OP ARTS AND SCIENCES. 337 



where m = the magnetization, ^ = a constant depending upon the 

 length, shape, etc., of the coil, i? = the resistance of the primary cir- 

 cuit, and t = tlie duration of the current. 



The phase of mean height will therefore be just half-way between 

 that of maximum and minimum, or 90° later than it would have 

 been were the rise of the magnetic wave instantaneou.s. 



The phase is still more retarded in moderately distant portions of 

 the bar, because the magnetization there depends, not merely upon the 

 direct pulse, but also upon displacements already existing in the bar ; 

 but since these displacements agree in phase with the primary, and 

 totally disappear with the return of the wave to its mean height, and 

 since these displacements cannot exert a much greater influence than 

 the primary itself (which causes them), the greatest possible retarda- 

 tion of phase due to these secondary effects cannot greatly exceed 

 45° or 50°, and may not reach that limit. We need not therefore be 

 surprised that the U)ta\ retardation is limited to 90° plus the above 

 amount, or, in practice, to 130°. 



I have left out all discussion of the oscillations of the induced cur- 

 rent, since these will not, as a whole, interfere with the results. They 

 are discussed in Gordon's " Electricity and Magnetism," vol. i. page 

 311 etseq. 



I have already alluded to the experiments of Professor Blaserna 

 upon a subject so closely allied to my own. The determination of the 

 interval of time between the establishment of the primary current and 

 the establishment of the induced current gives rise to a series of values 

 of the rate of propagation of the pulse through air and other non- 

 conductors, just as my own experiments have endeavored to do through 

 iron. The results of the latter would indicate that the assumption 

 apparently made by Professor Blaserna that the rate of propagation 

 through air, etc., is constant, is at least open to criticism. 



The obvious application of the results of the above investigation 

 to the Gramme ring, the construction of electro-magnetic engines, and 

 the whole subject of magneto-acoustics, I am obliged, for the present, 

 to leave untouched ; together with the exact mathematical solution of 

 the problem of phase-retai-dation. 



We have seen that magnetism, like electricity, can be said to have, 

 no proper velocity ; that when one end of a conductor is magnetized 

 or electrified, the other begins instantaneously to feel an influence, 

 however slight ; that the electric or magnetic pulse is not measurable 

 for a short time, then rises very rapidly with the increase of time, 

 then less and less rapidly, and finally becomes constant. Not only 



VOL. XVI. (n. 8. VIII.) 22 



