6 



SCIENCE 



[N. S. Vol. XXXI. No. 7S 



force. A discussion of all misfitting names 

 ■would, however, lead us too far from the 

 subject under consideration. 



e. Though I do not wish to tire you by 

 an enumeration of all examples of incon- 

 sistency in our teaching, I can not pass by 

 in silence a case where our lack of accu- 

 racy introduces the most serious difficulties. 

 It is the indiscriminate use of "lines of 

 force," not alone for "lines of intensity," 

 but also for "lines of induction." These 

 two are very different things, as well in 

 electrostatics as in magnetism, and neither 

 the intensity nor induction is a force. 



Let us consider a magnet and the field 

 surrounding it. According to the old 

 theory of action at a distance there is no 

 magTtetic disturbance anywhere in the 

 space about the magnet, until we intro- 

 duce a magnetic pole. Then, it is true, we 

 have a force between magnet and pole. 

 But this theory has long been overthrown. 

 We know now that at every point of a 

 magnetic field there exists a certain dis- 

 turbance, call it a stress, if you please, 

 whose magnitude and direction are given by 

 the intensity of the field at that point. 

 Moreover, the intensity of the magnetic 

 field has nothing to do with a force, except 

 that we may measure it by the force acting 

 on pole strength m according to the equa- 

 tion, defining intensity H 



It is usually stated that the lines of force 

 show the direction of the intensity, and 

 their number through unit area, drawn at 

 right angles to the direction, represents 

 the magnitude of the intensity. 



The use of a misleading name is not my 

 main objection. The trouble begins at this 

 point. After having used lines of force as 

 synonymous with lines of intensity, it is 

 serenely asserted that the cutting of lines 

 of force produces an induced electromotive 

 force in a conductor. You know that the 



magnitude of this electromotive force does 

 not depend upon the intensity, but upon 

 the rate with which the lines of induction 

 are cut. 



Only very few text-books give the cor- 

 rect expression for the induced electromo- 

 tive force as 



E = Blv. 



To write H instead of B in this formula is 

 radically wrong. The numerical value of 

 E will be correct, provided the medium is 

 air. The dimensional formulae for the 

 left and right hand sides of the equation 

 balance only if we use B. Every experi- 

 ment in electromagnetic induction is an 

 example of the correctness of this state- 

 ment. We all teach that the intensity of 

 the field is analogous to a stress, the induc- 

 tion to a strain in an elastic medium, both 

 being connected by the equation 

 B = /j.H. 



No one would tolerate such a confusion of 

 stress and strain in mechanics. 



The historical development of lines of 

 force is very interesting and explains to a 

 certain extent the origin of our troubles. 

 Faraday introduced the lines of force, 

 but not in the sense of lines of intensity. 

 Many quotations from his writings might 

 be given, all showing that he meant by 

 lines of force what I have called lines of 

 induction. For example he says:^ 



I have not referred in the foregoing considera- 

 tions to the view I have recently supported by 

 experimental evidence that the lines of force, con- 

 sidered simply as representants of the magnetic 

 power, are closed curves, passing in one part of 

 their course through the magnet and in the other 

 part through the space about it. These lines are 

 identical in their nature, qualities and amount, 

 ioth within the magnet and roithout. 



It is true, Faraday also speaks of lines 

 in connection with field intensity, but here 

 he uses various terms. Thus he writes:^ 



^ Faraday, " Researches," Vol. III., p. 417. 

 ""Researches," Vol. I., p. 411. 



