60 ALEXANDER JOUNSON ON 



magnetic force " as conceutrated in centres of action as the poles of magnets," or due to the 

 diffusion of north and south magnetism as fluids. 



The difficulty of distinguishing between the two senses in which he purposed to use 

 the term was so great that in the twenty-eighth series of his ' Experimental Researches ' 

 (October, 1851) he says: "Whilst writing this paper I perceive that in the late series of 

 these ' Eesearches,' Nos, 25, 26, 2*1, I have sometimes used the term lines efforce so vaguely 

 as to leave the reader doubtful whether I intended it as a merely representative idea of 

 the forces or as the description of the path along which the power was continuously 

 exerted." Faraday applied it to electric as well as to magnetic forces. When the origin- 

 ator found this difficulty, it is not wonderful that great confusion should subsequently 

 arise in its use by others. The following is a protest from Professor Minchin in his 

 " Statics '" against the result : 



" The way most in vogue with electricians for expressing the charge on one surface 

 of a conductor is the following : Imagine all the field filled with lines of force, then the 

 number of these that intersect the surface in the positive direction is a measure of the 

 charge on it. A A'ery inconvenient measure truly. Not only is this mode of speaking 

 unjustifiable, but it is mathematically impossible to attach the slightest logical meaning 

 toit." 



Other names have been proposed for these lines of force, and for the phrase " number 

 of lines of force." Mascart and Joubert suggest quantity or flow or flux of force as an 

 equivalent. If F be the force at any point and dS the element of an equipotential sur- 

 face drawn through the point — then if we imagine a liquid flowing through the element- 

 ary area dS, at right angles to it, with the velocity F, the expression FdS may by 

 analogy be called the flow of force corresponding to this element. Hence, in employing 

 a theorem of Gaviss, they speak of J FdS as the flow or flux of force, or (for magnetism) 

 of magnetic induction, proceeding from a surface S. Maxwell calls it the surface integral 

 of magnetic induction extended over any surface. 



At present there seems to be a tendency to substitute the term tubes of force, instead 

 of lines of force, Avhen taken in the second of the two senses. In doing this an idea of 

 Faraday's is followed out. In a paper published in June, 1852, he spoke of the " physical 

 existence of an atmosphere of power about a magnet," which " may be considered as dis- 

 posed in sphondyloids, determined by the lines or rather shells of force." 



Following out this idea, if the magnetic field be divided up by equipotential surfaces, 

 and if any curve whatever be described on any one of these and lines of force drawn 

 through it, these lines, which are at right angles to all the equipotential surfaces, will 

 form what is called a tube of force. If at any point where the force is F, an elementary 

 area of equipotential surface ô is taken, such that jF tf := 1, we have what is termed a 

 unit-tube. It is this term " unit-tube " which is now coming into use, instead of line, 

 when we talk of the " number of lines of force." But no short name has, as far as I am 

 aware, been suggested for it. It is for this reason that I would now propose a name sug- 

 gested by a term of Maxwell's. Maxwell called the tubes " solenoids," but this term had 

 already another application, and he did not himself adhere to it. In a note he gives the 

 derivation of solenoid from the Greek word for a tube. If we are to seek for a name 

 for a tube of force, and if the idea of the tube is to be predominant, we cannot do better 

 than follow the scientific practice of seeking terms from the Greek — as, e. g., the word 



