and the Theory of the Induction-balance. 141 



of metal completely by moving the other pair of coils a little 

 farther apart, though it may be done partially. Both effects 

 would then be superposed, and the two sounds would be sepa- 

 rately heard and might differ in pitch, because there would be 

 more oscillations in the tertiary current than in the secondary. 

 It is quite possible that a musical ear would perceive that the 

 quasi-note produced by the insertion of a piece of metal con- 

 tains a trace of a tone an octave above that produced by a shift 

 of the coils. Equation (42), however, appears to show that 

 when the battery- and telephone-circuits are similar the secon- 

 dary and tertiary currents are expressible by the same func- 

 tion of the time, and that, therefore, in this case the effect of 

 introducing metal may be counteracted by a shifting of the 

 coils. 



Next, we see that the effect is independent" of M (that is, 

 of the mutual induction between the primary and secondary 

 coils); and therefore it may occasionally be well to place them 

 in some nearly conjugate position, so as more easily to obtain a 

 balance. In fact the four coils are unnecessary; two coils 

 placed so as not to act on each other will do; and a piece of metal 

 placed near them will produce disturbance; only it will not be 

 so easy to bring the metal close or parallel to both coils. 



Next the effect is proportional to the produced m/j, ; of which 

 fi is the potential of the primary, and m that of the secondary, 

 on the coin. Hence, if the two coils are equal in size, every 

 thing is symmetrical with respect to them, so that it does not 

 matter whether the coin is nearest the primary or the secon- 

 dary ; moreover the middle point halfway between the two 

 coils must be either a maximum or a minimum position of the 

 coin. 



Prof. Hughes long ago stated, from experimental obser- 

 vation, that the position of the coin which gave the loudest 

 sound was half way between primary and secondary, the two 

 coils being pretty close together and being equal in all respects. 

 Before investigation I had felt inclined to doubt whether this 

 were more than approximately true (as it was by no means 

 evident a. priori that every thing was symmetrical with respect 

 to both coils, and the middle of the primary coil seemed a not 

 improbable place for the maximum). Accordingly I arranged 

 two pairs of coils as an induction-balance, the components of 

 each pair being 4 or 5 inches apart, but with their planes 

 parallel as usual ; and I then moved a coin about along the 

 common axis of one pair to see what happened. The maxi- 

 mum was not in the middle : but there were two maxima, one 

 on each side the middle, and every thing appeared symme- 

 trical with respect to both coils. The preceding investigation 



