FOOTNOTES [1]I.e., the time-curve.—ED.

[2]The author seems to refer to the fact that in the standard metre, the measurement is taken from the central one of three marks at each end of the bar. The transverse section of the bar is an X, and the reading is made by a microscope.—ED.

[3]I.e. 1/2000 of a millimetre.—ED.

[4]These are the magnitudes and units adopted at the International Congress of Electricians in 1904. For their definition and explanation, see Demanet, Notes de Physique Expérimentale (Louvain, 1905), t. iv. p. 8.—ED.

[5]“Nothing is created; nothing is lost”—ED.

[6]By isothermal diagram is meant the pattern or complex formed when the isothermal lines are arranged in curves of which the pressure is the ordinate and the volume the abscissa.—ED.

[7]Mr Preston thus puts it: “The law [of corresponding states] seems to be not quite, but very nearly true for these substances [i.e. the halogen derivatives of benzene]; but in the case of the other substances examined, the majority of these generalizations were either only roughly true or altogether departed from” (Theory of Heat, London, 1904, p. 514.)—ED.

[8]Methode avec retour en arriere.—ED

[9]Professor Soddy, in a paper read before the Royal Society on the 15th November 1906, warns experimenters against vacua created by charcoal cooled in liquid air (the method referred-to in the text), unless as much of the air as possible is first removed with a pump and replaced by some argon-free gas. According to him, neither helium nor argon is absorbed by charcoal. By the use of electrically-heated calcium, he claims to have produced an almost perfect vacuum.—ED.

[10]Another view, viz. that these inert gases are a kind of waste product of radioactive changes, is also gaining ground. The discovery of the radioactive mineral malacone, which gives off both helium and argon, goes to support this. See Messrs Ketchin and Winterson’s paper on the subject at the Chemical Society, 18th October 1906.—ED.

[11]M. Poincaré is here in error. Helium has never been liquefied.—ED.

[12]Professor Quincke’s last hypothesis is that all liquids on solidifying pass through a stage intermediate between solid and liquid, in which they form what he calls “foam-cells,” and assume a viscous structure resembling that of jelly. See Proc. Roy. Soc. A., 23rd July 1906.—ED.

[13]The metal known as “invar."—ED.

[14]The “second principle” referred to has been thus enunciated: “In every engine that produces work there is a fall of temperature, and the maximum output of a perfect engine—i.e. the ratio between the heat consumed in work and the heat supplied—depends only on the extreme temperatures between which the fluid is evolved."—Demanet, Notes de Physique Expérimentale, Louvain, 1905, fasc. 2, p. 147. Clausius put it in a negative form, as thus: No engine can of itself, without the aid of external agency, transfer heat from a body at low temperature to a body at a high temperature. Cf. Ganot’s Physics, 17th English edition, § 508.—ED.

[15]See next note.—ED.

[16]M. Stephane Leduc, Professor of Biology of Nantes, has made many experiments in this connection, and the artificial cells exhibited by him to the Association française pour l’avancement des Sciences, at their meeting at Grenoble in 1904 and reproduced in their “Actes,” are particularly noteworthy.—ED.

[17]That is, without receiving or emitting any heat.—ED.

[18]Dissociation must be distinguished from decomposition, which is what occurs when the whole of a particle (compound, molecule, atom, etc.) breaks up into its component parts. In dissociation the breaking up is only partial, and the resultant consists of a mixture of decomposed and undecomposed parts. See Ganot’s Physics, 17th English edition, § 395, for examples.—ED.

[19]The valency or atomicity of an element may be defined as the power it possesses of entering into compounds in a certain fixed proportion. As hydrogen is generally taken as the standard, in practice the valency of an atom is the number of hydrogen atoms it will combine with or replace. Thus chlorine and the rest of the halogens, the atoms of which combine with one atom of hydrogen, are called univalent, oxygen a bivalent element, and so on.—ED.

[20]Since this was written, however, men of science have become less unanimous than they formerly were on this point. The veteran chemist Professor Mendeléeff has given reasons for thinking that the ether is an inert gas with an atomic weight a million times less than that of hydrogen, and a velocity of 2250 kilometres per second (Principles of Chemistry, Eng. ed., 1905, vol. ii. p. 526). On the other hand, the well-known physicist Dr A.H. Bucherer, speaking at the Naturforscherversammlung, held at Stuttgart in 1906, declared his disbelief in the existence of the ether, which he thought could not be reconciled at once with the Maxwellian theory and the known facts.—ED.

[21]A natural chlorate of potassium, generally of volcanic origin.—ED.

[22]That is to say, he reflected the beam of polarized light by a mirror placed at that angle. See Turpain, Leçons élementaires de Physique, t. ii. p. 311, for details of the experiment.—ED.

[23]It will no doubt be a shock to those whom Professor Henry Armstrong has lately called the “mathematically-minded” to find a member of the Poincaré family speaking disrespectfully of the science they have done so much to illustrate. One may perhaps compare the expression in the text with M. Henri Poincaré’s remark in his last allocution to the Académie des Sciences, that “Mathematics are sometimes a nuisance, and even a danger, when they induce us to affirm more than we know” (Comptes-rendus, 17th December 1906).

[24]See footnote 3.

[25]I.e. 10,000 metres.—ED.

[26]By this M. Poincaré appears to mean a radiometer in which the vanes are not entirely free to move as in the radiometer of Crookes but are suspended by one or two threads as in the instrument devised by Professor Poynting.—ED.

[27]See especially the experiments of Professor E. Marx (Vienna), Annalen der Physik, vol. xx. (No. 9 of 1906), pp. 677 et seq., which seem conclusive on this point.—ED.

[28]M. Sagnac (Le Radium, Jan. 1906, p. 14), following perhaps Professors Elster and Geitel, has lately taken up this idea anew.—ED.

[29]At least, so long as it is not introduced between the two coatings of a condenser having a difference of potential sufficient to overcome what M. Bouty calls its dielectric cohesion. We leave on one side this phenomenon, regarding which M. Bouty has arrived at extremely important results by a very remarkable series of experiments; but this question rightly belongs to a special study of electrical phenomena which is not yet written.

[30]A full account of these experiments, which were executed at the Cavendish Laboratory, is to be found in Philosophical Transactions, A., vol. cxcv. (1901), pp. 193 et seq.—ED.

[31]The whole of this argument is brilliantly set forth by Professor Lorentz in a lecture delivered to the Electrotechnikerverein at Berlin in December 1904, and reprinted, with additions, in the Archives Néerlandaises of 1906.—ED.

[32]In his work on L’Évolution de la Matière, M. Gustave Le Bon recalls that in 1897 he published several notes in the Académie des Sciences, in which he asserted that the properties of uranium were only a particular case of a very general law, and that the radiations emitted did not polarize, and were akin by their properties to the X rays.

[33]Polonium has now been shown to be no new element, but one of the transformation products of radium. Radium itself is also thought to be derived in some manner, not yet ascertained, from uranium. The same is the case with actinium, which is said to come in the long run from uranium, but not so directly as does radium. All this is described in Professor Rutherford’s Radioactive Transformations (London, 1906).—ED.

[34]This is admitted by Professor Rutherford (Radio-Activity, Camb., 1904, p. 141) and Professor Soddy (Radio-Activity, London, 1904, p. 66). Neither Mr Whetham, in his Recent Development of Physical Science (London, 1904) nor the Hon. R.J. Strutt in The Becquerel Rays (London, same date), both of whom deal with the historical side of the subject, seem to have noticed the fact.—ED.

[35]It has now been shown that polonium when freshly separated emits beta rays also; see Dr Logeman’s paper in Proceedings of the Royal Society, A., 6th September 1906.—ED.

[36]According to Professor Rutherford, in 3.77 days.—ED

[37]Professor Rutherford has lately stated that uranium may possibly produce an emanation, but that its rate of decay must be too swift for its presence to be verified (see Radioactive Transformations, p. 161).—ED.

[38]An actinium X was also discovered by Professor Giesel (Jahrbuch d. Radioaktivitat, i. p. 358, 1904). Since the above was written, another product has been found to intervene between the X substance and the emanation in the case of actinium and thorium. They have been named radio-actinium and radio-thorium respectively.—ED.

[39]Such a table is given on p. 169 of Rutherford’s Radioactive Transformations.—ED.

[40]This opinion, no doubt formed when Sir William Ramsay’s discovery of the formation of helium from the radium emanation was first made known, is now less tenable. The latest theory is that the alpha particle is in fact an atom of helium, and that the final transformation product of radium and the other radioactive substances is lead. Cf. Rutherford, op. cit. passim.—ED.

[41]See Radioactive Transformations (p. 251). Professor Rutherford says that “each of the alpha ray products present in one gram of radium product (sic) expels 6.2 x 1010 alpha particles per second.” He also remarks on “the experimental difficulty of accurately determining the number of alpha particles expelled from radium per second."—ED.

[42]See Rutherford, op. cit. p. 150.—ED.

[43]This view of the case has been made very clear by M. Gustave le Bon in L’Évolution de la Matière (Paris, 1906). See especially pp. 36-52, where the amount of the supposed intra-atomic energy is calculated.—ED.

[44]This is the main contention of M. Gustave Le Bon in his work last quoted.—ED.

[45]See last note.—ED.

[46]In reality M. Sagnac operated in the converse manner. He took two equal weights of a salt of radium and a salt of barium, which he made oscillate one after the other in a torsion balance. Had the durations of oscillation been different, it might be concluded that the mechanical mass is not the same for radium as for barium.

[47]Many theories as to the cause of the lines and bands of the spectrum have been put forward since this was written, among which that of Professor Stark (for which see Physikalische Zeitschrift for 1906, passim) is perhaps the most advanced. That of M. Jean Becquerel, which would attribute it to the vibration within the atom of both negative and positive electrons, also deserves notice. A popular account of this is given in the Athenæum of 20th April 1907.—ED.

[48]An objection not here noticed has lately been formulated with much frankness by Professor Lorentz himself. It is one of the pillars of his theory that only the negative electrons move when an electric current passes through a metal, and that the positive electrons (if any such there be) remain motionless. Yet in the experiment known as Hall’s, the current is deflected by the magnetic field to one side of the strip in certain metals, and to the opposite side in others. This seems to show that in certain cases the positive electrons move instead of the negative, and Professor Lorentz confesses that up to the present he can find no valid argument against this. See Archives Néerlandaises 1906, parts 1 and 2.—ED.

[49]This cannot be said to be yet completely proved. Cf. Sir Oliver Lodge, Electrons, London, 1906, p. 200.—ED.

[50]The reader should, however, be warned that a theory has lately been put forth which attempts to account for crystallisation on purely mechanical grounds. See Messrs Barlow and Pope’s “Development of the Atomic Theory” in the Transactions of the Chemical Society, 1906.—ED.

[51]There is much reason for thinking that the canal rays do not contain positive particles alone, but are accompanied by negative electrons of slow velocity. The X rays are thought, as has been said above, to contain neither negative nor positive particles, but to be merely pulses in the ether.—ED.