tenon arrangement which distinguishes Lumbricus from Allolo- view, mathematical formulæ could ever have been constructed. bophora. The male pore is situated normally on segment 15, but as the papilla which carry the pores are large, they extend over the adjoining segments on either side. Earthworms vary greatly in this respect. Rosa says that spermathecæ are absent in this species, a peculiarity which has been noted in worms belonging to several other genera. I have not sufficient material to enable me to confirm or dispute this statement at present. I have counted the segments of three specimens, and found them to be in each instance 106. As the year advances I hope to be able to obtain mature adults for dissection, when it will be possible to give a detailed account of the internal anatomy. Meanwhile the external characters are amply sufficient for distinguishing the worm if the girdle is properly developed, as its nearest British ally (Lumbricus purpureus, Eisen) has the clitellum on segments Idle, Bradford. 28 to 33. HILDERIC FRIEND. The Implications of Science. WILL you allow me to say something in answer to Mr. Dixon's letter on this subject in NATURE of January 21 (p. 272)? (1) I admit that there is a verbal or symbolic "convention if two (or more) persons agree to understand any given words or symbols in a way arbitrarily chosen by themselves. But the scope of such convention is exceedingly limited: if people wish to be understood, or even to understand themselves, they must use the same words as others use, and use them in the same sense (except in an infinitesimal proportion of case). If it is said that the common application and use of current words is a mere convention, the word convention is taken in an extremely strained and metaphorical sense, since nothing like an explicit agreement has ever been made. The "convention as to the use of language is as fictitious as the social contract of Locke and Rousseau. But in the one case, as in the other, there is a solid basis of facts, to suit which the hypothesis has been produced. Language has been moulded by thought and feeling, which, in their turn, have been impressed by facts; and it is facts and relations of facts that language seeks to express. As Mill says (in the first chapter of his "Logic ") names are a clue to things, and bring before us "all the distinctions which have been recognized not by a single inquirer but by all inquirers taken together." No one, I imagine, would say that a particular case of the impossibility of affirming and denying a given statement, depends "solely on the law of contradiction"; but in the case of any particular assertion, the impossibility, in that case, is seen, and to a mind that has reached the generalizing stage, the universal is discernible in the particular. As regards the question of real propositions," I will not occupy space with quotations, but will only refer to Mr. Dixon's letter of December 10, in which the passages occur which led me to think that he regarded assertions (or denials) of the existence of particular objects as the only "real" propositions. 66 (2) As regards induction, I agree with Mr. Dixon that the starting point in induction is hypothesis or discovery. But with reference to the rest of the procedure, and its relation to so-called "formal" logic, I differ from him. For I think that an inductive generalization may be set out syllogistically; e.g., What has once produced X will always produce X; A has once produced X; .. A will always produce X (= all A is X). If space allowed, I should like to consider the justification for the major premiss, and also to say something about the grounds on which the minor (which indicates the hypothesis or discovery) asserts causation [or concomitance] in a given instance. (3) Mr. Dixon says: "We do not, in mathematics, conclude a universal proposition from a single concrete instance." But it appears to me that, as far as my own experience goes, in every concrete mathematical proposition which I understand this is exactly what happens; and I do not see how, on Mr. Dixon's "A mathematical formula," Mr. Dixon remarks, "does not imply the existence of any instance whatever of its application, any more than a definition implies the reality of the thing defined." But if a definition is always of a thing, what more is wanted? The definition is admitted to be of something; and what is something must, I suppose, exist somehow. = (4) I still think that in the passage in Mr. Dixon's letter which I referred to under (4) he is not consistent. For if, as he asserts, the definition of four as I + I + I, makes it false to say that Twice two are four, this is surely because the facts referred to by four are no longer what they were when the statement in question was true. If definitions were purely arbitrary, as Mr. Dixon holds, what would prevent my saying that Four (1+1+1) means twice two (1 + 1) + (I + 1)? It is surely only the reference to things which makes it absurd-(and, however four (4) may be defined, how is one (1) to be understood, except by reference to things?). That words and symbols used intelligibly do, and must, refer to something beyond themselves, seems to me indisputable. If they did not, no assertion of the form S is P could ever be made, for the symbol S is certainly not the symbol P. And for any statement, of the form S is P, to be possible and significant, it is further necessary that S and P should have identical application, but diverse signification. If application and signification were the same, we should get S is S and P is P; if application were not the same, we must say, S is not P. Hence, no term can ever be taken in mere denotation (or application), nor in mere connotation (signification); but both momenta of each term have to be taken into account in every assertion. If (to take a case given by Mr. Dixon in his " Essay on Reasoning," p. 8) we "define metal "the list of denotation, iron, copper, tin, zinc, lead, gold, and silver," then iron, &c., can only be pointed out by taking some specimen of iron, and saying, This and all other things which are LIKE it in certain respects. An absolutely arbitrary denotation can be given only if the whole of the objects denoted are severally pointed out; and even then, unless they are labelled, they can only be remembered and identified by means of their characteristics; if labelled, by that characteristic. as Mr. Dixon objects to my attributing to him the view that "mathematical truths in as far as 'real' are obtained by induction, and are therefore not necessary." But in his letter of December 10 he says:-"For example, the assertion Two straight lines cannot inclose a space' is certainly not a neces sary truth.' Either its terms are defined by connotation, so that its truth depends solely on those definitions, or else its terms are defined by denotation, as representing real things in space; and the truth of the assertion can only be proved by induction from actual experience with those things. In the first case, the might conceivably be false, as was shown by Helmholtz." truth is arbitrary, not necessary; and in the second case it was this passage which led me to the opinion which I expressed. Cambridge, January 31. E. E. C. JONES. Vacuum Tubes and Electric Oscillations. It I HAVE not had the advantage of hearing the lecture of M. Nikola Tesla nor of seeing his experiments, but it does not seem out of place to recall the attention of your readers to an article by Dr. Dragoumis in your issue for April 4, 1889, in vol. xxxix. P. 548. OLIVER J. LODGE. SINC THE NEW STAR IN AURIGA. INCE our last article was written the weather has continued very bad for astronomical observations. The only new results obtained which have reached us consist of a paper read by Mr. Norman Lockyer at the Royal Society on Thursday last, and an important telegram from Prof. Pickering, which appeared in Wednesday's Standard. We will take these in order. Mr. Lockyer's communication to the Royal Society was dated February 8: it stated that two more photographs, containing many more lines than the former ones. were taken on Sunday night, February 7, and it went on to make the important announcement that "The bright lines K, H, h, and G are accompanied by dark lines on their more refrangible sides." This was substantially the substance of the telegram which appeared in the Standard on the following Wednesday (February 10), with the additional remark that the Harvard astronomers thought it possible that the phenomena presented by the new star had been caused by the collision of two celestial bodies. On the next day the detailed observations made on Sunday night at Kensington, together with the approximate wave-lengths of the lines measured on the photographs, were sent on by Mr. Lockyer to the Royal Society. From these we learn that the Nova on Sunday appeared to be slightly brighter than on February 3. With the 10-inch refractor and Maclean spectroscope, C was seen to be very brilliant, and there were four very conspicuous lines in the green. Several fainter lines were also seen, and a dark line was suspected in the orange. Mr. Lockyer noticed that some of the lines, especially the bright one near F, on the less refrangible side, appeared to change rapidly in relative brightness, and this was confirmed by Mr. Fowler. Observations of the spectrum were made by Mr. Fowler with the 3-foot reflector and the Hilger 3-prism spectroscope. These call for no special remark. the Twenty bright lines have been measured on photographs, and their wave-lengths are given in the accompanying table :Lines in the spectrum of Nova Auriga. The table also shows probable coincidences with the lines in the spectra of the Wolf-Rayet stars as photographed by Prof. Pickering, dark lines in Orion stars photographed at Kensington, and bright lines in the Orion nebula photographed at Mr. Lockyer's observatory at Westgate. In addition to the lines recorded in the table, the photographs in the spectrum of the Nova show several lines more refrangible than K. They probably include some of the ultra-violet hydrogen lines. All the lines in the spectrum of the Nova are broad, although in a photograph of the spectrum of Arcturus, taken with the same instrumental conditions, the lines were perfectly sharp. It is also important to note that the broadening of the lines is not accompanied by any falling off of intensity at the edges, as in the case of the hydrogen lines in such a star as Sirius. With the method employed in taking the photographs, long exposures are liable to result in a thickening of all the lines on account of atmospheric tremors. The lines would also be thick if the Nova be hazy. In the photograph, however, all the lines are not equally thick. If the lines are similarly broadened when a slit spectroscope is employed, the effect must be due to internal agitations, for if different regions of the Nova are moving with varying velocity, or with the same velocity in different directions, a normally fine line might be widened in the manner observed in the photographs. With regard to the bright and dark lines the paper states as follows: “A somewhat similar phenomenon has already been recorded by Prof. Pickering in the case of ẞ Lyra, and this has been confirmed by a series of photographs taken at Kensington. In this case the bright lines are alternately more or less refrangible than the dark ones, with a period probably corresponding to the known period of variation in the light of the star. The maximum relative velocity indicated is stated by Prof. Pickering as approximately 300 English miles per second. "In the case of Nova Auriga, the dark lines in all four photographs taken at Kensington are more refrangible than the bright ones, so that as yet there is no evidence of revolution. "The relative velocity indicated by the displacement of the dark lines with respect to the bright ones appears to be over rather than under 500 miles per second. The reduction is not yet complete. 66 Should the photographs which may be obtained in the future continue to show the dark lines displaced to the more refrangible side of the bright ones, it will be a valuable confirmation of my hypothesis as to the causes which produce a new star-namely, the collision of two meteor-swarms On this supposition the spectrum of Nova Aurigæ would suggest that a moderately dense swarm is now moving towards the earth with a great velocity and is disturbed by a sparser one which is receding. The great agitations set up in the dense swarm would produce the dark-line spectrum, while the sparser swarm would give the bright lines." ELECTRODYNAMIC THEORIES AND THE ELECTROMAGNETIC THEORY OF LIGHT IN N a former article we endeavoured to give an account of the first part of M. Poincaré's "Électricité et Optique," in which he dealt with the electric and magnetic theories expounded in Maxwell's treatise. In Part II. he now compares the theory of electromagnetic action given by Maxwell with the somewhat more general theory put forward by Helmholtz in his celebrated paper on the equations of motion of electricity (Pogg. Ann., cii. p. 529, or Wissensch. Abhand., vol. i.); discusses the condition which must hold in order that the two theories may coincide; and, after a masterly exposition of the various consequences which flow from Maxwell's theory, finishes with a very valuable analysis of the theoretical and experimental work of Hertz. In the first chapter M. Poincaré deals with the formula of Ampère for the mutual action of two current elements. The method adopted is founded on the following three principles assumed from Ampère's experiments : (1) That a current in a conductor may be replaced by an equal current in a sinuous conductor nowhere deviating from the first by a distance comparable with the distance of the latter from any element of the other conductor acted upon. 1 Electricité et Optique." II. Les Théories de Helmholtz et les Expériences de Hertz. Par H. Poincaré, Membre de l'Institut. (Paris: Georges Carré, 1891.) (2) The action of a closed circuit carrying a current upon any current element is normal to the element. (3) The action of a closed (non-varying) solenoid upon a current element is zero. It is besides assumed that the action of a circuit upon a current element is the sum, in the dynamical sense, of the individual actions of the elements of the circuit; and that the action between two elements is a force in the straight line joining their centres. The process used for the deduction of Ampère's formula from these premisses is very elegant. If ds, ds' be the lengths of the two elements, 7, 7' the currents in them, the angle between the elements, 0, ' the angles they make with the line joining their centres, the action of ds on ds' may be represented by f(r, 0, 0', e)yy'dsds'. But the action of ds may, by the first principle stated above, be replaced by the actions, of its components dr, dy, dz; so that dz ds' dx ƒ = A ds dy + B + C ds the currents being each unity, and the integrals being taken round the circuits. The determination of U is then effected by means of the third principle. It is first shown that T may be written as the integral of Fdx + Gdy + Hdz round the circuit to which ds belongs, F denoting the integral round the other circuit of Uds'drids' . (x − x')/r, and G, H similar expressions. F, G, H are, in this theory, what Maxwell has called the components of vector potential. These values of F, G, H, it is to be remarked, fulfil the relation dF/dx+dG/dy + dH/dz (= J) = 0. After a The theory of induction is next taken up. short discussion of some objections made by M. Bertrand to the received method of deducing the laws of induction from the observed facts of electromagnetism, M. Poincaré proceeds to show that the electrokinetic energy of two currents is equal to the electrodynamic potential, and recalls Maxwell's application of Lagrange's dynamical equations to the theory of inductive action. He then deals at some length with the celebrated theory put forward by Weber for the action between two quantities, e, e, of electricity, as depending on their distance apart and their motion. This we pass over, with the remark that Poincaré here discusses certain difficulties to which the theory leads in connection with the value it gives for the action between two current elements, and concludes with a short analysis of Maxwell's examination of the theory of induction as deduced from Weber's law. According to Maxwell El. and Mag., vol. ii. p. 445, second edition), Weber's theory gives, for the inductive electromotive force exerted by the circuit in which the current y flows on the other, the equation M. Poincaré points out that this apparent agreement of the two theories is due to the fact that Maxwell has overlooked certain terms which contribute to the value of E, and which do not give a zero result when integrated round a closed circuit. The expressions given by Weber and Neumann for the mutual potential of two current elements are next considered, and shown to be included in the general expression given for the same potential by Helmholtz. By means of this expression Helmholtz's general electrodynamic theory is introduced, and then follows an Maxwell. It is shown that Helmholtz's theory leads to elaborate comparison of the theories of Helmholtz and the value of T for conduction in three dimensions given by the equation T (Fu+ Gv + Hw)d☎, ป · = · jvds' ‚ år/ds'. Ifp be the density of free electricity at any point, By applying the third principle it is proved that, if where have its ordinary signification, and f'(r) = U'2/r, (U' = dU{dr), vf(r) must be a constant, in order that the action of a closed non-varying solenoid on a complete circuit may be zero. Since (r) must be zero at infinity, this gives f(r) = kr; and if the ordinary electromagnetic definition of unit current be taken, k must be unity, so that U'1/r. Hence the attraction between the elements is = I 2yy'dsds' (cos € - cos e cos e'), Ampère's well-known expression. dp/dt, and this, when instead of y'drds' is substituted its value in terms of u, v, w', gives, by an application of Green's theorem, the result 4 = ['rdp'{dt . að', where da' is an element of the space in which the current &c., = 4π11 λ If X, Y, Z are not zero, the electrostatic energy becomes 2π/K. (f)d (which is Maxwell's expression), provided We have to inquire what reasons can be adduced = o in this theory. is λ = 0. for putting These coincide with the equations of currents given by M. Poincaré shows that the velocity of propagation of Maxwell when the last terms are omitted. We must therefore either put a wave of longitudinal displacement in Helmholtz's theory o, or (since do/dt is not in general K/(K - λ)λ. On the other hand, the velocity of zero) o to reduce to Maxwell's theory. Poincaré next proves that unless the in Helmholtz's propagation of a wave of transverse displacement is theory be not less than zero, the sum of the electrostatic/(KA). Thus there will be no longitudinal wave and electrokinetic energies may diminish indefinitely last condition would make the velocity of propagation of if one of the conditions, k = o, λ = o, K = à, hold. The from an infinitely small value. so that there would be unstable equilibrium. This affords another reason for waves of transverse displacement infinite, and must be rejecting the theory of Weber, in which k = 1. rejected for every medium, even so-called vacuum, in which light is propagated. Poincaré adopts the second hypothesis. In chapter v. Poincaré passes from the theory of Helmholtz to that of Maxwell. He first considers magnetic and dielectric polarization according to a modified and corrected version of the theory of Poisson. He supposes the dielectric space filled with conducting particles separated by other material, the dielectric proper, which completely insulates these bodies from one another. These conducting bodies are supposed to be electrically polarized, so that electric displacement (f, g, h) is set up in the medium. A parallel theory of magnetic polarization is considered, and the electric displacement is simply the electric analogue of the intensity of magnetization of the medium-that is, the magnetic moment at each point per unit of volume. If e be the ratio of the volume occupied by the conducting particles to the whole volume of the dielectric space in which they are embedded, the specific inductive capacity, K, of the medium is found to be λ(e), where (e) is a function analogous to (1 + 2€)/(1 − e) (the corresponding function for the case in which the conducting particles are spheres) in that it becomes infinite when (= I. In According to Poincaré, is the specific inductive capacity of the dielectric medium proper, or insulator between these conducting bodies, and is very small. order, therefore, that K may be finite, it is necessary that may be very nearly equal to unity. The electrostatic potential, o, at any point is that due to the free electricity present on conductors, and to the electricity developed throughout the medium by its polarization. The electrification, in fact, consists of two parts-a volume density on the dielectric depending on the electric displacement, and of amount - (df/dx+ dg/dy+dh/dz), and a resultant surface density, o' (f+mg + nh), where σ is the surface density of the electricity present in the form of charges on conductors, and If+mg+nh (in which 7, m, n are the direction cosines of the normal to the surface directed inwards = σ Further, if to a positive value sensibly greater than zero be assigned, a wave of transverse displacement will be given a velocity sensibly greater than that of light. Thus, to pass to Maxwell's theory, it is necessary to make a insensible, as this gives for the velocity of waves of transverse displacement his value 1K, which is known by experiment to be the velocity of light. The adoption of this value of λ leads to all the electromagnetic equations of Maxwell, and to the conditions Jo, du/dx + dv\dy + dw\dz o, the last of which expresses that electricity considered as the analogue of a fluid is incompressible-that is, that all currents flowing are closed currents. = It may be pointed out here that this conclusion agrees with that arrived at by Mr. R. T. Glazebrook in his comparison of Maxwell's electromagnetic equations with those of Helmholtz and Lorentz, and in his further paper on the general equations of the electromagnetic field (Proc. Camb. Phil. Soc., vol. v., Part ii., 1884). Mr. Glazebrook's result is that, the electrostatic potential of Helmholtz's paper must be zero everywhere in order to pass from Helmholtz's theory to that of Maxwell. But is what Poincaré has denoted by λp, so that the conditions are the same. It has been attempted to make the transition to Maxwell's theory by putting k = 0. This would not suffice alone, as Poincaré points out. For, while giving at once J o, it would fail to give Maxwell's velocity for transverse waves unless further X o, which by itself would suffice to effect the transition irrespective of the value of k. = = Poincaré thus supposes, in opposition to the older dielectric theories, that even vacuum, or the ether of the inter-planetary spaces, consists of polarizable conducting matter embedded in an insulating medium of infinitely small inductive capacity, λ. According to Mossotti's theory, which is the starting-point of all tions. = = the first, since du/dx + dvdy + dw/dz λ(e), where p(e) is a quantity which be o, and the second because the magnetic force in the medium, being supposed purely inductive, must fulfil the solenoidal condition, except at the (vortex) origin of the disturbance. There is therefore, in Maxwell's theory, a perfect reciprocity of relation between the electric and magnetic quantities. Hence we might infer, from the magnetic phenomena following from electric currents or flow of electricity, an analogous set of electric phenomena follow It may be said that the infinitely small inductive capa-ing from the flow of magnetism. Now we know that if city, A, of the medium, itself requires physical explanation. This is quite true; but so also does the specific inductive capacity equal to unity assumed for vacuum or air in the ordinary theories. In fact, such dielectric theories as have been put forward, involving merely polarization of the medium, only give an explanation of the difference between the electric behaviour of one medium and another, and furnish none whatever of the real rationale of the propagation of electric action. That the value of o may be finite, it is necessary that the values of the volume density, p, and the surface density, o', may be infinitely small, since Φ Ξ λε σ d'S. λε d☎ + Here p is the volume density due to the surface distributions on the opposite faces of the partitions between the conducting particles, and this, it is easy to see, will be infinitely small. Also, o' is the sum of the actual density (surface density of charge) on the surface of the conductors, and the density, which is the surface manifestation of the polarization of the conducting particles, or = σ − (lf + mg + nh). This also can be conceived as exceedingly small, so that o may have a finite value. Further reasons for preferring the theory of Maxwell are discussed in chapter vi., which is entitled "The Unity of Electric Force." This chapter consists of an exposition of Hertz's modification of Maxwell's electromagnetic theory-a modification, it is to be remarked, practically given also, but in vector form, by Mr Oliver Heaviside, in various papers in the Philosophical Magazine. When made, it exhibits a striking parallelism between the equations of electric and magnetic force, and leads to some remarkable theorems. Using Maxwell's equations, and deviating slightly from Poincaré's mode of presenting the equations, we have, if k now denote electric conductivity of the medium, and P, Q, R components of electric force K d k+ 4π dt P = I (dry - dB). 4 \dy with two similar equations for Q and R. But also we μ da have = I dR dQ a magnet varies in strength it produces an electromotive force of components P, Q, R, at every point of the surrounding space. This we may suppose due to a current of magnetism flowing from one end of the magnet to the other, and thus producing the variation in the magnet's force at any point are in fact coincident with those of the strength. The directions of the components of electric components of vector potential produced by the magnet at that point, and are equal to the time-rates of variation of these components. But why should this not be regarded as an electrostatic field in the ordinary sense of the term? For example, a current of electricity, flowing round a closed circuit, produces a magnetic field equivalent to that which would be produced by a magnetic shell of proper strength, and having its edge coincident with the circuit. Of this current a closed solenoid varying continuously in magnetic strength (for example, a closed solenoid in which the magnetizing current is varying in strength) is the magnetic analogue, and ought in the same way to be equivalent to an electric shell, in the sense of producing an identical electric field. Such a shell ought to be subject in an electric field to dynamical action; and further, two such varying solenoids ought to exert the same mutual dynamical action, as would the two equivalent electric shells if placed in the same configuration. The second of these conclusions asserts that the dynamical action on such a shell depends only on the electric field in which it is placed, and that its action on the other varying solenoid is due to its producing exactly the same electric field as the equivalent electric shell would produce. This is what Poincaré gives as Hertz's principle of the unity of electric force. Of course, it is to be noticed that the second conclusion does not follow from the first. We cannot reason that because the mutual action of an electric shell and a varying solenoid is the same as that of two electric shells, therefore the mutual action of two solenoids is the same as that of two electric shells. If, however, we assume that the dynamical action on a closed varying solenoid depends only on the electric field in which it is placed, we can say that the mutual action of two varying solenoids is the same as that of their equivalent electric shells. M. Poincaré calculates the work done in effecting a relative displacement of two such varying solenoids, and finds that it is equal to the change in the electrostatic energy of the system, as the change in the electrokinetic energy is all accounted for otherwise. Now, the electrostatic energy of a system is given as we have seen by the equation |