May 11, 1883.] 



SCIENCE). 



391 



The fact cannot be concealed, however, that 

 the eruptive apparatus of this last upheaval 

 has been left in a state which furnishes a con- 

 stant menace to the neighboring villages. On 

 account of the sudden cessation of action, the 

 secondary' phenomena have not taken place, 

 by which nature usually brings about a perma- 

 nent end to these parasitic craters. It is, then, 

 among the possibilities of the near future, that 

 another eruption may take place on the same 

 spot where the late one has proved abortive. 



. MA GNE TO-MO TI VE FOR CE. 



" Faraday compared a magnet to a voltaic battery 

 immersed in water; ^ and be established by experi- 

 ment tlie principal analogies on wbicb tbis comparison 

 is founded." Mr. E. H. M. Bosanquet, from whom 

 the above is quoted,'-' tbinlis tbat too little bas been 

 made of tbis analogy, wbicb seems to bim to furnish 

 the only sound view of magnetism. He would speali 

 of a permanent magnet as possessing a certain ' mag- 

 neto-motive force,' which, acting througb a circuit 

 made up of tbe magnet and the bodies or medium sur- 

 rounding tbe magnet, jiroduces tbrougbout tbis cir- 

 cuit a total magnetic induction, equal to tbe quotient 

 of tbe magneto-motive force by tbe ' magnetic resist- 

 ance.' So-called magnetic substances are those in 

 wbicb tbe marinetic conductioity is great; and bodies 

 of this sort, when brought near a magnet, become 

 parts of the magnetic circuit, whose resistance they 

 lessen, just as masses of metal jjlaced in the water 

 forming part of an electric circuit would lessen tbe 

 total electrical resistance of such a circuit. 



Moreover, a new distribution of tbe lines of mag- 

 netic induction is brougbt about by tbe entrance of 

 the magnetic body into tbe field ; tbis body receiv- 

 ing and transmitting a larger proportion of the lines 

 of magnetic induction than the space it now occupies 

 received and transmitted when filled by air. Tbe 

 body is now said, in ordinary terms, to be magnetized. 

 At tbe same time, tbe lines of magnetic induction, 

 being deflected from tbeir most direct course, and 

 buncbed together where they approach tbe magnetic 

 body to enter it, encounter in tbat region an increased 

 air-resistance. A like condition of tbings exists in 

 the air-region wbere tbey are departing from tbe 

 magnetic body ; and tbe effect of these increased air- 

 resistances is to make tbe number of lines of mag- 

 netic induction tbrough tbe body less than it would 

 otherwise be. Tliis air-resistance near the surface 

 has for its equivalent in tbe ordinary tbeory tbe 

 ' demagnetizing ' actioji wbicb tbe induced magne- 

 tism of a body exerts upon the interior jjarticles of 

 the body itself.-^ In tbe case of a very tbin disk, 

 magnetized by induction in a direction normal to its 

 surface, the ordinary tbeory says that tbe demagne- 

 tizing action of tbe free magnetism of tbe surfaces 

 almost neutralizes witbin tbe disk the effect of the 

 external magnetizing forces, so tbat the magnetic 

 induction in tbe disk is scarcely more intense than 

 that in the air about it. The other tbeory explains 

 the fact by saying tbat the superior magnetic con- 

 ductivity of tbe disk is not able, acting for so short 

 a distance, to seriously affect tbe course of the lines 

 of induction in its neighborhood by making it advan- 



1 Exp. res., iii. § 3276. 

 3 Faraday, Exp. ros., ii 

 old edition. 



tageous for these lines to bend from their normal 

 course in order to pass through the disk. 



Mr. Bosanquet's article is an attempt to prepare 

 Faraday's theory for use in numerical calculations by 

 furnishing it with exact quantitative definitions, and 

 to show by tbe results of experiment tbat tbe tbeory 

 is fitted for such work. In doing tbis he thinks it 

 necessary to make essential changes in well-known 

 and widely received formulas. 



Mr. Bosanquet states tbe ordinary theory thus : 

 " Now, the fundamental hypothesis at the base of 

 the ordinary mathematical theory of magnetism is, 

 that there are magnetizing forces ^ which are of the 

 dimensions of tbe magnetic Induction i!3 which they 

 produce, and that tbe magnetizing force permeates 

 every medium, and produces in magnetic media mag- 

 netic induction proportional to the force and to a 

 co-efBcient of permeability n, quite indeiiendently of 

 tbe existence of any magnetic circuit." To this Mr. 

 Bosanquet objects; one of bis objections being, that 

 " we have to suppose that the magnetizing force ip 

 witbin a magnetic body has the power of remaining 

 separate and distinct from the magnetic induction as 

 a whole, though tbe two are quantities of tbe same 

 nature." In bis theory "tbe quantity !0 becomes 

 merely the magnetic induction in vacant space, and 

 4* tbat in magnetic matter. 5S replaces to, and is not 

 supposed to include it as before." 



Instead of remaining 



ii = .<!) -t- 4 ff 3, or It = 1 + inK,^ 

 " our fundamental equation becomes 



|U = 47r/c, or SB = 47r3." 



The formula 



33 = .'p -f- 4 IT oi, or fi = 1 + 4 •n'li, 

 adopted by Maxwell and others, might, according to 

 Mr. Bosanquet, lead to serious errors. Thus in a 

 sphere of infinite magnetic permeability, magnetized 

 by induction, Stefan, he says, has shown tbat " tbe 

 ratio of tbe number of lines of force tbrough its 

 equatorial section to tbe number through the same 

 section in air" is .3. Practically tbe same result is 

 obtained from one of Thomson's papers, and Mr. 

 Bosanquet confirms these results by a calculation in 

 accordance with tbe views be is advocating. 



He attempts now to show that Maxwell, using the 

 formulas above, would make tbis ratio 4 instead of 3. 

 A similar error would, be thinks, occur in calculat- 

 ing, according to Maxwell, the corresponding ratio 

 for the case of a disk of infinite conductivity. 



However interesting and suggestive certain parts 

 of Mr. Bosanquet's paper maybe, there is little doubt 

 tbat be bas here met tbe usual fate of those who at- 

 tempt to convict Maxwell of error in reasoning. It is 

 easy to show that Maxwell's formulas are in complete 

 accord with the result above obtained from Stefan 

 and Thomson. Thus (p. 66, vol. ii., old edition) 

 Maxwell says tbat " in the case of a sphere the ratio 

 of tbe magnetization to the magnetizing force is . . ., 

 and if ic were infinite the ratio would be as 1 to 

 4.19," etc. This result Mr. Bosanquet quotes, but 

 from tbat point he goes wrong. On the next page of 

 Maxwell, where be is discussing tbe demagnetizing 

 forces which tbe poles of a magnetized body exert 

 upon the 'interior particles' of the body itself, we 

 read, "If the magnet were a sphere the demagnetiz- 

 ing force would be ij-ffl." The symbol I here, like 

 3 in tbe formula above, means the intensity of 

 magnetization. 



Now, according to Maxwell, $'■' is not merely the 

 original magnetizing force, which we will call ^. 

 It is this minus the demar/netizing force, which in 

 this case is JttI. We have, therefore, from Maxwell, 



Maxwell, art. 42S. 



- Maxwell, al-tn. 398 and i 



