June 30, 1 88 1 J 



NATURE 



205 



netic Attractions, and to the Theory of the Magnetic Rotation 

 of the Plane of Polarisation of Light." The papers, in addi- 

 tion to v.h it is stated in their title, contain the mathematical 

 consideration of that action of magnetism on electric currents 

 which was lately di-covered by Mr. Hall, and it is proved in 

 them that, if M^ixvvell's theory of light be true, this action will 

 explain the magnetic rotation of the plane of polarisation of 

 li^ht. These papers will no doubt be very extensively read, 

 both on account of the interest of their contents and the 

 great reputation of their author, and a brief discussion of them 

 may therefore not prove uninteresting to the readers of 

 Nature. 



We shall commence with the " New Theory of Mag:netic 

 Attraetions." This theory is of the simplest kind, and obviously 

 suggested by the mathematics of the subject. Siuce the mag- 

 netic induction is related to the distribution of the vector poten- 

 tial of masinetic induction in exactly the same way as the angular 

 rotation of an element of fluid is to the distribution of velocity 

 in the fluid. Prof. Rowland suggests that the magnetic field 

 consists of a perfect fluid, whose velocity at any point is repre- 

 sented in magnitude and direction by the magnetic vector poten- 

 tial at the point, the vortex lines in this fluid are the lines of 

 magnetic induction, and the velocity of angular rotation, is 

 proportional to the magnitude of the magnetic force. Again, 

 since 4 t times the electric current is related to magnetic induction 

 in the same way as magnetic induction to the vector potential, 

 Prof. Rowland considers that an electric current consists of, as 

 it were, vortices of vortices, or in other words, that certain 

 irreiJular distributions of the vortices constitutes currents. 



Maxwell has proved that the forces existing in the magnetic 

 field could be produced by a certain distribution of stress in a 

 medium filling the field. This stress in the simplest case consists 



of a tension along the lines of force equal to ;— , along with a 



ST 



pressure at right angles to the lines of force equal also to 



— , H being the intensity of the magnetic force. 



Prof. Rowland goes on to show that this state of stress exists 

 in the medium, which, according to his theory, fills the magnetic 

 field ; his proof is as follows : — "Conceive the fluid in a tube to 

 be rotating around the axis with a certain velocity, and suppose 

 the ends of the tube to be closed with movable pistons. Then, if 

 the pistons are left free, there will be a centrifugal force against 

 the sides of the tube proportional to the square of the velocity of 

 angular rotation. If the walls are flexible and the piston im- 

 movable, then there will be a force tending to press the pistons 

 in, and proportional also to the square of the velocity. 

 According to our theory the magnetic force is the velocity of 

 rotation, and so we have in the medium a tension along the lines 

 of force and a pressure at right angles to them." Prof. Rowland 

 does not seem to have noticed that this explanation requires 

 the vortices to be of a finite size. It is easy to prove 

 that in a cylindrical vortex of radius a, density p and 

 angular rotation to, the intensity of pressure on the cir- 

 cumference of the cylinder is greater than the mean intensity 



of pressure on the ends by- 



; but if this is to explain 



H2 



Hence 



the magnetic attractions the difference must be — 



4" 

 if H = c a, where f is a constant, we must have 7rp«- = c-, 



a = — = ; we thus get a definite value for a, and the vortices 



must not be capable of division into bundles of smaller radius 

 than a. Thus the fluid by which Prof. Rowland explains mag- 

 netic action cannot be the indefinitely divisible fluid treated of 

 in theoretical hydrodynamics. It is w orthy of remark that in 

 the theory of magnetism put forth by Maxwell in the /%//. Ma^, 

 for 1861-62, and which agrees with the theory we are consider- 

 ing in explaining magnetic force by the ancrnlar rotation of a 

 fluid, the vortices have a finite size, being done up as it were 

 into cells, the space between the cells being filled with par- 

 ticles whose motion, according to Maxwell, constitutes electric 

 currents. 



Let us now go on to the explanation Prof. Rowland gives of 

 the production of the magnetic field. He says: "Let the 

 nature of electromotive force be such that it tends to form 

 vortex-rings immediately round itself, not by action at a distance, 

 but by direct action on the fluid in the immediate vicinity. The 

 first ring will then move forward, another one will form, and so 



on uiitil the whole space is filled with them, when there will be 

 equilibrium." The consequences of this explanation, va»ue as 

 it is, are somewhat startling. In the first place it is clearf from 

 the proijerties of vortex motion, that every chain of particles of 

 the fluid which possess rotation at any time must at some pre- 

 vious time have been in the immediate vicinity of the electro- 

 motive force; and since according to the theory there is rotation 

 of the fluid at every point in the magnetic field, it follows that 

 in the time taken to set up the field every particle of fluid in it 

 has been in the immediate neighbourhood of the electromotive 

 force. But magnetic disturbance is propagated, according to 

 Maxwell's "Theory of Light" (which Prof. Rowdand accepts), 

 with the velocity of light ; hence the streams of the fluid must 

 be flowing with the velocity of light, and in addition every par- 

 ticle of fluid in the field must have rushed through the small space 

 occupied by the seat of the electromotive force in the short time 

 it takes lo establish the magnetic field. Another difficulty 

 which Prof. Rowland does not explain is the following: If we 

 take a small element of electromotive force we know that to agree 

 with the distribution of magnetic force all the vortex-rings must 

 have the same sense of rotation ; but if vortex-rings have the 

 same sense of rotation they move through the fluid in the same 

 direction, so that these vortex-rings when produced would all 

 move off in the same du-ection, and thus le.Tve one half of the 

 field without rings, i.e., without magnetic force. Again, the 

 way in which these rings spread out so as to fill the field would 

 seem to be in contradiction to the laws of vortex-motion ; but as 

 the author says he is investigating the dynamics of the subject, 

 we may leave further comment on this poiut till the result of his 

 investigation appears. 



The explanation of the stress in the medium which we have 

 referred to before is the only application of the theory worked 

 out by Prof. Rowland. He does not explain by it any of the 

 phenomena of induction, nor does he get from it any connection 

 between statical and current electricity ; yet he does not hesitate 

 to speak of his theory "as one link in the chain, the first three 

 links of which have been added by Thomson, Helmholtz, and 

 Maxwell." 



We must now leave this part of the subject and pass 

 on to that portion of the paper which treats of the general 

 equations of the electro-magnetic field. The mathematics 'of 

 this is merely an application of the theory of the vector- potential 

 to currents. The most important feature in the treatment of the 

 subject is that Prof. Rowland always writes the product of the 

 conductivity into the electromotive force instead of the intensity 

 of the current, and claims that this is an important advance ; 

 but if there is any diflTercnce either Ohm's law must not be true, 

 or Prof. Rowland must mean by electromotive for-e something 

 different from that meant by ordinary users of the term. Prof. 

 Rowland asserts that in an unlimited medium the action is not 

 between magnets and currents, but between magnets and elec- 

 tromotive forces ; he bases this assertion on the theorem that in 

 an unlimited medium unclosed electric currents have no magnetic 

 action. It is hard to see how this proposition can be true, for 

 the current through any area is measured by the line integral of 

 the magnetic force round the boundary of the area ; but if the 

 magnetic force is everywhere zero, then the line integral of it 

 round any curve must vanish, and thus the current at any point 

 must vanish. The proposition is based on reasoning of the 

 following kind : the force between an electric point (by an 

 electric point he means a point from which electricity is stream- 

 ing, in fact what is usually called a source) and a magnetic pole 

 must by symmetry be along the line joining them. But a mag- 

 netic pole of any size is always accompanied by one of the 

 opposite sign, and the two form a vector quantity ; and we think 

 from the relation that one pole necessarily bears to another, it is 

 not safe to reason about it as if it were a purely scalar quantity. 

 Prof. Rowland himself acknowledges what is equivalent to this, 

 for after saying that the force due to the unclosed currents on 

 each pole of the magnet is zero, yet he says there is probably a 

 force on the magnet as a whole tending to place it across the 

 currents. 



Although we think that the reasoning given for the assertion 

 that the action is not between magnets and currents, but between 

 magnets and electromotive forces, is unsatisfactory ; yet we 

 think that, understood in a certain sense, the proposition is 

 mathematically true For we can prove directly from theordi- 

 nary expressions for the magnetic action of currents, that if we 

 have a source and a sink of equal intensities Uirm) placed 

 close together, the magnetic action of ihe currents produced is 



