therefore, that the title and author of a small tract which accorded with my views in numerous details and which I remember having caught a glance of in a very busy period (1879-1880), have so completely disappeared from my memory that all efforts to obtain a clue to them have hitherto been fruitless.

[69] Inaugural Address, delivered on assuming the Rectorate of the University of Prague, October 18, 1883.

The idea presented in this essay is neither new nor remote. I have touched upon it myself on several occasions (first in 1867), but have never made it the subject of a formal disquisition. Doubtless, others, too, have treated it; it lies, so to speak, in the air. However, as many of my illustrations were well received, although known only in an imperfect form from the lecture itself and the newspapers, I have, contrary to my original intention, decided to publish it. It is not my intention to trespass here upon the domain of biology. My statements are to be taken merely as the expression of the fact that no one can escape the influence of a great and far-reaching idea.

[70] At first sight an apparent contradiction arises from the admission of both heredity and adaptation; and it is undoubtedly true that a strong disposition to heredity precludes great capability of adaptation. But imagine the organism to be a plastic mass which retains the form transmitted to it by former influences until new influences modify it; the one property of plasticity will then represent capability of adaptation as well as power of heredity. Analogous to this is the case of a bar of magnetised steel of high coercive force: the steel retains its magnetic properties until a new force displaces them. Take also a body in motion: the body retains the velocity acquired in (inherited from) the interval of time just preceding, except it be changed in the next moment by an accelerating force. In the case of the body in motion the change of velocity (AbÄnderung) was looked upon as a matter of course, while the discovery of the principle of inertia (or persistence) created surprise; in Darwin's case, on the contrary, heredity (or persistence) was taken for granted, while the principle of variation (AbÄnderung) appeared novel.

Fully adequate views are, of course, to be reached only by a study of the original facts emphasised by Darwin, and not by these analogies. The example referring to motion, if I am not mistaken, I first heard, in conversation, from my friend J. Popper, Esq., of Vienna.

Many inquirers look upon the stability of the species as something settled, and oppose to it the Darwinian theory. But the stability of the species is itself a "theory." The essential modifications which Darwin's views also are undergoing will be seen from the works of Wallace [and Weismann], but more especially from a book of W. H. Rolph, Biologische Probleme, Leipsic, 1882. Unfortunately, this last talented investigator is no longer numbered among the living.

[71] Written in 1883.

[72] See Pfaundler, Pogg. Ann., Jubelband, p. 182.

[73] See the beautiful discussions of this point in Hering's Memory as a General Function of Organised Matter (1870), Chicago, The Open Court Publishing Co., 1887. Compare also Dubois, Ueber die Uebung, Berlin, 1881.

[74] Spencer, The Principles of Psychology. London, 1872.

[75] See the article The Velocity of Light, page 63.

[76] I am well aware that the endeavor to confine oneself in natural research to facts is often censured as an exaggerated fear of metaphysical spooks. But I would observe, that, judged by the mischief which they have wrought, the metaphysical, of all spooks, are the least fabulous. It is not to be denied that many forms of thought were not originally acquired by the individual, but were antecedently formed, or rather prepared for, in the development of the species, in some such way as Spencer, Haeckel, Hering, and others have supposed, and as I myself have hinted on various occasions.

[77] Compare, for example, Schiller, Zerstreute Betrachtungen Über verschiedene Ästhetische GegenstÄnde.

[78] We must not be deceived in imagining that the happiness of other people is not a very considerable and essential portion of our own. It is common capital, which cannot be created by the individual, and which does not perish with him. The formal and material limitation of the ego is necessary and sufficient only for the crudest practical objects, and cannot subsist in a broad conception. Humanity in its entirety may be likened to a polyp-plant. The material and organic bonds of individual union have, indeed, been severed; they would only have impeded freedom of movement and evolution. But the ultimate aim, the psychical connexion of the whole, has been attained in a much higher degree through the richer development thus made possible.

[79] C. E. von Baer, the subsequent opponent of Darwin and Haeckel, has discussed in two beautiful addresses (Das allgemeinste Gesetz der Natur in aller Entwickelung, and Welche Auffassung der lebenden Natur ist die richtige, und wie ist diese Auffassung auf die Entomologie anzuwenden?) the narrowness of the view which regards an animal in its existing state as finished and complete, instead of conceiving it as a phase in the series of evolutionary forms and regarding the species itself as a phase of the development of the animal world in general.

[80] An address delivered before the General Session of the German Association of Naturalists and Physicians, at Vienna, Sept. 24, 1894.

[81] Inaugural lecture delivered on assuming the Professorship of the History and Theory of Inductive Science in the University of Vienna, October 21, 1895.

[82] The phrase is, Er hat das Pulver nicht erfunden.

[83] "Quod si quis tanta industria exstitisset, ut ex naturae principiis at geometria hanc rem eruere potuisset, eum ego supra mortalium sortem ingenio valuisse dicendum crederem. Sed hoc tantum abest, ut fortuito reperti artificii rationem non adhuc satis explicari potuerint viri doctissimi."—Hugenii Dioptrica (de telescopiis).

[84] I must not be understood as saying that the fire-drill has played no part in the worship of fire or of the sun.

[85] Compare on this point the extremely interesting remarks of Dr. Paul Carus in his Philosophy of the Tool, Chicago, 1893.

[86] MÖbius, Naturwissenschaftlicher Verein fÜr Schleswig-Holstein, Kiel, 1893, p. 113 et seq.

[87] I am indebted for this observation to Professor Hatscheck.

[88] Cf. Hoppe, Entdecken und Finden, 1870.

[89] See the lecture "Sensations of Orientation," p. 282 et seq.

[90] This story was related to me by Jolly, and subsequently repeated in a letter from him.

[91] I do not know whether Swift's academy of schemers in Lagado, in which great discoveries and inventions were made by a sort of verbal game of dice, was intended as a satire on Francis Bacon's method of making discoveries by means of huge synoptic tables constructed by scribes. It certainly would not have been ill-placed.

[92] "Crescunt disciplinae lente tardeque; per varios errores sero pervenitur ad veritatem. Omnia praeparata esse debent diuturno et assiduo labore ad introitum veritatis novae. Jam illa certo temporis momento divina quadam necessitate coacta emerget."

Quoted by Simony, In ein ringfÖrmiges Band einen Knoten zu machen, Vienna, 1881, p. 41.

[93] A lecture delivered on February 24, 1897, before the Verein zur Verbreitung naturwissenschaftlicher Kenntnisse in Wien.

[94] Wollaston, Philosophical Transactions, Royal Society, 1810. In the same place Wollaston also describes and explains the creaking of the muscles. My attention was recently called to this work by Dr. W. Pascheles.—Cf. also Purkinje, Prager medicin. JahrbÜcher, Bd. 6, Wien, 1820.

[95] Similarly many external forces do not act at once on all parts of the earth, and the internal forces which produce deformations act at first immediately only upon limited parts. If the earth were a feeling being, the tides and other terrestrial events would provoke in it similar sensations to those of our movements. Perhaps the slight alterations of the altitude of the pole which are at present being studied are connected with the continual slight deformations of the central ellipsoid occasioned by seismical happenings.

[96] For the popular explanation by unconscious inference the matter is extremely simple. We regard the railway carriage as vertical and unconsciously infer the inclination of the trees. Of course the opposite conclusion that we regard the trees as vertical and infer the inclination of the carriage, unfortunately, is equally clear on this theory.

[97] It will be observed that my way of thinking and experimenting here is related to that which led Knight to the discovery and investigation of the geotropism of plants. Philosophical Transactions, January 9, 1806. The relations between vegetable and animal geotropism have been more recently investigated by J. Loeb.

[98] This experiment is doubtless related to the galvanotropic experiment with the larvÆ of frogs described ten years later by L. Hermann. Compare on this point my remarks in the Anzeiger der Wiener Akademie, 1886, No. 21. Recent experiments in galvanotropism are due to J. Loeb.

[99] Wiener Akad., 6 November, 1873.

[100] Wiener Gesellschaft der Aerzte, 14 November, 1874.

[101] I have made a contribution to this last question in my Analysis of the Sensations, (1886), English translation, 1897.

[102] In my Grundlinien der Lehre von den Bewegungsempfindungen, 1875, the matter occupying lines 4 to 13 of page 20 from below, which rests on an error, is, as I have also elsewhere remarked, to be stricken out. For another experiment related to that of Foucault, compare my Mechanics, p. 303.

[103] Anzeiger der Wiener Akad., 30 December, 1875.

[104] The experiment was specially interesting for me as I had already attempted in 1874, although with very little confidence and without success, to excite electromagnetically my own labyrinth through which I had caused a current to pass.

[105] Perhaps the discussion concerning the peculiarity of cats always falling on their feet, which occupied the Parisian Academy, and, incidentally, Parisian society a few years ago, will be remembered here. I believe that the questions which arose are disposed of by the considerations advanced in my Bewegungsempfindungen (1875). I also partly gave, as early as 1866, the apparatus conceived by the Parisian scientists to illustrate the phenomena in question. One difficulty was left untouched in the Parisian debate. The otolith apparatus of the cat can render it no service in free descent. The cat, however, while at rest, doubtless knows its position in space and is instinctively conscious of the amount of movement which will put it on its feet.

[106] See the Appendix to the English edition of my Analysis of the Sensations, Chicago, 1897.

[107] Compare my Analysis of Sensations, p. 123 ff.

[108] E. H. Weber, De aure et auditu hominis et animalium, Lipsiae, 1820.

[109] StÖrensen, Journ. Anat. Phys., London, Vol. 29 (1895).

[110] A lecture delivered on Nov. 10, 1897.

[111] Christiansen, Wiedemann's Annalen, XXIII. S. 298, XXIV., p. 439 (1884-1885).

[112] The German phrase is Schlierenmethode, by which term the method is known even by American physicists. It is also called in English the "shadow-method." But a term is necessary which will cover all the derivatives, and so we have employed alternatively the words striate and differential. The etymology of schlieren, it would seem, is uncertain. Its present use is derived from its technological signification in glass-manufacturing, where by die Schlieren are meant the wavy streaks and imperfections in glass. Hence its application to the method for detecting small optical differences and faults generally. Professor Crew of Evanston suggests to the translator that schlieren may be related to our slur (L. G., slÜren, to trail, to draggle), a conjecture which is doubtless correct and agrees both with the meaning of schlieren as given in the large German dictionaries and with the intransitive use of our own verb slur, the faults in question being conceived as "trailings," "streakings," etc.—Trans.

[113] An address delivered before the Congress of Delegates of the German RealschulmÄnnerverein, at Dortmund, April 16, 1886. The full title of the address reads: "On the Relative Educational Value of the Classics and the Mathematico-Physical Sciences in Colleges and High Schools."

Although substantially contained in an address which I was to have made at the meeting of Natural Scientists at Salzburg in 1881 (deferred on account of the Paris Exposition), and in the Introduction to a course of lectures on "Physical Instruction in Preparatory Schools," which I delivered in 1883, the invitation of the German RealschulmÄnnerverein afforded me the first opportunity of putting my views upon this subject before a large circle of readers. Owing to the place and circumstances of delivery, my remarks apply of course, primarily, only to German schools, but, with slight modifications, made in this translation, are not without force for the institutions of other countries. In giving here expression to a strong personal conviction formed long ago, it is a matter of deep satisfaction to me to find that they agree in many points with the views recently advanced in independent form by Paulsen (Geschichte des gelehrten Unterrichts, Leipsic, 1885) and Frary (La question du latin, Paris, Cerf, 1885). It is not my desire nor effort here to say much that is new, but merely to contribute my mite towards bringing about the inevitable revolution now preparing in the world of elementary instruction. In the opinion of experienced educationists the first result of that revolution will be to make Greek and mathematics alternately optional subjects in the higher classes of the German Gymnasium and in the corresponding institutions of other countries, as has been done in the splendid system of instruction in Denmark. The gap between the German classical Gymnasium and the German Realgymnasium, or between classical and scientific schools generally, can thus be bridged over, and the remaining inevitable transformations will then be accomplished in relative peace and quiet. (Prague, May, 1886.)

[114] Maupertuis, Œuvres, Dresden, 1752, p. 339.

[115] F. Paulsen, Geschichte des gelehrten Unterrichts, Leipsic, 1885.

[116] There is a peculiar irony of fate in the fact that while Leibnitz was casting about for a new vehicle of universal linguistic intercourse, the Latin language which still subserved this purpose the best of all, was dropping more and more out of use, and that Leibnitz himself contributed not the least to this result.

[117] As a rule, the human brain is too much, and wrongly, burdened with things which might be more conveniently and accurately preserved in books where they could be found at a moment's notice. In a recent letter to me from DÜsseldorf, Judge Hartwich writes:

"A host of words exist which are out and out Latin or Greek, yet are employed with perfect correctness by people of good education who never had the good luck to be taught the ancient languages. For example, words like 'dynasty.' ... The child learns such words as parts of the common stock of speech, or even as parts of his mother-tongue, just as he does the words 'father,' 'mother,' 'bread,' 'milk.' Does the ordinary mortal know the etymology of these Saxon words? Did it not require the almost incredible industry of the Grimms and other Teutonic philologists to throw the merest glimmerings of light upon the origin and growth of our own mother-tongue? Besides, do not thousands of people of so-called classical education use every moment hosts of words of foreign origin whose derivation they do not know? Very few of them think it worth while to look up such words in the dictionaries, although they love to maintain that people should study the ancient languages for the sake of etymology alone."

[118] Standing remote from the legal profession I should not have ventured to declare that the study of Greek was not necessary for the jurists; yet this view was taken in the debate that followed this lecture by professional jurists of high standing. According to this opinion, the preparatory education obtained in the German Realgymnasium would also be sufficient for the future jurists and insufficient only for theologians and philologists. [In England and America not only is Greek not necessary, but the law-Latin is so peculiar that even persons of good classical education cannot understand it.—Tr.]

[119] In emphasising here the weak sides of the writings of Plato and Aristotle, forced on my attention while reading them in German translations, I, of course, have no intention of underrating the great merits and the high historical importance of these two men. Their importance must not be measured by the fact that our speculative philosophy still moves to a great extent in their paths of thought. The more probable conclusion is that this branch has made very little progress in the last two thousand years. Natural science also was implicated for centuries in the meshes of the Aristotelian thought, and owes its rise mainly to having thrown off those fetters.

[120] I would not for a moment contend that we derive exactly the same profit from reading a Greek author in a translation as from reading him in the original; but the difference, the excess of gain in the second case, appears to me, and probably will to most men who are not professional philologists, to be too dearly bought with the expenditure of eight years of valuable time.

[121] "The temptation," Judge Hartwich writes, "to regard the 'taste' of the ancients as so lofty and unsurpassable appears to me to have its chief origin in the fact that the ancients were unexcelled in the representation of the nude. First, by their unremitting care of the human body they produced splendid models; and secondly, in their gymnasiums and in their athletic games they had these models constantly before their eyes. No wonder, then, that their statues still excite our admiration! For the form, the ideal of the human body has not changed in the course of the centuries. But with intellectual matters it is totally different; they change from century to century, nay, from decennium to decennium. It is very natural now, that people should unconsciously apply what is thus so easily seen, namely, the works of sculpture, as a universal criterion of the highly developed taste of the ancients—a fallacy against which people cannot, in my judgment, be too strongly warned."

[122] English: "In the beginning God created the heaven and the earth. And the earth was without form and void; and darkness was upon the face of the deep. And the spirit of God moved upon the face of the waters."—Dutch: "In het begin schiep God den hemel en de aarde. De aarde nu was woest en ledig, en duisternis was op den afgrond; en de Geest Gods zwefde op de wateren."—Danish: "I Begyndelsen skabte Gud Himmelen og Jorden. Og Jorden var ode og tom, og der var morkt ovenover Afgrunden, og Guds Aand svoevede ovenover Vandene."—Swedish: "I begynnelsen skapade Gud Himmel och Jord. Och Jorden war Öde och tom, och mÖrker war pÄ djupet, och Gods Ande swÄfde Öfwer wattnet."—German: "Am Anfang schuf Gott Himmel und Erde. Und die Erde war wÜst und leer, und es war finster auf der Tiefe; und der Geist Gottes schwebte auf dem Wasser."

[123] Compare Herzen's excellent remarks, De l'enseignement secondaire dans la Suisse romande, Lausanne, 1886.

[124] Geschichte der Mathematik, Leipsic, 1874.

[125] Geometrische Analyse, Ulm, 1886.

[126] In his text-books of elementary mathematics

[127] Abhandlungen aus dem Gebiete der Mathematik, WÜrzburg, 1883.

[128] My idea here is an appropriate selection of readings from Galileo, Huygens, Newton, etc. The choice is so easily made that there can be no question of difficulties. The contents would be discussed with the students, and the original experiments performed with them. Those scholars alone should receive this instruction in the upper classes who did not look forward to systematical instruction in the physical sciences. I do not make this proposition of reform here for the first time. I have no doubt, moreover, that such radical changes will only be slowly introduced.

[129] Die Mathematik als Lehrgegenstand des Gymnasiums, Berlin, 1883.

[130] Wrong as it is to burden future physicians and scientists with Greek for the sake of the theologians and philologists, it would be just as wrong to compel theologians and philologists, on account of the physicians, to study such subjects as analytical geometry. Moreover, I cannot believe that ignorance of analytical geometry would be a serious hindrance to a physician that was otherwise well versed in quantitative thought. No special advantage generally is observable in the graduates of the Austrian gymnasiums, all of whom have studied analytical geometry. [Refers to an assertion of Dubois-Reymond.]

[131] Compare M. Cantor, Geschichte der Mathematik, Leipsic, 1880, Vol. I. p. 193.

[132] Compare Paulsen, l. c., pp. 607, 688.

[133] It is to be hoped that the Americans will jealously guard their schools and universities against the influence of the State.

[134] This article, which appeared in the Proceedings of the German Mathematical Society of Prague for the year 1892, is printed as a supplement to the article on "The Causes of Harmony," at page 32.

[135] The present exposition is taken from the volumes for 1700 (published in 1703) and for 1701 (published in 1704), and partly also from the Histoire de l'AcadÉmie and partly from the MÉmoires. Sauveur's later works enter less into consideration here.

[136] Euler, Tentamen novae theoriae musicae, Petropoli, 1739.

[137] In attempting to perform his experiment of beats before the Academy, Sauveur was not quite successful. Histoire de l'AcadÉmie, AnnÉe 1700, p. 136.

[138] Histoire de l'AcadÉmie, AnnÉe 1701, p. 134.

[139] Ibid., p. 298.

[140] Histoire de l'AcadÉmie, AnnÉe 1702, p. 91.

[141] From the Histoire de l'AcadÉmie, AnnÉe 1700, p. 139.

[142] Because all octaves in use in music offer too great differences of rates of vibration.

[143] "Les battemens ne plaisent pas À l'Oreille, À cause de l'inÉgalitÉ du son, et l'on peut croire avec beaucoup d'apparence que ce qui rend les Octaves si agrÉables, c'est qu'on n'y entend jamais de battemens.

"En suivant cette idÉe, on trouve que les accords dont on ne peut entendre les battemens, sont justement ceux que les Musiciens traitent de Consonances, et que ceux dont les battemens se font sentir, sont les Dissonances, et que quand un accord est Dissonance dans une certaine octave et Consonance dans une autre, c'est qu'il bat dans l'une, et qu'il ne bat pas dans l'autre. Aussi est il traitÉ de Consonance imparfaite. Il est fort aisÉ par les principes de Mr. Sauveur qu'on a Établis ici, de voir quels accords battent, et dans quelles Octaves au-dessus on au-dessous du son fixe. Si cette hypothÈse est vraye, elle dÉcouvrira la vÉritable source des RÈgles de la composition, inconnue jusqu'À prÉsent À la Philosophie, qui s'en remettait presque entiÈrement au jugement de l'Oreille. Ces sortes de jugemens naturels, quelque bisarres qu'ils paroissent quelquefois, ne le sont point, ils ont des causes trÈs rÉelles, dont la connaissance appartient À la Philosophie, pourvue qu'elle s'en puisse mettre en possession."

[144] Harmonics or the Philosophy of Musical Sounds, Cambridge, 1749. I saw this book only hastily in 1864 and drew attention to it in a work published in 1866. I did not come into its actual possession until three years ago and then only did I learn its exact contents.

[145] Harmonics, pp. 118 and 243.

[146] "Short cycle" is the period in which the same phases of the two co-operant tones are repeated.

[147] This article, designed to illustrate historically that on Symmetry, at page 89, first appeared in Fichte's Zeitschrift fÜr Philosophie, for 1865.

[148] Comp. Cornelius, Ueber das Sehen; Wundt, Theorie der Sinneswahrnehmung.

[149] Comp. Mach, Ueber das Sehen von Lagen and Winkeln. Sitzungsb. der Wiener Akademie, 1861.

[150] Comp. Mach, Zur Theorie des GehÖrorgans. Sitsungsber, der Wiener Akad., 1863.—Ueber einige Erscheinungen der physiolog. Akustik. Ibid., 1864.






                                                                                                                                                                                                                                                                                                           

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