May 28, 1903] 



NATURE 



79 



the other. So there is complete failure of the theory of metallic 

 circuits. 



But the needed extension is easily made by following Lord 

 Kelvin's method, and using the enlarged meaning of electric 

 current. Let e be the intrinsic voltage per unit length due to 

 reversible thermal action, and let C be the current density. Then 

 eC is the heat per unit volume absorbed per second, and the 

 second thermodynamic law requires that2eC/9 = o,if Ois tempera- 

 ture, the summation to be complete as regards e. Here C may be 

 any circuital current, so e/O is polar ; that is, e= - Qvp, where 

 / is a scalar, the thermoelectric power. In a homogeneous 

 conductor, ;* is a function of the temperature only, to suit 

 Magnus's results. But it is also a function of the material. In 

 what way is not known, but it shows itself at the junction of 

 different metals. Then / changes, say, from /i to /j, so the 

 intrinsic voltage at the junction is Pi2 = ^(/i -/^a)- This is the 

 Peltier force from the first to the second metal. So far is all 

 that is necessary for steady currents. But when the current 

 varies, part of it leaves the metals. Now at a metal-air junction, 

 the thermoelectric power falls from / to o, so there is an 

 additional thermoelectric force FN or /^N acting outwards, 

 N being the unit normal. It is here assumed that the thermo- 

 electric power of air is zero. It does not seem likely that its 

 value is important compared with / in a metal. This FN 

 multiplied by the current leaving the conductor measures the 

 reversible thermal effect at the boundary. The system is now 

 complete, provided there is no external e. But should there 

 be, then it must be counted too, if, for instance, a current is 

 induced in an external conductor. In any case, e= - Qyp will 

 be valid, with the usual proper interpretation of discontinuities, 

 and the Maxwellian meaning of the current. 



It will be sufficient to suppose that p = o outside a circuit of two 

 metals. Then there is the Thomson force in the metals, the Feltier 

 force at the metal junctions, and the metal-air force 

 PN of variable intensity all over the circuit. In 

 the extreme case with which I commenced, there 

 may be only one Peltier force in operation, or 

 even none at all, but just the metal-air force 

 alone. If so, there is reversible evolution of heat 

 at some parts, and absorption at other parts of the 

 boundary. 



As regards the application of the second thermo- 

 dynamic law, it seems to be justified by experi- 

 mental results with steady currents. I see no 

 reason why it should not be applied to variable 

 currents, even when varying very rapidly. For p 

 is a property of the material and its temperature at 

 any place, and has nothing to do at the moment 

 with what is going on at other places. Yet 

 a reservation is necessary. For the second law 

 results from averages. So there must be some 

 limit to the rapidity with which the current at any 

 spot may vary, if the second law is to be fully 

 valid there. 



The Volta contact force must not be forgotten in 

 connection with the metal-air thermoelectric force. 

 Mr. J. Brown has lately made the Volta force 

 disappear by heating it away in oil. If this is fully 

 confirmed, it perhaps proves that chemical action 

 between the metal and an electrolytic film of 

 moisture is the real source of the energy of the 

 transient Volta current, as Mr. Brown maintains. 

 How will this affect the thermal force ? If we 

 allow properly for the change in / in passing 

 through the film from the metal to the air, it 

 seems likely that the thermoelectric effects will be 

 simply superposed upon the Volta effects, because 

 the sources of energy are different. Yet they might 

 have to be combined in some unknown way. 



Returning to the steady current in a circuit of two metals, 

 Lord Kelvin showed that the complete intrinsic voltage amounted 

 10 IpdQ. This does not express the real distribution of intrinsic 

 force in the circuit, and seems to have no meaning. But it has 

 a curious interpretation, which is of importance in the extended 

 theory. The necessity of the metal-air force is shown in another 

 way. I have shown that the source of H in varying states is 

 the curl of e everywhere. Here this is f=Vv/V^. It is zero 

 in a homogeneous conductor, and also at the metal junctions, 

 but has the boundary value VNflv/, which would represent 

 the source of H if there were no metal air force. But add on 



the curl of the metal-air force FN or />flN. It is - VNvP, and 

 the sum of the two is - VN/vfl. Now this is also the curl of 

 the fictitious intrinsic force referred to, that is, pvQ in the metals 

 only. So we come to this striking result, that Lord Kelvin's 

 IpdQ in the metal circuit alone is a fictitious distribution which 

 not only gives the same steady current as the real distribution 

 of intrinsic force, but also gives the true E and H everywhere 

 in variable states as well, provided the real intrinsic forces 

 include the metal-air forces along with the Peltier and Thomson 

 forces. Oliver Heaviside. 



May 18. 



H 



THE FARTHEST NORTH. 

 R.H. Prince Luigi Amedeo of Savoy, Duke of the 

 Abruzzi, has given to the English-reading public 

 a superb account of his great Arctic expedition. ^ Though 

 he has fortunately adopted a smaller size of volume 

 than his Imperial namesake, the Archduke Ludwig 

 Salvator, devotes to his luxurious memoirs on Medi- 

 terranean islands, the book is still both ponderous and 

 imposing. Although in otftavo, it is as large as most 

 quartos, and it is a credit to the publishers in every 

 way. A royal opulence is reflected from the burnished 

 pages, which reflect the light also so perfectly that 

 at night it is impossible, without elaborate precautions, 

 to prevent the image of the lamp-flame from concealing 

 part of the text. The very fine half-tone reproduc- 

 tions of photographs with which the book is crammed 

 profit by the quality of the paper. The portraits of 

 Admiral Markham and Dr. Nansen, illustrating th^ 



■'^'^ 



Fig. I.— Cape Saule 



' On the Fo^uf Star in ihe 



NO. 1752, VOL. 68] 



introduction, are not, however, very happily chosen, 

 and we miss a satisfactory portrait of Captain Cagni, 

 the hero of the memorable journey to the farthest 

 north. 



The royal author writes modestly and well, his 



1 "()n the Polar Star in the Arctic Sea." By His Royal Highness. 

 Luigi Amedeo of Savoy, Di ke of the Abruzzi, with the Statements of 

 Commander U. C?gni upon Ihe Sledge Expedition 10 86° 34' N., and of Dr. 

 A. Cavalli Molimlh upon his Return to the Bay of Teplitz. Translated by- 

 William Le Queux. In two vols. ; with 212 illustrations in the text, 16 fulj- 

 page photogravure plates, 2 panoramas and 5 maps. Pp. 702 -i- xxii + xii. 

 (London : Huichinson and Co., 1903) 



