444 



Mr. E. Shida. 



obtained, if necessary, from the value of m, because evidently the 

 curve represented by the equation, 



_ m . r f 1 _ 1 



X ~^0 ' l(r8+(Z'-2,)3)f (f+(l'+y)*)i 



in which r, S, 0, V, &c, retain the same meaning as before, will be the 

 one required, namely, one in which the ordinates are proportional to 

 the vertical distances of the magnetometer needle from the centre of 

 the coil, and the abscissae to the deflections of the needle due to the 

 coil. 



A theoretical curve representing the effect due to the magnetism of 

 the wire or bar solenoidally distributed, that is to say, with a certain 

 quantity of free magnetic matter of northern polarity at one extremity 

 and the same quantity of free magnetic matter of southern polarity at 

 the other extremity of the wire or bar, can be obtained in a similar 

 way ; in fact, the equation (9) will represent such a curve, if we sub- 

 stitute the quantity of the free magnetic matter at either end of the 

 wire or bar for m' and half the length of the wire or bar for X . 



Now the curves (1), (2), (3), and (4), in the Plate 16, were obtained in 

 the way just explained from the results given in 1, 2, 4, and 7, and the 

 Tables I and II (that is, the results for the " Dark Wire ") ; they repre- 

 sent the curves showing the effects due to the magnetism of the wire 

 alone, and correspond respectively to '545 (in vertical force), 2*35, 

 14*08, and 80 '7 units of the magnetising force, while (5) is a theoretical 

 curve representing the effect which should have been obtained had the 

 same wire been magnetised solenoidally, so as to contain 8 units of the 

 quantity of free magnetic matter of one polarity at one end of it, and 

 the same quantity of matter of opposite polarity at the other end. 

 These curves form the true comparisons of the magnetisations of the 

 wire in the different cases, because they are all reduced to the same 

 standard, that is to say, they are all so drawn that their abscissae 

 represent the deflections of the magnetometer needle which should 

 have been obtained had the field S been one and the same, namely, 

 1'873 units in all cases. 



The comparisons of the curves (1), (2), (3), and (4) show that the 

 greater tbe magnetising force the greater is the distance from the 

 centre or origin of the points of the ordinates corresponding to the 

 maximum deflections of the magnetometer needle, while the com- 

 parison of the curves (4) and (5) shows that these points in the case 

 of the curve (4) are almost, if not exactly, coinciding with those in the 

 case of (5) ; showing quite distinctly that the magnetisation of the wire 

 for a low magnetising force is far from being solenoidal, but stronger 

 at the central parts of the wire than in the other parts ; but that as 

 this force is made stronger and stronger, the magnetism of the wire 

 becomes more and more equally distributed to the ends until the dis- 



} • • (9), 



