In the condensed edition the cartouches of Egyptian kings which stood at the head of the chapters in the second English edition have been placed at the beginning of the book, and Miss Brodrick has added five pages of matter on the Dêr el-Bahari mummies.

We have long hoped that Dr. Brugsch would issue a new edition of his Aegypten unter den Pharaonen," revising his facts in some places, and correcting his statements in others, and also adding the new facts relating to the periods between the VII.-XIth and XIII. XVIIth Dynasties, which have recently come to light; failing this, which is much to be desired, we hoped that one of his pupils would do the work under his guidance. That, however, the English translation made by Seymour and Smith, mutilated and robbed of its notes, and of the additions of the author, should be issued as a popular text-book of Egyptian history under Brugsch's name is a fact which we deplore.

OUR BOOK SHELF.

The Story of the Hills: a Popular Account of Mountains, and how they were made. By the Rev. H. N. Hutchinson, B.A., F.G.S. (London: Seeley and Co., 1892.) THIS is a pleasant, chatty book, all the more welcome because wholly unpretentious; not too deep for "human nature's daily food" when roaming among the hills of which it treats. It will be read with pleasure and profit by the tourist, who likes to know just enough about the sundry points of interest connected with the scene of his wanderings to make the enjoyment of his outing intelligent, but who is not haunted by a feverish anxiety to be for ever, in season and out of season, improving his mind. Many who would shrink from a formal scientific treatise with horror or disgust will find themselves able to enjoy this book, and through its channel scraps of useful knowledge may insinuate themselves into their minds which would never have found their way there by any other road.

Part I. is multifarious, and touches on a vast variety of matters more or less connected with mountains, and principally of human interest-mountain races, mountain legends, the uses of mountains to mankind, mountain storms, avalanches, and the plants and animals of mountains. Scientific explanations of facts and phenomena are interspersed the severe critic may detect a little vagueness and looseness here and there in these, but no very serious lapse. Well-chosen quotations from Ruskin and other authors give brilliancy to the narrative. There are landscape views reproduced from photographs, which have all the excellences and the artistic failings of this class of illustration.

Part II. is mainly taken up with a geological history of mountains. Here all the main geological truths that bear on the subject are expounded clearly, and with great fullness of detail. In fact, an epitome is given of a large number of the leading doctrines of geology, which will suffice for the needs of many a general reader. A separate chapter is devoted to volcanic mountains and volcanic activity. We may note that the three stages in the life of a volcano mentioned on p. 266 are not such as are usually defined by geologists. A. H. G.

The Optics of Photography and Photographic Lenses. By J. Traill Taylor. (London: Whittaker and Co., 1892.)

ALTHOUGH photography is so widely practised at the present day, it is surprising how little is known by

amateurs about the principles that underlie the costruction of photographic lenses.

those who wish to gain this information, and should be The present work will serve as an excellent guide: found to be of great practical use. The author has dea with the subject in a very popular manner, and althoug the mathematics is reduced to a minimum, he has made his meaning very clear throughout.

In the first few chapters the nature and properties light are discussed, together with explanations of photo graphic definition, single and achromatic lenses, cause of the inverted image, spherical aberration, nature and furt tion of diaphragms, nature and cure of distortion, optic centres of single and combination lenses, &c. Chapters xi. to xv. treat solely of lenses, including accounts copying, and universal lenses. As there are thirty-nine of the non-distorting, wide-angle, portrait, landscape. chapters in all, we may mention that of those remainin there are many on subjects which may be of special interest to individual readers. Thus we have a chapter dealing with photo-telescopic lenses, a short one on the grinding of lenses, and another on enlarging and prejecting in relation to lantern optics.

It will be seen that the author has dealt with a wide range of subjects in which the lens makes its ap pearance, and the reader will find that the explanations are lucid, while the illustrations bring out the points which they are intended to show with equal clearness

W.

The Evolution of Life; or, Causes of Change in Anima Forms. A Study in Biology. By Hubbard Winsler Mitchell, M.D. (New York and London: G. 1. Putnam's Sons, 1891.)

DR. MITCHELL says in the preface to this book that he has accomplished in it "all that can be reasonably ex pected from a medical man deeply immersed in the dutie of his profession." What most people expect from medica men in this position is that they will not write books ar vast and complicated subjects, for the proper treatme of which an author must have not only exceptional abrits but ample opportunities for philosophic study. So far a we have examined the work, it has neither freshness thought nor charm of style. Dr. Mitchell mentions the he has travelled in many different parts of the world. he was determined to write a book, he would have bee better employed in recording his reminiscences as traveller than in tediously discussing questions whic have occupied so many of the foremost intellects of th present age.

LETTERS TO THE EDITOR.

[The Editor does not hold himself responsible for opinions pressed by his correspondents. Neither can he unions to return, or to correspond with the writers of res manuscripts intended for this or any other part of Nats No notice is taken of anonymous communications.]

A Magnetic Disturbance.

OUR attention having been directed for some days past tow-a spot of unusual size upon the sun's disk, we were not by a means surprised to observe, as doubtless many of your res elsewhere also did, an aurora of great beauty on Saturday ri last; nor was our anticipation of seeing a magnetic disturba portrayed upon the magnetograph records disappointed ir morning, for when the sheets were changed and the photograp developed, we saw that perturbations more violent than a which had been recorded at Kew for the past ten years bil been in progress since about 5.45 a.m. of February 13.

The magnets were very quiet on Friday, but early on S day morning they became disturbed. The easterly declina

slightly increased until about 5.40 p.m., whilst both horizontal and vertical forces similarly increased in intensity, more especially between 4 and 6 p.m. They further diminished in force after 10 p.m., and their changes became very rapid from 12 midnight to 2 a.m., whilst at the same time the declination proceeded to its extreme westerly position. Subsequently, the fluctuations in magnetism became much reduced in extent, and the whole disturbance gradually diminished and died out about 4 p.m. of Sunday.

The Kew magnetometers were not able to record the complete extent of the vibrations to which free needles were subjected, nor could the entire change of force be secured in the field of the instrument. The limits, however, clearly recorded were 2° of declination from 1760 to 1830 of horizontal force, and from 4350 to 4420 units of vertical force expressed in C.G.S. measure in absolute force. G. M. WHIPPLE, Superintendent.

Kew Observatory, Richmond, Surrey, February 16.

The New Star in Auriga,

PROF. COPELAND has suggested to me that as I am the writer of the anonymous postcard mentioned by you a fortnight ago (p. 325), I should tell your readers what I know about the Nova.

It was visible as a star of the fifth magnitude certainly for two or three days, very probably even for a week, before Prof. Copeland received my postcard. I am almost certain that at two o'clock on the morning of Sunday, the 24th ult., I saw a fifth magnitude star making a very large obtuse angle with 8 Tauri and x Auriga, and I am positive that I saw it at least twice subsequently during that week. Unfortunately, I mistook it on each occasion for 26 Auriga, merely remarking to myself that 26 was a much brighter star than I used to think it. was only on the morning of Sunday, the 31st ult., that I satisfied myself that it was a strange body. On each occasion of my seeing it, it was slightly brighter than x. How long before the 24th ult. it was visible to the naked eye I cannot tell, as it was many months since I had looked minutely at that region of the heavens.

It

IN the morning of the 30th ult. there was a magnificent display of the nacreous (or iridescent, as they were first called) clouds, which formed such a striking feature of the sunset and sunrise sky for some days in succession in December 1884 and 1885 (vol. xxxi. pp. 148, 192, 316, 360, &c.). They were not exactly the same in appearance, but I should say they were of the same nature. I had not seen them in the interval of six years, and have only noticed them lately on the one day mentioned. They were confined to the southern part of the sky. As the sun rose higher their colours were less visible, and the clouds disappeared about noon; though in the afternoon some reappeared, but never became very striking. At 5h. 44m. G.M.T. there was only one group, which was too far from the sun to show any nacreous colours; its centre was about at hour-angle 1h. 2m. west, and declination 23 south. Although conspicuous they were no longer very bright, and I should say the sun evidently not shining on them, for they were the same bluishgreen colour as the western sky, and I apprehend were illuminated by the sky. T. W. BACKHOUSE.

Sunderland, February 9.

The Cause of an Ice Age,

was

In his very kindly review Prof. Darwin thinks I might have stated my argument with more completeness if I had preserved its generality by the use of a symbol instead of taking a special

case.

WITH reference to the letter on the subject of ice crystals which appeared in NATURE of the 4th inst. (p. 319), it is perhaps worth mentioning that a paper on the subject, entitled Eine Eiskrystallgrotte," by C. A. Hering, appeared in Groth's Zeitschrift für Krystallographie und Mineralogie, Band xiv. (1888), pp. 250-253, and Plate vi.

The crystals occurred in an old mine on the Waschgang near Döllach in Carinthia. Large fans, as much as 300 mm. long x 200 mm. broad, of ice-crystals grow out horizontally from the vertical walls. The stalk, consisting of a series of hexagonal prisms, hollow, like thermometer-tubes, was in the middle 25 mm. thick and thickened towards the point of attachment to the rock. The fan surface was a large hexagonal plate with strong prismatic ribs running from the centre to the angles. The interspaces between the ribs were filled by prisms arranged with the greatest regularity. Upon the ribs of the fan either single crystals or funnel-shaped structures with step-like sides consisting of prisms were borne. The individual crystals were almost all thick tabular forms, with prism, basal pinacoid, and rhombohedral faces. BERNARD HOBSON.

Owens College, Manchester, February 8.

A Rare British Earthworm.

IN the summer of 1890, during my researches into the Vermes of Cumberland, I discovered a species of earthworm which proved to be new to Britain (Lumbricus Eiseni, Levinsen). As I have recently had the good fortune to receive specimens of the same worm from another part of the country, it seems desirable to place the same on record. A correspondent writes

from Gloucestershire as follows:-
:-

66

"Last Saturday (January 30, 1892), I walked up to one of my favourite woods here on the Cotswolds, about 700 feet above the sea-a damp old beech wood, the Frith Wood of Withering's Arrangement," seventh edition, 1830-and seeing a stump of some 10 inches diameter with a growth of the black 'Candle Snuff Fungus' on it, I examined the rotten wood, which gave way to the pokes of my stick. Among this rotten wood I saw some earthworms, two or three of which I inclose, hoping they may prove an addition to our worm fauna."

I

I have placed on record all the known earthworms of Gloucestershire in The Field Club for 1891, to which this may now be added. The worms were small, but in good form for identification, and prove to be specimens of Eisen's worm. have, unfortunately, been unable hitherto to consult Levinsen's original description; nor have I been able to obtain Rosa's memoir published in the Boll. Mus. Zoot., Torino, 1889 (vol. iv., No. 71). I am therefore obliged to content myself with a description of the specimens in my possession.

Lumbricus Eiseni, Lev., as found in Britain, is a small species of earthworm, measuring about 1 inches in length when adult. It has the usual colour of the allied species-the purple and red worms--being of a ruddy hue, with iridescence. The clitellum or girdle, which occupies segments (24) 25 to 31, is a reddish-brown, being lighter in colour than the anterior portion of the worm's body on the dorsal surface. Ventrally the worm is, as usual, of a lighter shade. No tubercula pubertatis have been seen under the girdle, but the first dorsal pore in every specimen examined is clearly detected behind the 5th segment. This may be indicated by the fractional sign; and as the most recent researches tend to demonstrate the constancy of this character for each species of earthworm, it is important to note the same. The lip or prostomium has the complete mortise and

The male pore is situated normally on segment 15, but as the papille 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 28 to 33. HILDERIC FRIEND.

Idle, Bradford.

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. 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.

As

(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

view, mathematical formulæ could ever have been constructed. "A mathematical formula," Mr. Dixon remarks, "does no 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 = 1+1+1, 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 refer ence to things which makes it absurd-(and, however four 4 may be defined, how is one (1) to be understood, except by refer ence 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 significa tion were the same, we should get S is S and P is P; if applica tion 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 as "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.

Mr. Dixon objects to my attributing to him the view that "mathematical truths in as far as 'real' are obtained by induc tion, 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 'necessary 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 truth is arbitrary, not necessary; and in the second case might conceivably be false, as was shown by Helmholtz." It was this passage which led me to the opinion which I expressed. Cambridge, January 31. E. E. C. JONES.

SINCE

THE NEW STAR IN AURIGA.

CE 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 com munication 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 photo graphs, 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.

Twenty bright lines have been measured on the photographs, and their wave-lengths are given in the accompanying table :Lines in the spectrum of Nova Aurige.

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 Lyræ, 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 Aurigæ, 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.

"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 Auriga 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 "Electricité 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 now here deviating from the first by a distance comparable with the distance of the latter from any element of the other conductor acted upon.

1 "Électricité et Optique." II. Les Théories de Helmholtz et les Expériences de Heitz. 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.

The above expressions for F, G, H reduce easily to

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, y, y' the currents in them, the angle between the elements, 0, 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 dx, dy, dz; so that dx dy dz ƒ = A + B + C ds ds ds'

where A, B, C are coefficients. Now, f depends upon r, 0, 0', e; r and e' do not depend on the direction cosines of ds; cos and cos are linear and homogeneous with respect to these direction-cosines. Hence ƒ must be linear and homogeneous with respect to cos and that is with respect to drds, and der dsds. Similarly, ƒ is linear and homogeneous with respect to drds',

COS €,

d'r dsds'. Hence we have

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' dr]ds' . (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

=

=

value of f(r), we get the well-known value of the mutual energy of the two circuits

The theory of induction is next taken up. After a 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. 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.

He

discusses certain difficulties to which the theory leads in This we pass over, with the remark that Poincaré here 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 According to Maxwell deduced from Weber's law. Weber's theory gives, for the inductive electromotive ("El. and Mag.," vol. ii. p. 445, second edition), force exerted by the circuit in which the current y flows on the other, the equation

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. 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=

1 f (Fu + Gv + Hw)d☎,

where da is an element of volume, u, v, w the components of currents, and the integral is extended throughout all space. F, G, H, are, of course, the components of vector potential, and in this theory are given by equations