434 



Mr. R. Shida. 



Let— 



(a-f a!)=th.Q area contained by the curve 1, the axis OY or OT', and 

 the line YW or the line Y'W. 



a'=the area contained by the curve 2, the axis OY or OY', and the 

 line YV or the line Y'V." ' 



Z=half the length of the wire or bar. 



l'= half the length of the coil. 



r=the distance of the middle line of the wire or bar from the 

 magnetometer needle. 



m=the sum of all the magnetic matter, northern or southern, on 

 either side of the centre of the wire or bar. 



m f =tlne strength of the solenoid or coil. 



S = the strength of the field at the point where the magnetometer 

 needle hangs. 



= the angle of deflection of the needle, in radian measure, corre- 

 sponding to the division of the scale. 



I=the intensity of the magnetisation of the wire at any cross- 

 section, or intensity of magnetisation of the bar ut its centre. 



F = the magnetising force. 



/t=the magnetising susceptibility. 



a=the area of the cross-section of the wire or bar. 



Then it can easily be proved, provided that the angles of deflections 

 are so small as to be proportional to their tangents, as in the case we 

 are considering, that 2ttt . S . 9 . a is the integral sum of all the normal 

 components of forces over the whole surface of a cylinder whose 

 height is the length of the wire or bar, and whose radius is r, due to 

 the magnetic matter m, situated at the centre of the cylinder, pro- 

 vided the length of the wire or bar be infinitely great ; the correction 



for this length being 21 instead of infinite, is such that 3m — - — '-^dr 



must be added to the above quantity to get the integral in question, 

 neglecting, however, the sum of all the normal components due to 

 — m, situated in the axis of the cylinder at a distance 21 from its 

 centre, over that end of the cylinder which is farthest from — m. But 

 the integral of the normal force N over any closed surface due to 

 magnetic matter m inside is, 



fNds=4i7rm 



2wr.l 



and hence 2irr . S . . *=4«7ra { f ^ j — —\ \ . 



Let now | . S , G=K : and (f _i_--^=P, 

 then R«=Pto (1). 



hence 2irr . S . 9 . « + 3m ' - dr—^irm : 



Jo 



