304 Mr. R. H. M. Bosanquet on Electromagnets. 



(Phil. Mag. xix. p. 76), so as to show the wide limits within 

 which specimens vary. The middle curve is that of the bars 

 with pole-pieces. The initial mean and adopted value are 

 both traced. The upper curve is that of the plain bars. 



This figure illustrates, and indeed proves, for approximate 

 purposes the rule I enunciated (Phil. Mag. xvii. p. 534), and 

 shows how the rule includes bars with pole-pieces, and where 

 it fails, viz. in the region spoken of as in the neighbourhood 

 of saturation. The rule is : — " The magnetic resistance of any 

 bar can be expressed as the sum of a resistance due to its form, 

 and a quantity formed by dividing the length by /a, the per- 

 meability of the metal." 



In the figure the lowest curve represents the resistance due 

 to the imperfect permeability of the metal. The two upper 

 curves obviously admit of derivation from the lower one by 

 addition of constants due to the respective shapes of the bars, 

 allowing for the capriciousness of the values in different 

 specimens, and for the difference in the region of saturation 

 (iS = 18,000 and thereabouts). 



As to the amount: — The analogy of the resistance to a fluid 

 flowing from the end of a pipe would give 2 x *6 of the radius, 

 or in the present case "012 centim., for the shape-resistance. 

 The fact that magnetism issues all along the bar, more or less, 

 diminishes this resistance ; so that we find in fact that in the 

 plain bar the addition for shape is somewhat over '005 centim., 

 as we can see in the figure. 



Again, the pole-pieces still further facilitate the flux of the 

 magnetic induction through the ends, and the shape-resistance 

 in this case is somewhat over '002 centim. 



I proceed to a more detailed examination of the numbers. 



For the plain bars, the shape-resistance calculated from the 

 formula at Phil. Mag. xvii. p. 534 exactly satisfies the require- 

 ments of the numbers. Hence the first step is to subtract 

 the value thus calculated from the number to be dealt with ; so 



' 1 



that -37 r 10-" oo6l >- = '00528 is subtracted, and p- '00528= - 



V* 

 gives the calculated values of fi. These are then fitted to 

 formulae in accordance with the theory of Phil. Mag. xix. 

 p. 92. With one exception, which is as follows : — Since the 

 saturation-curve approximates to an inclined asymptote, it is 

 impossible that IS can have finite maximum values ; and the 

 best way of making allowance for this has appeared to be, to 

 substitute for the definite maximum 2$^, a sum made up of 

 a constant B and a term proportional to the magnetizing 



